THE Psychological Review

 _EDITED BY_

 J. McKEEN CATTELL and J. MARK BALDWIN COLUMBIA UNIVERSITY PRINCETON UNIVERSITY

 _WITH THE CO-OPERATION OF_

 ALFRED BINET, ÉCOLE DES HAUTES-ÉTUDES, PARIS; JOHN DEWEY, H. H. DONALDSON, UNIVERSITY OF CHICAGO; G. S. FULLERTON, UNIVERSITY OF PENNSYLVANIA; G. H. HOWISON, UNIVERSITY OF CALIFORNIA; JOSEPH JASTROW, UNIVERSITY OF WISCONSIN; G. T. LADD, YALE UNIVERSITY; HUGO MÜNSTERBERG, HARVARD UNIVERSITY; M. ALLEN STARR, COLLEGE OF PHYSICIANS AND SURGEONS, NEW YORK; CARL STUMPF, UNIVERSITY, BERLIN; JAMES SULLY, UNIVERSITY COLLEGE, LONDON. 

H. C. WARREN, PRINCETON UNIVERSITY, _Associate Editor and Business Manager_. 

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 Series of Monograph Supplements, Vol. IV. , No. 1 (Whole No. 17), January, 1903. 

 HARVARD PSYCHOLOGICAL STUDIES, Volume I CONTAINING

 Sixteen Experimental Investigations from the Harvard Psychological Laboratory. 

 EDITED BY HUGO MÜNSTERBERG. 

 PUBLISHED BI-MONTHLY BY THE MACMILLAN COMPANY, 41 N. QUEEN ST. , LANCASTER, PA. 66 FIFTH AVENUE, NEW YORK. 

 AGENT: G. E. STECHERT, LONDON (2 Star Yard, Cary St. , W. C. ) Leipzig (Hospital St. , 10); PARIS (76 rue de Rennes). 

 PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA. 

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PREFACE. 

The appearance of the HARVARD PSYCHOLOGICAL STUDIES does not indicatean internal change in the work of the Harvard PsychologicalLaboratory. But while up to this time the results of ourinvestigations have been scattered in various places, and have oftenremained unpublished through lack of space, henceforth, we hope tohave in these STUDIES the opportunity to publish the researches of theHarvard Laboratory more fully and in one place. Only contributionsfrom members of the Harvard Psychological Laboratory will be printedin these volumes, which will appear at irregular intervals, and thecontributions will represent only our experimental work;non-experimental papers will form an exception, as with the presentvolume, wherein only the last one of the sixteen papers belongs totheoretical psychology. 

This first volume does not give account of all sides of our laboratorywork. An essential part of the investigations every year has been thestudy of the active processes, such as attention, apperception, andvolition. During the last year several papers from these fields havebeen completed, but we were unable to include them in this volume onaccount of the space limits; they are kept back for the second volume, in which accordingly the essays on the active functions will prevail, as those on perception, memory, and feeling prevail in this volume. Itis thus clear that we aim to extend our experimental work over thewhole field of psychology and to avoid one-sideness. Neverthelessthere is no absence of unity in our work; it is not scattered work asmight appear at a first glance; for while the choice of subjects isalways made with relation to the special interests of the students, there is after all one central interest which unifies the work and hasinfluenced the development of the whole laboratory during the years ofmy direction. 

I have always believed--a view I have fully discussed in my 'Grundzügeder Psychologie'--that of the two great contending theories of modernpsychology, neither the association theory nor the apperception theoryis a satisfactory expression of facts, and that a synthesis of bothwhich combines the advantages without the defects of either can beattained as soon as a psychophysical theory is developed which shallconsider the central process in its dependence, not only upon thesensory, but also upon the motor excitement. This I call the _actiontheory_. In the service of this theory it is essential to study morefully the rōle of the centrifugal processes in mental life, and, although perhaps no single paper of this first volume appears to offera direct discussion of this motor problem, it was my interest in thismost general question which controlled the selection of all theparticular problems. 

This relation to the central problem of the rōle of centrifugalprocesses involves hardly any limitation as to the subject matter;plenty of problems offer themselves in almost every chapter ofpsychology, since no mental function is without relation to thecentrifugal actions. Yet, it is unavoidable that certain groups ofquestions should predominate for a while. This volume indicates, forinstance, that the ęsthetic processes have attracted our attention inan especially high degree. But even if we abstract from theirimportant relation to the motor functions, we have good reasons forturning to them, as the ęsthetic feelings are of all feeling processesdecidedly those which can be produced in the laboratory most purely;their disinterested character makes them more satisfactory forexperimental study than any other feelings. 

Another group of researches which predominates in our laboratory isthat on comparative psychology. Three rooms of the laboratory arereserved for psychological experiments on animals, under the specialcharge of Dr. Yerkes. The work is strictly psychological, notvivisectional; and it is our special purpose to bring animalpsychology more in contact with those methods which have found theirdevelopment in the laboratories for human psychology. The use of thereaction-time method for the study of the frog, as described in thefifteenth paper, may stand as a typical illustration of our aim. 

All the work of this volume has been done by well-trainedpost-graduate students, and, above all, such advanced students werenot only the experimenters but also the only subjects. It is the ruleof the laboratory that everyone who carries on a special research hasto be a subject in several other investigations. The reportingexperimenters take the responsibility for the theoretical views whichthey express. While I have proposed the subjects and methods for allthe investigations, and while I can take the responsibility for theexperiments which were carried on under my daily supervision, I haveleft fullest freedom to the authors in the expression of their views. My own views and my own conclusions from the experiments would notseldom be in contradiction with theirs, as the authors are sometimesalso in contradiction with one another; but while I, of course, havetaken part in frequent discussions during the work, in the completedpapers my rōle has been merely that of editor, and I have nowhereadded further comments. 

In this work of editing I am under great obligation to Dr. Holt, theassistant of the laboratory, for his helpful coöperation. 

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CONTENTS. 

Preface: Hugo Münsterberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

STUDIES IN PERCEPTION. 

 Eye-Movement and Central Anęsthesia: Edwin B. Holt . . . . . . . . . . . 3 Tactual Illusions: Charles H. Rieber . . . . . . . . . . . . . . . . . . . . . . . . . 47 Tactual Time Estimation: Knight Dunlap . . . . . . . . . . . . . . . . . . . . . . . 101 Perception of Number through Touch: J. Franklin Messenger . . . . 123 The Subjective Horizon: Robert MacDougall . . . . . . . . . . . . . . . . . . . . 145 The Illusion of Resolution-Stripes on the Color-Wheel: Edwin B. Holt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

STUDIES IN MEMORY. 

 Recall of Words, Objects and Movements: Harvey A. Peterson . . . 207 Mutual Inhibition of Memory Images: Frederick Meakin . . . . . . . . . 235 Control of the Memory Image: Charles S. Moore . . . . . . . . . . . . . . . . 277

STUDIES IN ĘSTHETIC PROCESSES. 

 The Structure of Simple Rhythm Forms: Robert MacDougall . . . . . . 309 Rhythm and Rhyme: R. H. Stetson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 Studies in Symmetry: Ethel D. Puffer . . . . . . . . . . . . . . . . . . . . . . . . . 467 The Ęsthetics of Unequal Division: Rosewell Parker Angier . . . . 541

STUDIES IN ANIMAL PSYCHOLOGY. 

 Habit Formation in the Crawfish, Camburus affinis: Robert M. Yerkes and Gurry E. Huggins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565 The Instincts, Habits and Reactions of the Frog: Robert Mearns Yerkes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

STUDIES IN PSYCHOLOGICAL THEORY. 

 The Position of Psychology in the System of Knowledge: Hugo Münsterberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

PLATES. 

 OPPOSITE PAGEPlate I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 " II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 " III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 " IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 " V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 " VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 " VII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 " VIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 " IX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 " X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436

Charts of the Sciences, at end of volume. 

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 STUDIES IN PERCEPTION. 

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EYE-MOVEMENT AND CENTRAL ANĘSTHESIA. 

BY EDWIN B. HOLT. 

I. THE PROBLEM OF ANĘSTHESIA DURING EYE-MOVEMENT. 

A first suggestion of the possible presence of anęsthesia duringeye-movement is given by a very simple observation. All near objectsseen from a fairly rapidly moving car appear fused. No furthersuggestion of their various contour is distinguishable than blurredstreaks of color arranged parallel, in a hazy stream which flowsrapidly past toward the rear of the train. Whereas if the eye is keptconstantly moving from object to object scarcely a suggestion of thisblurred appearance can be detected. The phenomenon is striking, since, if the eye moves in the same direction as the train, it is certainthat the images on the retina succeed one another even more rapidlythan when the eye is at rest. A supposition which occurs to one atonce as a possible explanation is that perchance during eye-movementthe retinal stimulations do not affect consciousness. 

On the other hand, if one fixates a fly which happens to be crawlingacross the window-pane and follows its movements continuously, theobjects outside swim past as confusedly as ever, and the image of thefly remains always distinct. Here the eye is moving, and it may berapidly, yet both the fly and the blurred landscape testify to athorough awareness of the retinal stimulations. There seems to be noanęsthesia here. It may be, however, that the eye-movement whichfollows a moving object is different from that which strikes outindependently across the visual field; and while in the former casethere is no anęsthesia, perhaps in the latter case there isanęsthesia. 

Cattell, [1] in considering a similar experience, gives his opinionthat not the absence of fusion for the moving eye, but its presencefor the resting eye, needs explanation. "More than a thousandinterruptions per second, " he believes, "give a series of sharplydefined retinal processes. " But as for the fusion of moving objectsseen when the eyes are at rest, Cattell says, "It is not necessary andwould probably be disadvantageous for us to see the separate phases. "Even where distinct vision would be 'disadvantageous' he half doubtsif fusion comes to the rescue, or if even the color-wheel everproduces complete fusion. "I have never been able, " he writes, "tomake gray in a color-wheel from red and green (with the necessarycorrection of blue), but when it is as nearly gray as it can be got Isee both red and green with an appearance of translucence. "

 [1] Cattell, J. McK. , PSYCHOLOGICAL REVIEW, 1900, VII. , p. 325. 

That the retina can hold apart more than one thousand stimulations persecond, that there is, in fact, no such thing as fusion, is asupposition which is in such striking contrast to all previousexplanations of optical phenomena, that it should be accepted only ifno other theory can do justice to them. It is hoped that the followingpages will show that the facts do not demand such a theory. 

Another simple observation is interesting in this connection. If atany time, except when the eyes are quite fresh, one closes one's eyesand attends to the after-images, some will be found which are so faintas to be just barely distinguishable from the idioretinal light. Ifthe attention is then fixed on one such after-image, and the eyes aremoved, the image will suddenly disappear and slowly emerge again afterthe eyes have come to rest. This disappearance during eye-movementscan be observed also on after-images of considerable intensity; these, however, flash back instantly into view, so that the observation issomewhat more difficult. Exner, [2] in speaking of this phenomenon, adds that in general "subjective visual phenomena whose origin lies inthe retina, as for instance after-images, Purkinje's vessel-figure, or the phenomena of circulation under discussion, are almostexclusively to be seen when the eye is rigidly fixed on a certainspot: as soon as a movement of the eye is made, the subjectivephenomena disappear. "

 [2] Exner, Sigmund, _Zeitschrift f. Psychologie u. Physiologie der Sinnesorgane_, 1890, I. , S. 46. 

The facts here mentioned in no wise contradict a phenomenon recentlydiscussed by McDougall, [3] wherein eye-movements revive sensationswhich had already faded. Thus an eye-movement will bring back anafter-image which was no longer visible. This return to vividnesstakes place after the movement has been completed, and there is nocontention that the image is seen just during the movement. 

 [3] McDougall, W. , _Mind_, N. S. , X. , 1901, p. 52. 

The disappearance of after-images during eye-movements is mentioned byFick and Gürber, [4] who seek to explain the phenomenon by ascribing itto a momentary period of recovery which the retina perhaps undergoes, and which would for the moment prevent further stimulations from beingtransmitted to the optic nerve. Exner observes that this explanationwould not, however, apply to the disappearance of the vessel-figure, the circulation phenomenon, the foveal figure, the polarization-sheafof Haidinger, Maxwell's spot, or the ring of Löwe; for these phenomenadisappear in a similar manner during movement. Exner offers anotherand a highly suggestive explanation. He says of the phenomenon (_op. Citat. _, S. 47), "This is obviously related to the following fact, that objective and subjective impressions are not to be distinguishedas such, so long as the eye is at rest, but that they are immediatelydistinguished if an eye-movement is executed; for then the subjectivephenomena move with the eye, whereas the objective phenomena are notdisplaced. . . . This neglect of the subjective phenomena is effected, however, not by means of an act of will, but rather by some centralmechanism which, perhaps in the manner of a reflex inhibition, withholds the stimulation in question from consciousness, without ourassistance and indeed without our knowledge. " The suggestion of acentral mechanism which brings about a reflex inhibition is thesignificant point. 

 [4] Fick, Eug. , and Gürber, A. , _Berichte d. Ophthalmologischen Gesellschaft in Heidelberg_, 1889. 

It is furthermore worth noting that movements of the eyelid andchanges in the accommodation also cause the after-images to disappear(Fick and Gürber), whereas artificial displacement of the eye, as bymeans of pressure from the finger, does not interfere with the images(Exner). 

Another motive for suspecting anęsthesia during eye-movement is foundby Dodge, [5] in the fact that, "One may watch one's eyes as closely aspossible, even with the aid of a concave reflector, whether one looksfrom one eye to the other, or from some more distant object to one'sown eyes, the eyes may be seen now in one position and now in another, but never in motion. " This phenomenon was described by Graefe, [6] whobelieved it was to be explained in the same way as the illusion whichone experiences in a railway coach when another train is movingparallel with the coach in which one sits, in the same direction andat the same speed. The second train, of course, appears motionless. 

 [5] Dodge, Raymond, PSYCHOLOGICAL REVIEW, 1900, VII. , p. 456. 

 [6] Graefe, A. , _Archiv f. Ophthalmologie_, 1895, XLI. , 3, S. 136. 

This explanation of Graefe is not to be admitted, however, since inthe case of eye-movement there are muscular sensations of one's ownactivity, which are not present when one merely sits in a coach. Thesesensations of eye-movement are in all cases so intimately connectedwith our perception of the movement of objects, that they may not bein this case simply neglected. The case of the eye trying to watch itsown movement in a mirror is more nearly comparable with the case inwhich the eye follows the movement of some independent object, as arace-horse or a shooting-star. In both cases the image remains onvirtually the same point of the retina, and in both cases muscularsensations afford the knowledge that the eye is moving. Theshooting-star, however, is perceived to move, and the questionremains, why is not the eye in the mirror also seen to move?

F. Ostwald[7] refutes the explanation of Graefe from quite differentconsiderations, and gives one of his own, which depends on thegeometrical relations subsisting between the axes of vision of thereal eye and its reflected image. His explanation is too long to behere considered, an undertaking which indeed the followingcircumstance renders unnecessary. While it is true that the eye cannotobserve the full sweep of its own movement, yet nothing is easier thanto observe its movement through the very last part of the arc. If oneeye is closed, and the other is brought to within about six inches ofan ordinary mirror, and made to describe little movements from someadjacent part of the mirror to its own reflected image, this image canalmost without exception be observed as just coming to rest. That is, the very last part of the movement _can_ be seen. The explanation ofOstwald can therefore not be correct, for according to it not alonesome parts of the movement, but absolutely all parts alike must remaininvisible. It still remains, therefore, to ask why the greater part ofthe movement eludes observation. The correct explanation will accountnot only for the impossibility of seeing the first part of themovement but also for the possibility of seeing the remainder. 

 [7] Ostwald, F. , _Revue Scientifique_, 1896, 4e Série, V. , p. 466. 

Apart from the experience of the eye watching itself in a glass, Dodge(_loc. Citat. _) found another fact which strongly suggestedanęsthesia. In the course of some experiments on reading, conducted byErdmann and Dodge, the question came up, how "to explain the meaningof those strangely rhythmic pauses of the eye in reading every page ofprinted matter. " It was demonstrated (_ibid. _, p. 457) "that therhythmic pauses in reading are the moments of significantstimulation. . . . If a simple letter or figure is placed between twofixation-points so as to be irrecognizable from both, no eye-movementis found to make it clear, which does not show a full stop betweenthem. "

With these facts in view Dodge made an experiment to test thehypothesis of anęsthesia. He proceeded as follows (_ibid. _, p. 458):"A disc of black cardboard thirteen inches in diameter, in which acircle of one-eighth inch round holes, one half inch apart, had beenpunched close to the periphery all around, was made to revolve at sucha velocity that, while the light from the holes fused to a brightcircle when the eye was at rest, when the eye moved in the directionof the disc's rotation from one fixation point, seen through the fusedcircle of light, to another one inch distant, three clear-cut roundholes were seen much brighter than the band of light out of which theyseemed to emerge. This was only possible when the velocity of theholes was sufficient to keep their images at exactly the same spot onthe retina during the movement of the eye. The significant thing isthat the individual round spots of light thus seen were much moreintense than the fused line of light seen while the eyes were at rest. Neither my assistant nor I was able to detect any difference inbrightness between them and the background when altogetherunobstructed. " Dodge finds that this experiment 'disproves' thehypothesis of anęsthesia. 

If by 'anęsthesia' is meant a condition of the retinal end-organs inwhich they should be momentarily indifferent to excitation bylight-waves, the hypothesis is indeed disproved, for obviously the'three clear-cut round holes' which appeared as bright as theunobstructed background were due to a summation of the light whichreached the retina during the movement, through three holes of thedisc, and which fell on the same three spots of the retina as long asthe disc and the eyeball were moving at the same angular rate. Butsuch a momentary anęsthesia of the retina itself would in any case, from our knowledge of its physiological and chemical structure, beutterly inconceivable. 

On the other hand, there seems to be nothing in the experiment whichshows that the images of the three holes were present to consciousnessjust during the movement, rather than immediately thereafter. Acentral mechanism of inhibition, such as Exner mentions, mightcondition a central anęsthesia during movement, although thefunctioning of the retina should remain unaltered. Such a centralanęsthesia would just as well account for the phenomena which havebeen enumerated. The three luminous images could be supposed to remainunmodified for a finite interval as positive after-images, and as suchfirst to appear in consciousness. Inasmuch as 'the arc of eyemovements was 4. 7°' only, the time would be too brief to make possibleany reliable judgment as to whether the three holes were seen duringor just after the eye-movement. With this point in view, the writerrepeated the experiment of Dodge, and found indeed nothing which gavea hint as to the exact time when the images emerged in consciousness. The results of Dodge were otherwise entirely confirmed. 

II. THE PHENOMENON OF 'FALSELY LOCALIZED AFTER-IMAGES. '

A further fact suggestive of anęsthesia during movement comes from anunexpected source. While walking in the street of an evening, if onefixates for a moment some bright light and then quickly turns the eyeaway, one will observe that a luminous streak seems to dart out fromthe light and to shoot away in either of two directions, either in thesame direction as that in which the eye moved, or in just theopposite. If the eye makes only a slight movement, say of 5°, thestreak jumps with the eye; but if the eye sweeps through a ratherlarge arc, say of 40°, the luminous streak darts away in the oppositedirection. In the latter case, moreover, a faint streak of lightappears later, lying in the direction of the eye-movement. 

This phenomenon was probably first described by Mach, in 1886. [8] Hisview is essentially as follows: It is clear that in whatever directionthe eye moves, away from its luminous fixation point, the streakdescribed on the retina by the luminous image will lie on the samepart of the retina as it would have lain on had the eye remained atrest but the object moved in the opposite direction. Thus, if the eyemoves to the right, we should expect the streak to appear to dart tothe left. If, however, the streak has not faded by the time the eyehas come to rest on a new fixation point (by supposition to the rightof the old), we should expect the streak to be localized to the leftof this, that is, to the right of the former fixation-point. In orderto be projected, a retinal image has to be localized with reference tosome point, generally the fixation-point of the eyes; and it istherefore clear that when two such fixation-points are involved, thelocalization will be ambiguous if for any reason the central apparatusdoes not clearly determine which shall be the point of reference. Withregard to the oppositely moving streak Mach says:[9] "The streak is, of course, an after-image, which comes to consciousness only on, orshortly before, the completion of the eye-movement, nevertheless withpositional values which correspond, remarkably enough, not to thelater but to the earlier position and innervation of the eyes. " Machdoes not further attempt to explain the phenomenon. 

 [8] Mach, Ernst, 'Beiträge zur Analyze der Empfindungen, ' Jena, 1886. 

 [9] Mach, _op. Citat. _, 2te Aufl. , Jena, 1900, S. 96. 

It is brought up again by Lipps, [10] who assumes that the streak oughtto dart with the eyes and calls therefore the oppositely moving streakthe 'falsely localized image. ' For sake of brevity we may call thisthe 'false image. ' The explanation of Lipps can be pieced together asfollows (_ibid. _, S. 64): "The explanation presupposes that sensationsof eye-movements have nothing to do with the projection of retinalimpressions into the visual field, that is, with the perception of themutual relations as to direction and distance, of objects which areviewed simultaneously. . . . Undoubtedly, however, sensations ofeye-movements, and of head-and body-movements as well, afford us ascale for measuring the displacements which our entire visual fieldand every point in it undergo within the surrounding _totality ofspace_, which we conceive of as fixed. We estimate according to thelength of such movements, or at least we deduce therefrom, thedistance through fixed space which our view by virtue of thesemovements has traversed. . . . They themselves are nothing for ourconsciousness but a series of purely intensive states. But inexperience they can come to _indicate_ distance traversed. " Now inturning the eye from a luminous object, _O_, to some otherfixation-point, _P_, the distance as simply contemplated is more orless subdivided or filled in by the objects which are seen to liebetween _O_ and _P_, or if no such objects are visible the distance isstill felt to consist of an infinity of points; whereas the muscularinnervation which is to carry the eye over this very distance is anundivided unit. But it is this which gives us our estimate of the arcwe move through, and being thus uninterrupted it will appear shorterthan the contemplated, much subdivided distance _OP_, just as acontinuous line appears shorter than a broken line. "After suchanalogies, now, the movement of the eye from _O_ to _P_, that is, thearc which I traverse, must be underestimated" (_ibid. _, S. 67). Thereis thus a discrepancy between our two estimates of the distance _OP_. This discrepancy is felt during the movement, and can be harmonizedonly if we seem to see the two fixation-points move apart, until thearc between them, in terms of innervation-feeling, feels equal to thedistance _OP_ in terms of its visual subdivisions. Now either _O_ and_P_ can both seem to move apart from each other, or else one can seemfixed while the other moves. But the eye has for its goal _P_, whichought therefore to have a definite position. "_P_ appears fixedbecause, as goal, I hold it fast in my thought" (_loc. Citat. _). Itmust be _O_, therefore, which appears to move; that is, _O_ must dartbackward as the eye moves forward toward _P_. Thus Lipps explains theillusion. 

 [10] Lipps, Th. , _Zeitschrift f. Psychologie u. Physiologie der Sinnesorgane_, 1890, I. , S. 60-74. 

Such an explanation involves many doubtful presuppositions, but if wewere to grant to Lipps those, the following consideration wouldinvalidate his account. Whether the feeling of innervation which hespeaks of as being the underestimated factor is supposed to be a trueinnervation-feeling in the narrower sense, or a muscular sensationremembered from past movements, it would in the course of experiencecertainly come to be so closely associated with the correspondingobjective distance as not to feel less than this. So far as aninnervation-feeling might allow us to estimate distance, it could haveno other meaning than to represent just that distance through whichthe innervation will move the organ in question. If _OP_ is a distanceand _i_ is the feeling of such an innervation as will move the eyethrough that distance, it is inconceivable that _i_, if it representany distance at all, should represent any other distance than just_OP_. 

Cornelius[11] brought up the matter a year later than Lipps. Corneliuscriticises the unwarranted presuppositions of Lipps, and himselfsuggests that the falsely localized streak is due to a slight reboundwhich the eye, having overshot its intended goal, may make in theopposite direction to regain the mark. This would undoubtedly explainthe phenomenon if such movements of rebound actually took place. Cornelius himself does not adduce any experiments to corroborate thisaccount. 

 [11] Cornelius, C. S. , _Zeitschrift f. Psychologie u. Physiologie der Sinnesorgane_, 1891, II. , S. 164-179. 

The writer, therefore, undertook to find out if such movementsactually are made. The observations were made by watching the eyes ofseveral subjects, who looked repeatedly from one fixation-point toanother. Although sometimes such backward movements seemed indeed tobe made, they were very rare and always very slight. Inasmuch as the'false' streak is often one third as long as the distance movedthrough, a movement of rebound, such as Cornelius means, would have tobe one third of the arc intended, and could therefore easily have beennoticed. Furthermore, the researches of Lamansky, [12] Guillery, [13]Huey, [14] Dodge and Cline, [15] which are particularly concerned withthe movements of the eyes, make no mention of such rebounds. Schwarz[16] above all has made careful investigations on this verypoint, in which a screen was so placed between the observer and theluminous spot that it intervened between the pupil and the light, justbefore the end of the movement. Thus the retina was not stimulatedduring the latter part of its movement, just when Cornelius assumedthe rebound to take place. This arrangement, however, did not in theleast modify the appearance of the false streak. 

 [12] Lamansky, S. , _Pflüger's Archiv f. D. Gesammte Physiologie_, 1869, II. , S. 418. 

 [13] Guillery, _ibid. _, 1898, LXXI. , S. 607; and 1898, LXXIII. , S. 87. 

 [14] Huey, Edmund B. , _American Journal of Psychology_, 1900, XI. , p. 283. 

 [15] Dodge, Raymond, and Cline, T. S. , PSYCHOLOGICAL REVIEW, 1901, VIII. , PP. 145-157. 

 [16] Schwarz, Otto, _Zeitschrift J. Psychologie u. Physiologie der Sinnesorgane_, 1892, III. , S. 398-404. 

This work of Schwarz certainly proves that the explanation ofCornelius is not correct. Schwarz found that the phenomenon takesplace as well when the head moves and the eyes are fixed relatively tothe head, as when the eyes alone move. He furthermore made thisobservation. Meaning by _a_ the point of departure and by _b_ the goalof either the eye-or the head-movement, movement, he says (_ibid. _, S. 400-2): "While oftentimes the streak of the after-image extendeduninterruptedly to the point _b_, or better seemed to proceed fromthis point, --as Lipps also reported--yet generally, under theexperimental conditions which I have indicated, _two streaks_ could beseen, _separated by a dark space between_; firstly the anomalous one"(the false streak) "rather brilliant, and secondly a fainter one ofabout equal or perhaps greater length, which began at the newfixation-point _b_ and was manifestly an after-image correctlylocalized with regard to the situation of this point. This lastafter-image streak did not always appear; but it appeared regularly ifthe light at _a_ was bright enough and the background dark. . . . It wasimpossible for this second after-image streak to originate in thepoint _b_, because it appeared equally when _b_ was only an imaginaryfixation-point. . . . This consideration makes it already conceivablethat the two parts of the total after-image _are two manifestations ofthe one identical retinal stimulation, which are differentlylocalized_. . . . Therefore we must probably picture to ourselves thatthe sensation from the strip of the retina stimulated during the quickeye-movement is, _during the interval of movement or at least duringthe greater part of it, localized as if the axis of vision were stilldirected toward the original fixation-point. And when the new positionof rest is reached and the disturbance on the retinal strip has notwholly died away, then the strip comes once more into consciousness, but this time correctly localized with reference to the new positionof the axis of vision_. By attending closely to the behavior asregards time of both after-image streaks, I can generally see thenormal after-image develop a moment later than the anomalous one"(that is, the false streak). Schwarz finally suggests (S. 404) thatprobably between the first and second appearances of the streak an'innervation-feeling' intervenes which affords the basis forlocalizing the second streak ('correctly') with reference to the newposition of the eye. 

After this digression we return to consider how this phenomenon isrelated to the hypothesis of anęsthesia during eye-movements. If weaccept the interpretation of Schwarz, there is one retinal processwhich is perceived as two luminous streaks in space, localizeddifferently and referred to different moments of time. It issurprising, then, that a continuous retinal process is subjectivelyinterpreted as two quite different objects, that is, as somethingdiscontinuous. Where does the factor of discontinuity come in? If wesuppose the retinal disturbance to produce a continuous sensation inconsciousness, we should expect, according to every analogy, that thissensation would be referred to one continuously existing object. Andif this object is to be localized in two places successively, weshould expect it to appear to move continuously through allintervening positions. Such an interpretation is all the more to beexpected, since, as the strobic phenomena show, even discontinuousretinal processes tend to be interpreted as continuously existingobjects. 

On the other hand, if there were a central anęsthesia duringeye-movement, the continuous process in the retina could not produce acontinuous sensation, and if the interval were long enough the imagemight well be referred to two objects; since also, in the strobicappearances, the stimulations must succeed at a certain minimal ratein order to produce the illusion of continuous existence and movement. 

This consideration seemed to make it worth while to perform someexperiments with the falsely localized after-images. The phenomenonhad also by chance been noted in the case of the eye moving past aluminous dot which was being regularly covered and uncovered. Theappearance is of a row of luminous spots side by side in space, whichunder conditions may be either falsely or correctly localized. Sincethese dots seemed likely to afford every phenomenon exhibited by thestreaks, with the bare chance of bringing out new facts, apparatus wasarranged as in Fig. 1, which is a horizontal section. 

_DD_ is a disc which revolves in a vertical plane, 56 cm. In diameterand bearing near its periphery one-centimeter holes punched 3 cm. Apart. _E_ is an eye-rest, and _L_ an electric lamp. _SS_ is a screenpierced at _H_ by a one-centimeter hole. The distance _EH_ is 34 cm. The disc _DD_ is so pivoted that the highest point of the circle ofholes lies in a straight line between the eye _E_ and the lamp _L_. The hole _H_ lies also in this straight line. A piece of milk-glass_M_ intervenes between _L_ and _H_, to temper the illumination. Thedisc _DD_ is geared to a wheel _W_, which can be turned by the hand ofthe observer at _E_, or by a second person. As the disc revolves, eachhole in turn crosses the line _EL_. Thus the luminous hole _H_ issuccessively covered and uncovered to the eye _E_; and if the eyemoves, a succession of points on the retina is stimulated by thesuccessive uncovering of the luminous spot. No fixation-points areprovided for the eye, since such points, if bright enough to be of usein the otherwise dark room, might themselves produce confusingstreaks, and also since an exact determination of the arc ofeye-movement would be superfluous. 

[Illustration: Fig. 1. ]

The eye was first fixated on the light-spot, and then movedhorizontally away toward either the right or the left. In the firstfew trials (with eye-sweeps of medium length), the observations didnot agree, for some subjects saw both the false and the correctstreaks, while others saw only the latter. It was found later thatall the subjects saw both streaks if the arc of movement was large, say 40°, and all saw only the correctly localized streak if the arcwas small, say 5°. Arcs of medium length revealed individualdifferences between the persons, and these differences, thoughmodified, persisted throughout the experiments. After the subjects hadbecome somewhat trained in observation, the falsely localized streaknever appeared without the correctly localized one as well. For thesake of brevity the word 'streak' is retained, although the appearancenow referred to is that of a series of separate spots of lightarranged in a nearly straight line. 

The phenomena are as follows. --(1) If the arc of movement is small, ashort, correctly localized streak is seen extending from the finalfixation-point to the light-spot. It is brightest at the end nearerthe light. (2) If the eye-movement is 40° or more, a streak having alength of about one third the distance moved through is seen on theother side of the light from the final fixation-point; while anotherstreak is seen of the length of the distance moved through, andextending from the final fixation-point to the light. The first is thefalsely, the second the correctly localized streak. The second, whichis paler than the first, feels as if it appeared a moment later thanthis. The brighter end of each streak is the end which adjoins theluminous spot. (3) Owing to this last fact, it sometimes happens, whenthe eye-movement is 40° or a trifle less, that both streaks are seen, but that the feeling of succession is absent, so that the two streakslook like one streak which lies (unequally parted) on both sides ofthe spot of light. It was observed, in agreement with Schwarz, thatthe phenomenon was the same whether the head or the eyes moved. Onlyone other point need be noted. It is that the false streak, whichappears in the beginning to dart from the luminous hole, does notfade, but seems to suffer a sudden and total eclipse; whereas thesecond streak flashes out suddenly _in situ_, but at a lesserbrilliancy than the other, and very slowly fades away. 

These observations thoroughly confirmed those of Schwarz. And onecould not avoid the conviction that Schwarz's suggestion of the twostreaks being separate localizations of the same retinal stimulationwas an extremely shrewd conjecture. The facts speak strongly in itsfavor; first, that when the arc of movement is rather long, there is adistinct feeling of succession between the appearances of the falselyand the correctly localized images; second, that when both streaks areseen, the correct streak is always noticeably dimmer than the falsestreak. 

It is of course perfectly conceivable that the feeling of successionis an illusion (which will itself then need to be explained), and thatthe streak is seen continuously, its spacial reference only undergoingan instantaneous substitution. If this is the case, it is singularthat the correctly seen streak seems to enter consciousness so muchreduced as to intensity below that of the false streak when it waseclipsed. Whereas, if a momentary anęsthesia could be demonstrated, both the feeling of succession and the discontinuity of theintensities would be explained (since during the anęsthesia theafter-image on the retina would have faded). This last interpretationwould be entirely in accordance with the observations ofMcDougall, [17] who reports some cases in which after-images areintermittently present to consciousness, and fade during theireclipse, so that they reappear always noticeably dimmer than when theydisappeared. 

 [17] McDougall, _Mind_, N. S. , X. , 1901, p. 55, Observation II. 

Now if the event of such an anęsthesia could be established, we shouldknow at once that it is not a retinal but a central phenomenon. Weshould strongly suspect, moreover, that the anęsthesia is not presentduring the very first part of the movement. This must be so if theinterpretation of Schwarz is correct, for certainly no part of thestreak could be made before the eye had begun to move; and yetapproximately the first third was seen at once in its originalintensity, before indeed the 'innervation-feelings' had reachedconsciousness. Apparently the anęsthesia commences, it at all, afterthe eye has accomplished about the first third of its sweep. Andfinally, we shall expect to find that movements of the head no lessthan movements of the eyes condition the anęsthesia, since neither bySchwarz nor by the present writer was any difference observed in thephenomena of falsely localized after-images, between the cases whenthe head, and those when the eyes moved. 

III. THE PERIMETER-TEST OF DODGE, AND THE LAW OF THE LOCALIZATION OFAFTER-IMAGES. 

We have seen (above, p. 8) how the evidence which Dodge adduces todisprove the hypothesis of anęsthesia is not conclusive, since, although an image imprinted on the retina during its movement wasseen, yet nothing showed that it was seen before the eye had come torest. 

Having convinced himself that there is after all no anęsthesia, Dodgedevised a very ingenious attachment for a perimeter 'to determine justwhat is seen during the eye-movement. '[18] The eye was made to movethrough a known arc, and during its movement to pass by a very narrowslit. Behind this slit was an illuminated field which stimulated theretina. And since only during its movement was the pupil opposite theslit, so only during the movement could the stimulation be given. Inthe first experiments nothing at all of the illuminated field wasseen, and Dodge admits (_ibid. _, p. 461) that this fact 'is certainlysuggestive of a central explanation for the absence of bands of fusionunder ordinary conditions. ' But "these failures suggested an increaseof the illumination of the field of exposure. . . . Under theseconditions a long band of light was immediately evident at eachmovement of the eye. " This and similar observations were believed 'toshow experimentally that when a complex field of vision is perceivedduring eye-movement it is seen fused' (p. 462). 

 [18] Dodge, PSYCHOLOGICAL REVIEW, 1900, VII. , p. 459. 

Between the 'failures' and the cases when a band of light was seen, nochange in the conditions had been introduced except 'an increase ofthe illumination. ' Suppose now this change made just the differencebetween a stimulation which left _no_ appreciable _after-image_, andone which left _a distinct one_. And is it even possible, in view ofthe extreme rapidity of eye-movements, that a retinal stimulation ofany considerable intensity should not endure after the movement, to be_then_ perceived, whether or not it had been first 'perceived duringthe movement'?

Both of Dodge's experiments are open to the same objection. They donot admit of distinguishing between consciousness of a retinal processduring the moment of stimulation, and consciousness of the sameprocess just afterward. In both his cases the stimulation was givenduring the eye-movement, but there was nothing to prove that it wasperceived at just the same moment. Whatever the difficulties ofdemonstrating an anęsthesia during movement, an experiment which doesnot observe the mentioned distinction can never disprove thehypothesis. 

[Illustration: Fig. 2. ]

For the sake of a better understanding of these bands of light ofDodge, a perimeter was equipped in as nearly the manner described byhim (_ibid. _, p. 460) as possible. Experiments with the eye movingpast a very narrow illuminated slit confirmed his observations. If thelight behind the slit was feeble, no band was seen; if moderatelybright, a band was always seen. The most striking fact, however, wasthat the band was not localized behind the slit, but was projected onto that point where the eye came to rest. The band seemed to appearat this point and there to hover until it faded away. This apparentanomaly of localization, which Dodge does not mention, suggests thelocalization which Schwarz describes of his streaks. Hereupon theapparatus was further modified so that, whereas Dodge had let thestimulation take place only during the movement of the eye across anarrow slit between two walls, now either one of these walls could betaken away, allowing the stimulation to last for one half of the timeof movement, and this could be either the first or the second half atpleasure. A plan of the perimeter so arranged is given in Fig. 2. 

_PBCDB'P_ is the horizontal section of a semicircular perimeter of 30cm. Radius. _E_ is an eye-rest fixed at the centre of the semicircle;_CD_ is a square hole which is closed by the screen _S_ fitted intothe front pair of the grooves _GG_. In the center of _S_ and on alevel with the eye _E_ is a hole _A_, 2 cm. In diameter, whichcontains a 'jewel' of red glass. The other two pairs of grooves aremade to hold pieces of milk-or ground-glass, as _M_, which may beneeded to temper the illumination down to the proper intensity. _L_ isan electric lamp. _B_ and _B'_ are two white beads fixed to theperimeter at the same level as _E_ and _A_, and used asfixation-points. Although the room is darkened, these beads catchenough light to be just visible against the black perimeter, and theeye is able to move from one to the other, or from _A_ to either one, with considerable accuracy. They leave a slight after-image streak, which is, however, incomparably fainter than that left by _A_ (thestreak to be studied), and which is furthermore white while that of_A_ is bright red. _B_ and _B'_ are adjustable along a scale ofdegrees, which is not shown in the figure, so that the arc ofeye-movement is variable at will. _W_ is a thin, opaque, perpendicularwall extending from _E_ to _C_, that is, standing on a radius of theperimeter. At _E_ this wall comes to within about 4 mm. Of the cornea, and when the eye is directed toward _B_ the wall conceals the red spot_A_ from the pupil. _W_ can at will be transferred to the position_ED_. _A_ is then hidden if the eye looks toward _B'_. 

The four conditions of eye-movement to be studied are indicated inFig. 3 (Plate 1. ). The location of the retinal stimulation is alsoshown for each case, as well as the corresponding appearance of thestreaks, their approximate length, and above all their localization. For the sake of simplicity the refractive effect of the lens andhumors of the eye is not shown, the path of the light-rays being ineach case drawn straight. In all four cases the eye moved withoutstopping, through an arc of 40°. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE I. Fig. 3. HOLT ON EYE-MOVEMENT. ]

To take the first case, Fig. 3:1. The eye fixates the light _L_, thensweeps 40° toward the right to the point _B'_. The retina isstimulated throughout the movement, _l-l'_. These conditions yield thephenomenon of both streaks, appearing as shown on the black rectangle. 

In the second case (Fig. 3:2) the wall _W_ is in position and the eyeso adjusted in the eye-rest that the light _L_ is not seen until theeye has moved about 10° to the right, that is, until the axis ofvision is at _Ex_. Clearly, then, the image of _L_ falls at first alittle to the right of the fovea, and continues in indirect vision tothe end of the movement. The stimulated part of the retina is _l-l'_(Fig. 3:2). Here, then, we have no stimulation of the eye during thefirst part of its movement. The corresponding appearance of the streakis also shown. Only the correctly localized streak is seen, extendingfrom the light _L_ toward the right but not quite reaching _B'_. Thusby cutting out that portion of the stimulation which was given duringthe first part of the movement, we have eliminated the whole of thefalse image, and the right-hand (foveal) part of the correct image. 

Fig. 3:3 shows the reverse case, in which the stimulation is givenonly during the first part of the movement. The wall is fixed on theright of _L_, and the eye so adjusted that _L_ remains in sight untilthe axis of vision reaches position _Ex_, that is, until it has movedabout 10°. A short strip of the retina next the fovea is herestimulated, just the part which in case 2 was not stimulated; and thepart which in case 2 was, is here not stimulated. Now here the falsestreak is seen, together with just that portion of the correct streakwhich in the previous case was not seen. The latter is relatively dim. 

Thus it looks indeed as if the streak given during the first part ofan eye-movement is seen twice and differently localized. But one maysay: The twice-seen portion was in both cases on the fovea; this mayhave been the conditioning circumstance, and not the fact of beinggiven in the early part of the movement. 

We must then consider Fig. 3, case 4. Here the eye moves from _B_ to_B'_, through the same arc of 40°. The wall _W_ is placed so that _L_cannot be seen until the axis of vision has moved from _EB_ to _EL_, but _then L_ is seen in direct vision. Its image falls full on thefovea. But one streak, and that the correctly localized one, is seen. This is like case 2, except that here the streak extending from _L_ tothe right quite reaches the final fixation-point _B'_. It is thereforenot the fact of a stimulation being foveal which conditions its beingseen in two places. 

It should be added that this experiment involves no particulardifficulties of observation, except that in case 4 the eye tends tostop midway in its movement when the spot of light _L_ comes in view. Otherwise no particular training of the subject is necessary beyondthat needed for the observing of any after-image. Ten persons made theforegoing observations and were unanimous in their reports. 

This experiment leaves it impossible to doubt that the conjecture ofSchwarz, that the correct image is only the false one seen over again, is perfectly true. It would be interesting to enquire what it is thatconditions the length of the false streak. It is never more than onethird that of the correct streak (Fig. 3:1; except of course under theartificial conditions of Fig. 3:3) and may be less. The false streakseems originally to _dart out_ from the light, as described by Lipps, visibly growing in length for a certain distance, and then to besuddenly eclipsed or blotted out _simultaneously_ in all its parts. Whereas the fainter, correct streak flashes into consciousness _allparts at once_, but disappears by fading gradually from one end, theend which lies farther from the light. 

Certain it is that when the false streak stops growing and iseclipsed, some new central process has intervened. One has next toask, Is the image continuously conscious, suffering only aninstantaneous relocalization, or is there a moment of centralanęsthesia between the disappearance of the false streak and theappearance of the other? The relative dimness of the second streak inthe _first moment_ of its appearance speaks for such a brief period ofanęsthesia, during which the retinal process may have partly subsided. 

We have now to seek some experimental test which shall demonstratedefinitely either the presence or the absence of a central anęsthesiaduring eye-movements. The question of head-movements will be deferred, although, as we have seen above, these afford equally the phenomenonof twice-localized after-images. 

IV. THE PENDULUM-TEST FOR ANĘSTHESIA. 

A. Apparatus must be devised to fulfil the following conditions. Aretinal stimulation must be given during an eye-movement. The momentof excitation must be so brief and its intensity so low that theprocess shall be finished before the eye comes to rest, that is, sothat no after-image shall be left to come into consciousness _after_the movement is over. Yet, on the other hand, it must be positivelydemonstrated that a stimulation of this _very same_ brief duration andlow intensity is amply strong enough to force its way intoconsciousness if no eye-movement is taking place. If such astimulation, distinctly perceived when the eye is at rest, should notbe perceptible if given while the eye is moving, we should have avalid proof that some central process has intervened during themovement, to shut out the stimulation-image during that brief momentwhen it might otherwise have been perceived. 

Obviously enough, with the perimeter arrangement devised by Dodge, where the eye moves past a narrow, illuminated slit, the light withinthe slit can be reduced to any degree of faintness. But on the otherhand, it is clearly impossible to find out how long the moment ofexcitation lasts, and therefore impossible to find out whether anexcitation of the same duration and intensity is yet sufficient toaffect consciousness if given when the eye is not moving. Unless thestimulation is proved to be thus sufficient, a failure to see it whengiven during an eye-movement would of course prove nothing at all. 

Perhaps the most exact way to measure the duration of a light-stimulusis to let it be controlled by the passing of a shutter which isaffixed to a pendulum. Furthermore, by means of a pendulum astimulation of exactly the same duration and intensity can be given tothe moving, as to the resting eye. Let us consider Fig. 4:1. If _P_ isa pendulum bearing an opaque shield _SS_ pierced by the hole _tt_, and_BB_ an opaque background pierced by the hole _i_ behind which is alamp, it is clear that if the eye is fixed on _i_, a swing of thependulum will allow _i_ to stimulate the retina during such a time asit takes the opening _tt_ to move past _i_. The shape of _i_ willdetermine the shape of the image on the retina, and the intensity ofthe stimulation can be regulated by ground-or milk-glass interposedbetween the hole _i_ and the lamp behind it. The duration of theexposure can be regulated by the width of _tt_, by the length of thependulum, and by the arc through which it swings. 

If now the conditions are altered, as in Fig. 4:2, so that the opening_tt_ (indicated by the dotted line) lies not in _SS_, but in the fixedbackground _BB_, while the small hole _i_ now moves with the shield_SS_, it necessarily follows that if the eye can move at just the rateof the pendulum, it will receive a stimulation of exactly the samesize, shape, duration, and intensity as in the previous case where theeye was at rest. Furthermore, it will always be possible to tellwhether the eye does move at the same rate as the pendulum, since ifit moves either more rapidly or more slowly, the image of _i_ on theretina will be horizontally elongated, and this fact will be given bya judgment as to the proportions of the image seen. 

It may be said that since the eye does not rotate like the pendulum, from a fulcrum above, the image of _i_ in the case of the moving eyewill be distorted as is indicated in Fig. 4, _a_. This is true, butthe distortion will be so minute as to be negligible if the pendulumis rather long (say a meter and a half) and the opening _tt_ rathernarrow (say not more than ten degrees wide). A merely horizontalmovement of the eye will then give a practically exact superpositionof the image of _i_ at all moments of the exposure. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE PLATE II. Fig. 4. Fig. 6. HOLT ON EYE-MOVEMENT. ]

Thus much of preliminary discussion to show how, by means of apendulum, identical stimulations can be given to the moving and to theresting eye. We return to the problem. It is to find out whether astimulation given during an eye-movement can be perceived if itsafter-image is so brief as wholly to elapse before the end of themovement. If a period of anęsthesia is to be demonstrated, twoobservations must be made. First, that the stimulation is brightenough to be _unmistakably visible_ when given to the eye at rest;second, that it is not visible when given to the moving eye. Hence, weshall have three cases. 

 Case 1. A control, in which the stimulation is proved intense enough to be seen by the eye at rest. 

 Case 2. In which the same stimulation is given to the eye during movement. 

 Case 3. Another control, to make sure that no change in the adaptation or fatigue of the eye has intervened during the experiments to render the eye insensible to the stimulation. 

Fig. 5 shows the exact arrangement of the experiment. The figurerepresents a horizontal section at the eye-level of the pendulum ofFig. 4, with accessories. _E_ is the eye which moves between the twofixation-points _P_ and _P_'. _WONW_ is a wall which conceals themechanism of the pendulum from the subject. _ON_ is a rectangular hole9 cm. Wide and 7 cm. High, in this wall. _SS_ is the shield whichswings with the pendulum, and _BB_ is the background (cf. Fig. 4). When the pendulum is not swinging, a hole in the shield lies behind_ON_ and exactly corresponds with it. Another in the background doesthe same. The eye can thus see straight through to the light _L_. 

Each of these three holes has grooves to take an opaque card, _x_, _y_, or _z_; there are two cards for the three grooves, and they arepierced with holes to correspond to _i_ and _tt_ of Fig. 4. Thebackground _BB_ has a second groove to take a piece of milk-glass _M_. These cards are shown in Fig. 6 (Plate II. ) Card _I_ bears a hole 5cm. High and shaped like a dumb-bell. The diameter of the end-circles(_e_, _e_) is 1. 3 cm. , and the width of the handle _h_ is 0. 2 cm. Card_T_ is pierced by two slits _EE_, _EE_, each 9 cm. Long and 1. 3 cm. High, which correspond to the two ends of the dumb-bell. These slitsare connected by a perforation _H_, 1. 5 cm. Wide, which corresponds tothe handle of the dumb-bell. This opening _EEHEE_ is covered by apiece of ground-glass which serves as a radiating surface for thelight. 

[Illustration: Fig. 5. ]

The distance _EA_ (Fig. 5) is 56 cm. , and _PP_' is 40 cm. ; so that thearc of eye-movement, that is, the angle _PEP_', is very nearly 40°, of which the 9-cm. Opening _ON_ 9° 11'. _SS_ is 2 cm. Behind _ON_, and_BB_ 2 cm. Behind _SS_; these distances being left to allow thependulum to swing freely. 

It is found under these conditions that the natural speed made by theeye in passing the 9-cm. Opening _ON_ is very well approximated by thependulum if the latter is allowed to fall through 23. 5° of its arc, the complete swing being therefore 47°. The middle point of thependulum is then found to move from _O_ to _N_ in 110[sigma][19]. Ifthe eye sweeps from _O_ to _N_ in the same time, it will be moving atan angular velocity of 1° in 11. 98[sigma] (since the 9 cm. Are 9° 11'of eye-movement). This rate is much less than that found by Dodge andCline (_op. Cit. _, p. 155), who give the time for an eye-movement of40° as 99. 9[sigma], which is an average of only 2. 49[sigma] to thedegree. Voluntary eye-movements, like other voluntary movements, canof course be slow or fast according to conditions. After the pendulumhas been swinging for some time, so that its amplitude of movement hasfallen below the initial 47° and therewith its speed past the middlepoint has been diminished, the eye in its movements back and forthbetween the fixation-points can still catch the after-image of _i_perfectly distinct and not at all horizontally elongated, as it wouldhave to be if eye and pendulum had not moved just together. It appearsfrom this that certain motives are able to retard the rate ofvoluntary movements of the eye, even when the distance traversed isconstant. 

 [19] The speed of the pendulum is measured by attaching a tuning-fork of known vibration-rate to the pendulum, and letting it write on smoked paper as the pendulum swings past the 9-cm. Opening. 

The experiment is now as follows. The room is darkened. Card _T_ isdropped into groove _z_, while _I_ is put in groove _y_ and swingswith the pendulum. One eye alone is used. 

Case 1. The eye is fixed in the direction _EA_. The pendulum isallowed to swing through its 47°. The resulting visual image is shownin Fig. 7:1. Its shape is of course like _T_, Fig. 6, but the part _H_is less bright than the rest because it is exposed a shorter time, owing to the narrowness of the handle of the dumb-bell, which swingsby and mediates the exposure. Sheets of milk-glass are now droppedinto the back groove of _BB_, until the light is so tempered thatpart _H_ (Fig. 7:1) is _barely but unmistakably_ visible as luminous. The intensity actually used by the writer, relative to that of _EE_, is fairly shown in the figure. (See Plate III. )

It is clear, if the eye were now to move with the pendulum, that thesame amount of light would reach the retina, but that it would beconcentrated on a horizontally narrower area. And if the eye movesexactly with the pendulum, the visual image will be no longer like 1but like 2 (Fig. 7). We do not as yet know how the intensities of _e_, _e_ and _h_ will relatively appear. To ascertain this we must put card_I_ into groove _x_, and let card _T_ swing with the pendulum ingroove _y_. If the eye is again fixed in the direction _EA_ (Fig. 5), the retina receives exactly the same stimulation that it would havereceived before the cards were shifted if it had moved exactly at therate of the pendulum. In the experiments described, the handle _h_ ofthis image (Fig. 7:2) curiously enough appears of the same brightnessas the two ends _e_, _e_, although, as we know, it is stimulated for abriefer interval. Nor can any difference between _e_, _e_ and _h_ bedetected in the time of disappearance of their after-images. Theseconditions are therefore generous. The danger is that _h_ of thefigure, the only part of the stimulation which could possibly quiteelapse during the movement, is still too bright to do so. 

Case 2. The cards are replaced in their first positions, _T_ in groove_z_, _I_ in groove _y_ which swings. The subject is now asked to makevoluntary eye-sweeps from _P_ to _P'_ and back, timing his moment ofstarting so as to bring his axis of vision on to the near side ofopening _ON_ at approximately the same time as the pendulum brings _I_on the same point. This is a delicate matter and requires practice. Even then it would be impossible, if the subject were not allowed toget the rhythm of the pendulum before passing judgment on theafter-images. The pendulum used gives a slight click at each end ofits swing, and from the rhythm of this the subject is soon able totime the innervation of his eye so that the exposure coincides withthe middle of the eye-movement. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE III. Fig. 7. HOLT ON EYE-MOVEMENT. ]

It is true that with every swing the pendulum moves more slowly past_ON_, and the period of exposure is lengthened. This, however, onlytends to make the retinal image brighter, so that its disappearanceduring an anęsthesia would be so much the less likely. The pendulummay therefore be allowed to 'run down' until its swing is too slow forthe eye to move with it, that is, too slow for a distinct, non-elongated image of _i_ to be caught in transit on the retina. 

With these eye-movements, the possible appearances are of two classes, according to the localization of the after-image. The image islocalized either at _A_ (Fig. 5), or at the final fixation-point (_P_or _P'_, according to the direction of the movement). Localized at_A_, the image may be seen in either of two shapes. First, it may beidentical with 1, Fig. 7. It is seen somewhat peripherally, judgmentof indirect vision, and is correctly localized at _A_. When thesubject's eye is watched, it is found that in this case it movedeither too soon or too late, so that when the exposure was made, theeye was resting quietly on one of the fixation-points and so naturallyreceived the same image as in case 1, except that now it lies inindirect vision, the eye being directed not toward _A_ (as in case 1)but towards either _P_ or _P'_. 

Second, the image correctly localized may be like 2 (Fig. 7), and thenit is seen to move past the opening _ON_. The handle _h_ looks asbright as _e_, _e_. This appearance once obtained generally recurswith each successive swing of the pendulum, and scrutiny of thesubject's eye shows it to be moving, not by separate voluntaryinnervations from _P_ to _P'_ and then from _P'_ to _P_, butcontinuously back and forth with the swing of the pendulum, much asthe eye of a child passively follows a moving candle. This movement ispurely reflex, [20] governed probably by cerebellar centers. It seemsto consist in a rapid succession of small reflex innervations, and isvery different from the type of movement in which one definiteinnervation carries the eye through its 42°, and which yielded thephenomena with the perimeter. A subject under the spell of this reflexmust be exercised in innervating his eye to move from _P_ to _P'_ andback in single, rapid leaps. For this, the pendulum is to bemotionless and the eye is not to be stimulated during its movement. 

 [20] Exner, Sigmund, _Zeitschrift f. Psychologie u. Physiologie der Sinnesorgane_, 1896, XII. , S. 318. 'Entwurf zu einer physiologischen Erklärung der psychischen Erscheinungen, ' Leipzig u. Wien, 1894, S. 128. Mach, Ernst, 'Beiträge zur Analyse der Empfindungen, ' Jena, 1900, S. 98. 

These two cases in which the image is localized midway between _P_ and_P'_ interest us no further. Localized on the final fixation-point, the image is always felt to flash out suddenly _in situ_, just as inthe case of the 'correctly localized' after-image streaks in theexperiments with the perimeter. The image appears in one of fourshapes, Fig. 7: 2 or 3, 4 or 5. 

First, the plain or elongated outline of the dumb-bell appears withits handle on the final fixation-point (2 or 3). The image is plainand undistorted if the eye moves at just the rate of the pendulum, elongated if the eye moves more rapidly or more slowly. The point thatconcerns us is that the image appears _with its handle_. Twoprecautions must here be observed. 

The eye does not perhaps move through its whole 42°, but stops insteadjust when the exposure is complete, that is, stops on either _O_ or_N_ and considerably short of _P_ or _P'_. It then follows that theexposure is given at the _very last_ part of the movement, so that theafter-image of even the handle _h_ has not had time to subside. Theexperiment is planned so that the after-image of _h_ shall totallyelapse during that part of the movement which occurs after theexposure, that is, while the eye is completing its sweep of 42°, from_O_ to _P_, or else from _N_ to _P'_. If the arc is curtailed at point_O_ or _N_, the handle of the dumb-bell will of course appear. Thefact can always be ascertained by asking the subject to notice verycarefully where the image is localized. If the eye does in fact stopshort at _O_ or _N_, the image will be there localized, although thesubject may have thoughtlessly said before that it was at _P_ or _P'_, the points he had nominally had in mind. 

But the image 2 or 3 may indeed be localized quite over the finalfixation-point. In this case the light is to be looked to. It is toobright, as it probably was in the case of Dodge's experiments. It mustbe further reduced; and with the eye at rest, the control (case I)must be repeated. In the experiments here described it was alwaysfound possible so to reduce the light that the distinct, entire imageof the dumb-bell (2, Fig. 7) never appeared localized on the finalfixation-point, although in the control, _H_, of Fig. 7:1, was alwaysdistinctly visible. 

With these two precautions taken, the image on the finalfixation-point is like either 3, 4, or 5. Shape 5 very rarely appears, while the trained subject sees 4 and 3 each about one half the times;and either may be seen for as many as fifteen times in succession. 

Shape 4 is of course exactly the appearance which this experimenttakes to be crucial evidence of a moment of central anęsthesia, beforethe image is perceived and during which the stimulation of the handle_h_ completely elapses. Eight subjects saw this phenomenon distinctlyand, after some training in timing their eye-movements, habitually. The first appearance of the handleless image was always a decidedsurprise to the subject (as also to the writer), and with someeagerness each hastened to verify the phenomenon by new trials. 

The two ends (_e_, _e_) of the dumb-bell seem to be of the sameintensity as in shape 2 when seen in reflex movement. But there is novestige whatsoever of a handle. Two of the subjects stated that forthem the place where the handle should have been, appeared of avelvety blackness more intense than the rest of the background. Thewriter was not able to make this observation. It coincidesinterestingly with that of von Kries, [21] who reports as to the phasesof fading after-images, that between the disappearance of the primaryimage and the appearance of the 'ghost, ' a moment of the most intenseblackness intervenes. The experiments with the pendulum, however, brought out no ghost. 

 [21] Von Kries, J. , _Zeitschr. F. Psych, u. Physiol. D. Sinnesorgane_, 1896, XII. , S. 88. 

We must now enquire why in about half the cases shape 3 is still seen, whereas shape 5 occurs very rarely. Some of the subjects, among whomis the writer, never saw 5 at all. We should expect that with theintensity of _H_ sufficiently reduced 4 and 5 would appear with equalfrequency, whereas 3 would be seen no oftener than 2; shape 5appearing when the eye did not, and 4 when it did, move at just therate of the pendulum. It is certain that when 4 is seen, the eye hascaught just the rate of the pendulum, and that for 3 or 5 it has movedat some other rate. We have seen above (p. 27) that to move with thependulum the eye must already move decidedly more slowly than Dodgeand Cline find the eye generally to move. Nothing so reliable inregard to the rate of voluntary eye-movements as these measurements ofDodge and Cline had been published at the time when the experiments onanęsthesia were carried on, and it is perhaps regrettable that in the'empirical' approximation of the natural rate of the eye through 40°the pendulum was set to move so slowly. 

In any case it is highly probable that whenever the eye did not moveat just the rate of the pendulum, it moved _more rapidly_ rather thanmore slowly. The image is thus horizontally elongated, by an amountwhich varies from the least possible up to 9 cm. (the width of theopening in _T_), or _even more_. And while the last of the movement(_O_ to _P_, or _N_ to _P'_), in which the stimulation of _H'_ issupposed to subside, is indeed executed, it may yet be done so_rapidly_ that after all _H'_ cannot subside, not even although it isnow less intense by being horizontally spread out (that is, lessconcentrated than the vanished _h_ of shape 4). This explanation isrendered more probable by the very rare appearance of shape 5, whichmust certainly emerge if ever the eye were to move more slowly thanthe pendulum. 

The critical fact is, however, that shape 4 _does_ appear to a trainedsubject in about one half the trials--a very satisfactory ratio whenone considers the difficulty of timing the beginning of the movementand its rate exactly to the pendulum. 

Lastly, in some cases no image appears at all. This was at first asource of perplexity, until it was discovered that the image of thedumb-bell, made specially small so as to be contained within the areaof distinct vision, could also be contained on the blind-spot. Withthe pendulum at rest the eye could be so fixed as to see not even theslight halo which diffuses in the eye and seems to lie about thedumb-bell. It may well occur, then, that in a movement the imagehappens to fall on the blind-spot and not on the fovea. That thisaccounts for the cases where no image appears, is proved by the factthat if both eyes are used, some image is always seen. A binocularimage under normal convergence can of course not fall on bothblind-spots. It may be further said that the shape 4 appears as wellwhen both eyes are used as with only one. The experiment may indeed aswell be carried on with both eyes. 

Some objections must be answered. It may be said that the image of _h_happens to fall on the blind-spot, _e_ and _e_ being above and belowthe same. This is impossible, since the entire image and its halo aswell may lie within the blind-spot. If now _h_ is to be on theblind-spot, at least one of the end-circles _e_, _e_ will be therealso, whereas shape 4 shows both end-circles of the dumb-bell withperfect distinctness. 

Again, it cannot properly be urged that during the movement theattention was distracted so as not to 'notice' the handle. The shapeof a dumb-bell was specially chosen for the image so that the weakerpart of the stimulation should lie between two points which should beclearly noticed. Indeed, if anything, one might expect this central, connecting link in the image to be apperceptively filled in, even whenit did not come to consciousness as immediate sensation. And itremains to ask what it is which should distract the attention. 

In this connection the appearance under reflex eye-movement comparesinterestingly with that under voluntary. If the wall _WONW_ (Fig. 5)is taken from before the pendulum, and the eye allowed to movereflexly with the swinging dumb-bell, the entire image is seen at eachexposure, the handle seeming no less bright than the end-circles. Moreover, as the dumb-bell opening swings past the place of exposureand the image fades, although the handle must fade more quickly thanthe ends, yet this is not discernible, and the entire image disappearswithout having at any time presented the handleless appearance. 

B. Another test for this anęsthesia during movement is offered in thefollowing experiment. It is clear that, just as a light-stimulation isnot perceived if the whole retinal process begins and ends during amovement, so also a particular phase of it should not be perceived ifthat phase can be given complete within the time of the movement. Thesame pendulum which was used in the previous experiment makes such athing possible. If in place of the perforated dumb-bell the pendulumexposes two pieces of glass of nearly complementary colors, one afterthe other coming opposite the place of exposure, the sensations willfuse or will not fuse according as the pendulum swings rapidly orslowly. But now a mean rate of succession can be found such as to letthe first color be seen pure before the second is exposed, and then toshow the second fused with the after-image of the first. Under someconditions the second will persist after the first has faded, and willthen itself be seen pure. Thus there may be three phases inconsciousness. If the first color exposed is green and the second red, the phases of sensation will be green, white, and perhaps red. Thesephases are felt to be not simultaneous but successive. A modificationof this method is used in the following experiment. (See Fig. 8, PlateIV. )

_T_ and _I_ here correspond to the cards _T_ and _I_ of Fig. 6. _T_ consists of a rectangular opening, 9×5 cm. , which contains threepieces of glass, two pieces of green at the ends, each 2. 8 cm. Wideand 7 cm. High, and a piece of red glass in the middle 3. 4 cm. Wideand only 1. 5 cm. High, the space above and below this width beingfilled with opaque material. The shape of the image is determined asbefore by the hole in _I_, which now, instead of being a dumb-bell, ismerely a rectangular hole 2 cm. Wide and 5 cm. High. Exactly asbefore, _T_ is fixed in the background and _I_ swings with thependulum, the eye moving with it. 

The speed of the pendulum must be determined, such that if _I_ lies inthe front groove (Fig. 5, _x_) and the eye is at rest, the image willclearly show two phases of color when _T_ swings past on the pendulum. With _T_ and _I_ as described above, a very slow pendulum shows theimage green, red (narrow), and green, in succession. A very fastpendulum shows only a horizontal straw-yellow band on a green field(Fig. 8:5). There is but one phase and no feeling of succession. Between these two rates is one which shows two phases--the first agreen field with a horizontal, reddish-orange band (Fig. 8:3), thesecond quickly following, in which the band is straw-yellow (5). Itmight be expected that this first phase would be preceded by anentirely green phase, since green is at first exposed. Such is howevernot the case. The straw-yellow of the last phase is of course thefusion-color of the red and green glasses. It would be gray but thatthe two colors are not perfectly complementary. Since the arrangementof colors in _T_ is bilaterally symmetrical, the successive phases arethe same in whichever direction the pendulum swings. 

[Illustration: MONOGRAPH SUPPLEMENT 17. PLATE IV. Fig. 8. HOLT ON EYE-MOVEMENT. ]

It is desirable to employ the maximum rate of pendulum which will givethe two phases. For this the illumination should be very moderate, since the brighter it is, the slower must be the pendulum. With thedegree of illumination used in the experiments described, it was foundthat the pendulum must fall from a height of only 9. 5° of its arc: atotal swing of 19°. The opening of _T_, which is 9 cm. Wide, thenswings past the middle point of _I_ in 275[sigma]. 

Now when the eye moves it must move at this rate. If the eye is 56 cm. Distant from the opening, as in the previous case, the 9 cm. Ofexposure are 9° 11' of eye-movement, and we saw above that 9° 11' in110[sigma] is a very slow rate of movement, according to the bestmeasurements. Now it is impossible for the eye to move so slowly as 9°11' in 275[sigma]. If, however, the eye is brought nearer to theopening, it is clear that the 9 cm. Of exposure become more than 9°11' of eye-movement. Therefore the eye and the fixation-points are soplaced that _EA_ (Fig. 5) = 26 cm. And _PP'_ = 18 cm. The totaleye-movement is thus 38° 11', of which the nine-centimeter distance ofexposure is 19° 38'. Now the eye is found to move very well through19° 38' in 275[sigma], although, again, this is much more than aproportionate part of the total time (99. 9[sigma]) given by Dodge andCline for a movement of the eye through 40°. The eye is in this casealso moving slowly. As before, it is permissible to let the pendulumrun down till it swings too slowly for the eye to move with it; sinceany lessened speed of the pendulum only makes the reddish-orange phasemore prominent. 

As in the experiment with the dumb-bell, we have also here threecases: the control, the case of the eye moving, and again a control. 

Case 1. _T_ swings with the pendulum. _I_ is placed in the frontgroove, and the eye looks straight forward without moving. Thependulum falls from 9. 5° at one side, and the illumination is soadjusted that the phase in which the band is reddish-orange, is_unmistakably_ perceived before that in which it is straw-yellow. Theappearance must be 3 followed by 5 (Fig. 8). 

Case 2. _T_ is fixed in the background, _I_ on the pendulum, and thephenomena are observed with the eye moving. 

Case 3. A repetition of case 1, to make sure that no differentadaptation or fatigue condition of the eye has come in to modify theappearance of the two successive phases as at first seen. 

The possible appearances to the moving eye are closely analogous tothose in the dumb-bell experiment. If the eye moves too soon or toolate, so that it is at rest during the exposure, the image is like _T_itself (Fig. 8) but somewhat fainter and localized midway between thepoints _P_ and _P'_. If the eye moves reflexly at the rate of thependulum, the image is of the shape _i_ and shows the two phases (3followed by 5). It is localized in the middle and appears to moveacross the nine-centimeter opening. 

A difficulty is met here which was not found in the case of thedumb-bell. The eye is very liable to come to a full stop on one of thecolored surfaces, and then to move quickly on again to the finalfixation-point. And this happens contrary to the intention of thesubject, and indeed usually without his knowledge. This stopping isundoubtedly a reflex process, in which the cerebellar mechanism whichtends to hold the fixation on any bright object, asserts itself overthe voluntary movement and arrests the eye on the not moving red orgreen surface as the exposure takes place. A comparable phenomenon wasfound sometimes in the experiment with the dumb-bell, where aneye-movement commenced as voluntary would end as a reflex following ofthe pendulum. In the present experiment, until the subject is welltrained, the stopping of the eye must be watched by a second personwho looks directly at the eye-ball of the subject during eachmovement. The appearances are very varied when the eye stops, but thetypical one is shown in Fig. 8:1. The red strip _AB_ is seldom longerand often shorter than in the figure. That part of it which issuperposed on the green seldom shows the orange phase, being almostalways of a pure straw-yellow. The localization of these images isvariable. All observations made during movements in which the eyestops, are of course to be excluded. 

If now the eye does not stop midway, and the image is not localized inthe center, the appearance is like either 2, 4, or 5, and is localizedover the final fixation-point. 2 is in all probability the case of theeye moving very much faster than the pendulum, so that if the movementis from left to right, the right-hand side of the image is the partfirst exposed (by the uncovering of the left-hand side of _T_), whichis carried ahead by the too swift eye-movement and projected inperception on the right of the later portion. 3 is the case of the eyemoving at very nearly but not quite the rate of the pendulum. Theimage which should appear 2 cm. Wide (like the opening _i_) appearsabout 3 cm. Wide. The middle band is regularly straw-yellow, extremelyseldom reddish, and if we could be sure that the eye moves more slowlythan the pendulum, so that the succession of the stimuli is evenslower than in the control, and the red phase is surely given, thisappearance (3) would be good evidence of anęsthesia during which thereddish-orange phase elapses. It is more likely, however, that the eyeis moving faster than the pendulum, but whether or not soinconsiderably faster as still to let the disappearance of the reddishphase be significant of anęsthesia, is not certain until one shallhave made some possible but tedious measurements of the apparent widthof the after-image. Both here and in the following case the _feelingof succession_, noticeable between the two phases when the eye is atrest, has _disappeared with the sensation of redness_. 

The cases in which 5 is seen are, however, indisputably significant. The image is apparently of just the height and width of _i_, and thereis not the slightest trace of the reddish-orange phase. The imageflashes out over the final fixation-point, green and straw-yellow, just as the end-circles of the dumb-bell appeared without theirhandle. The rate of succession of the stimuli, green--red--green, onthe retina, is identical with that rate which showed the two phases tothe resting eye: for the pendulum is here moving at the very samerate, and the eye is moving exactly with the pendulum, as is shown bythe absence of any horizontal elongation of the image seen. Thetrained subject seldom sees any other images than 4 and 5, and thesewith about equal frequency, although either is often seen in ten orfifteen consecutive trials. As in the cases of the falsely localizedimages and of the handleless dumb-bell, movements of both eyes, aswell as of the head but not the eyes, yield the same phenomena. It isinteresting again to compare the appearance under reflex movement. Ifat any time during the experiments the eye is allowed to follow thependulum reflexly, the image is at once and invariably seen to passthrough its two phases as it swings past the nine-centimeter opening. 

The frequent and unmistakable appearance of this band of straw-yellowon a non-elongated green field _without the previous phase in whichthe band is reddish-orange_, although this latter was unmistakablewhen the same stimulation was given to the eye at rest, isauthenticated by eight subjects. _This appearance, together with thatof the handleless dumb-bell, is submitted as a demonstration thatduring voluntary movements of the eyes, and probably of the head aswell, there is a moment in which stimulations are not transmitted fromthe retina to the cerebral cortex, that is, a moment of centralanęsthesia_. The reason for saying 'and _probably_ of the head aswell, ' is that although the phenomena described are gotten equallywell from movements of the head, yet it is not perfectly certain thatwhen the head moves the eyes do not also move slightly within thehead, even when the attempt is made to keep them fixed. 

Most of the criticisms which apply to this last experiment apply tothat with the dumb-bell and have already been answered. There is onehowever which, while applying to that other, more particularly applieshere. It would be, that these after-images are too brief andindistinct to be carefully observed, so that judgments as to theirshape, size, and color are not valid evidence. This is a perfectlysensible criticism, and a person thoroughly convinced of its forceshould repeat the experiments and decide for himself what reliance hewill place on the judgments he is able to make. The writer and thoseof the subjects who are most trained in optical experiments find thejudgments so simple and easily made as not to be open to doubt. 

In the first place, it should be remembered that only those cases arecounted in which the movement was so timed that the image was seen indirect vision, that is, was given on or very near the fovea. In suchcases a nice discrimination of the shape and color of the images iseasily possible. 

Secondly, the judgments are in no case quantitative, that is, they inno case depend on an estimate of the absolute size of any part of theimage. At most the proportions are estimated. In the case of thedumb-bell the question is, Has the figure a handle? The otherquestion, Are the end-circles horizontally elongated? has not to beanswered with mathematical accuracy. It is enough if the end-circlesare approximately round, or indeed are narrower than 9 cm. Horizontally, for at even that low degree of concentration the handlewas still visible to the resting eye. Again, in the experiment withthe color-phases, only two questions are essential to identify theappearance 5: Does the horizontal yellow band extend quite to bothedges of the image? and, Is there certainly no trace of red or orangeto be seen? The first question does not require a quantitativejudgment, but merely one as to whether there is any green visible tothe right or left of the yellow strip. Both are therefore strictlyquestions of quality. And the two are sufficient to identifyappearance 5, for if no red or orange is visible, images 1, 2, and 3are excluded; and if no green lies to the right or left of the yellowband, image 4 is excluded. Thus if one is to make the somewhatsuperficial distinction between qualitative and quantitativejudgments, the judgments here required are qualitative. Moreover, thesubjects make these judgments unhesitatingly. 

Finally, the method of making judgments on after-images is not new inpsychology. Lamansky's well-known determination of the rate ofeye-movements[22] depends on the possibility of counting accuratelythe number of dots in a row of after-images. A very much bolderassumption is made by Guillery[23] in another measurement of the rateof eye-movements. A trapezoidal image was generated on the movingretina, and the after-image of this was projected on to a planebearing a scale of lines inclining at various angles. On this thedegree of inclination of one side of the after-image was read off, andthence the speed of the eye-movement was calculated. In spite of theboldness of this method, a careful reading of Guillery's first articlecited above will leave no doubt as to its reliability, and theaccuracy of discrimination possible on these after-images. 

 [22] Lamansky, S. , (Pflüger's) Archiv f. D. Gesammte Physiologie, 1869, II. , S. 418. 

 [23] Guillery, (Pflüger's) Archiv f. D. Ges. Physiologie, 1898, LXXI. , S. 607; and 1898, LXXIII. , S. 87. 

As to judgments on the color and color-phases of after-images, thereis ample precedent in the researches of von Helmholtz, Hering, Hess, von Kries, Hamaker, and Munk. It is therefore justifiable to assumethe possibility of making accurately the four simple judgments ofshape and color described above, which are essential to the two proofsof anęsthesia. 

V. SUMMARY AND COROLLARIES OF THE EXPERIMENTS, AND A PARTIAL, PHYSIOLOGICAL INTERPRETATION OF THE CENTRAL ANĘSTHESIA. 

We have now to sum up the facts given by the experiments. The fact ofcentral anęsthesia during voluntary movement is supported by twoexperimental proofs, aside from a number of random observations whichseem to require this anęsthesia for their explanation. The first proofis that if an image of the shape of a dumb-bell is given to the retinaduring an eye-movement, and in such a way that the handle of theimage, while positively above the threshold of perception, is yet ofbrief enough duration to fade completely before the end of themovement, it then happens that both ends of the dumb-bell are seen butthe handle not at all. The fact of its having been properly given tothe retina is made certain by the presence of the now disconnectedends. 

The second proof is that, similarly, if during an eye-movement twostimulations of different colors are given to the retina, superposedand at such intensity and rate of succession as would show to theresting eye two successive phases of color (in the case taken, reddish-orange and straw-yellow), it then happens that the firstphase, which runs its course and is supplanted by the second beforethe movement is over, is not perceived at all. The first phase wascertainly given, because the conditions of the experiment require theorange to be given if the straw-yellow is, since the straw-yellowwhich is seen can be produced only by the addition of green to theorange which is not seen. 

These two phenomena seem inevitably to demonstrate a moment duringwhich a process on the retina, of sufficient duration and intensityordinarily to determine a corresponding conscious state, isnevertheless prevented from doing so. One inclines to imagine aretraction of dendrites, which breaks the connection between thecentral end of the optic nerve and the occipital centers of vision. 

The fact of anęsthesia demonstrated, other phenomena are now availablewith further information. From the phenomena of the 'falselylocalized' images it follows that at least in voluntary eye-movementsof considerable arc (30° or more), the anęsthesia commencesappreciably later than the movement. The falsely localized streak isnot generated before the eye moves, but is yet seen before thecorrectly localized streak, as is shown by the relative intensities ofthe two. The anęsthesia must intervene between the two appearances. The conjecture of Schwarz, that the fainter streak is but a secondappearance of the stronger, is undoubtedly right. 

We know too that the anęsthesia depends on a mechanism central of theretina, for stimulations are received during movement but nottransmitted to consciousness till afterward. This would be furthershown if it should be found that movements of the head, no less thanthose of the eyes, condition the anęsthesia. As before said, it is notcertain that the eyes do not move slightly in the head while the headmoves. The movement of the eyes must then be very slight, and theanęsthesia correspondingly either brief or discontinuous. Whereas, thephenomena are the same when the head moves 90° as when the eyes movethat amount. It seems probable, then, that voluntary movements of thehead do equally condition the anęsthesia. 

We have seen, too, that in reflex eye-or head-movements no anęsthesiais so far to be demonstrated. The closeness with which the eye followsthe unexpected gyrations of a slowly waving rush-light, proves thatthe reflex movement is produced by a succession of brief impulses(probably from the cerebellum), each one of which carries the eyethrough only a very short distance. It is an interesting question, whether there is an instant of anęsthesia for each one of theseinvoluntary innervations--an instant too brief to be revealed by theexperimental conditions employed above. The seeming continuity of thesensation during reflex movement would of course not argue againstsuch successive instants of anęsthesia, since no discontinuity ofvision during voluntary movement is noticeable, although a relativelylong moment of anęsthesia actually intervenes. 

But decidedly the most interesting detail about the anęsthesia is thatshown by the extreme liability of the eye to stop reflexly on the redor the green light, in the second experiment with the pendulum. Suppose the eye to be moving from _P_ to _P'_ (Fig. 5); theanęsthesia, although beginning later than the movement, is presentwhen the eye reaches _O_, while it is between _O_ and _N_, that is, during the anęsthetic moment, that the eye is reflexly caught and heldby the light. This proves again that the anęsthesia is not retinal, but it proves very much more; namely, that _the retinal stimulation istransmitted to those lower centers which mediate reflex movements, atthe very instant during which it is cut off from the higher, consciouscenters_. The great frequency with which the eye would stop midway inits movements, both in the second pendulum-experiment and in therepetition of Dodge's perimeter-test, was very annoying at the time, and the observation cannot be questioned. The fact of the habitualreflex regulation of voluntary movements is otherwise undisputed. Exner[24] mentions a variety of similar instances. Also, with themoving dumb-bell, as has been mentioned, the eye having begun avoluntary sweep would often be caught by the moving image and carriedon thereafter reflexly with the pendulum. These observations hangtogether, and prove a connection between the retina and the reflexcenters even while that between the retina and the conscious centersis cut off. 

 [24] Exner, Sigmund, 'Entwurf zu einer physiologischen Erklärung der psychischen Erscheinungen, ' Leipzig und Wien, 1894, S. 124-129. 

But shall we suppose that the 'connection' between the retina and theconscious centers is cut off during the central anęsthesia? All thatthe facts prove is that the centers are at that time not conscious. Itwould be at present an unwarrantable assumption to make, that thesecenters are therefore disconnected from the retina, at the opticthalami, the superior quadrigeminal bodies, or wheresoever. On broadpsychological grounds the action-theory of Münsterberg[25] hasproposed the hypothesis that cerebral centers fail to mediateconsciousness not merely when no stimulations are transmitted to them, but rather when the stimulations transmitted are not able to passthrough and out. The stimulation arouses consciousness when it finds aready discharge. And indeed, in this particular case, while we have noother grounds for supposing stimulations _to_ the visual centers to becut off, we do have other grounds for supposing that egress _from_these cells would be impeded. 

 [25] Münsterberg, Hugo, 'Grundzüge der Psychologie, ' Leipzig, 1900, S. 525-561. 

The occipital centers which mediate sensations of color are of coursemost closely associated with those other centers (probably theparietal) which receive sensations from the eye-muscles and which, therefore, mediate sensations which furnish space and position to thesensations of mere color. Now it is these occipital centers, mediatorsof light-sensations merely, which the experiments have shown mostspecially to be anęsthetic. The discharge of such centers meansparticularly the passage of excitations on to the parietallocalization-centers. There are doubtless other outlets, but these arethe chief group. The movements, for instance, which activity of thesecells produces, are first of all eye-movements, which have to be_directly_ produced (according to our present psychophysicalconceptions) by discharges from the centers of eye-muscle sensation. The principal direction of discharge, then, from the color-centers istoward the localization-centers. 

Now the experiment with falsely and correctly localized after-imagesproves that before the anęsthesia all localization is with referenceto the point of departure, while afterwards it is with reference tothe final fixation-point. The transition is abrupt. During theanęsthesia, then, the mechanism of localization is suffering areadjustment. It is proved that during this interval of readjustmentin the centers of eye-muscle sensation the way is closed to oncomingdischarges from the color-centers; but it is certain that any suchdischarge, during this complicated process of readjustment, would takethe localization-centres by surprise, as it were, and mightconceivably result in untoward eye-movements highly prejudicial to thesafety of the individual as a whole. The much more probable event isthe following:

Although Schwarz suggests that the moment between seeing the false andseeing the correct after-image is the moment that consciousness istaken up with 'innervation-feelings' of the eye-movement, this isimpossible, since the innervation-feelings (using the word in the onlypermissible sense of remembered muscle-sensations) must _precede_ themovement, whereas even the first-seen, falsely localized streak is notgenerated till the movement commences. But we do have to suppose thatduring the visual anęsthesia, muscle-sensations of _present_ movementare streaming to consciousness, to form the basis of the newpost-motum localization. And these would have to go to those verycenters mentioned above, the localization-centers or eye-musclesensation centers. One may well suppose that these incoming currentsso raise the tension of these centers that for the moment no dischargecan take place thither from other parts of the brain, among which arethe centers for color-sensations. The word 'tension' is of course afigure, but it expresses the familiar idea that centers which are inprocess of receiving peripheral stimulations, radiate that energy_to_ other parts of the brain (according to the neural dispositions), and probably do not for the time being receive communicationstherefrom, since those other parts are now less strongly excited. Itis, therefore, most probable that during the incoming of theeye-muscle sensations the centers for color are in fact not able todischarge through their usual channels toward the localization-centers, since the tension in that direction is too high. If, now, their otherchannels of discharge are too few or too little used to come intoquestion, the action-theory would find in this a simple explanation ofthe visual anęsthesia. 

The fact that the anęsthesia commences appreciably later than themovement so far favors this interpretation. For if the anęsthesia isconditioned by high tension in the localization-centers, due toincoming sensations from the eye-muscles, it could not possiblycommence synchronously with the movement. For, first the sensoryend-organs in the eye-muscles (or perhaps in the ligaments, surfacesof the eye-sockets, etc. ) have their latent period; then thestimulation has to travel to the brain; and lastly it probably has toinitiate there a summation-process equivalent to another latentperiod. These three processes would account very readily for what wemay call the latent period of the anęsthesia, as observed in theexperiments. It is true that this latent period was observed only inlong eye-and head-movements, but the experiments were not delicateenough in this particular to bring out the finer points. 

Finally, the conditioning of anęsthesia by movements of the head, ifreally proved, would rather corroborate this interpretation. For ofcourse the position of the head on the shoulders is as important forlocalization of the retinal picture as the position of the eyes in thehead, so that sensations of head-movements must be equally representedin the localization centers; and head movements would equally raisethe tension on those centers against discharge-currents from thecolor-centers. 

The conclusion from the foregoing experiments is that voluntarymovements of the eyes condition a momentary, visual, centralanęsthesia. 

 * * * * *

TACTUAL ILLUSIONS. 

BY CHARLES H. RIEBER. 

I. 

Many profound researches have been published upon the subject ofoptical illusions, but in the field of tactual illusions no equallyextensive and serious work has been accomplished. The reason for thisapparent neglect of the illusions of touch is obviously the fact thatthe studies in the optical illusions are generally thought to yieldmore important results for psychology than corresponding studies inthe field of touch. Then, too, the optical studies are more attractiveby reason of the comparative ease and certainty with which thestatistics are gathered there. An optical illusion is discovered in asingle instance of the phenomenon. We are aware of the illusion almostimmediately. But in the case of most of the illusions of touch, alarge number of experiments is often necessary in order to reveal anyapproximately constant error in the judgments. Nevertheless, it seemsto me that the factors that influence our judgments of visual space, though their effects are nearly always immediately apparent, are of nomore vital significance for the final explanation of the origin of ournotion of space than the disturbing factors in our estimations oftactual space whose effects are not so open to direct observation. 

The present investigation has for its main object a criticalexamination of the tactual illusions that correspond to some of thewell-known optical illusions, in the hope of segregating some of thevarious disturbing factors that enter into our very complex judgmentsof tactual space. The investigation has unavoidably extended into anumber of near-lying problems in the psychology of touch, but thefinal object of my paper will be to offer a more decisive answer thanhas hitherto been given to the question, _Are the optical illusionsalso tactual illusions, or are they reversed for touch?_

Those who have given their attention to illusions of sight and touchare rather unequally divided in their views as to whether thegeometrical optical illusions undergo a reversal in the field oftouch, the majority inclining to the belief that they are reversed. And yet there are not wanting warm adherents of the opposite view. Acomparison of the two classes of illusions, with this question inview, appears therefore in the present state of divergent opinion tobe a needed contribution to experimental psychology. Such anexperimental study, if it succeeds in finding the solution to thisdebate, ought to throw some further light upon the question of theorigin of our idea of space, as well as upon the subject of illusionsof sense in general. For, on the one hand, if touch and sight functionalike in our judgment of space, we should expect that like peripheraldisturbances in the two senses would cause like central errors injudgment, and every tactual analogue of an optical illusion should befound to correspond both in the direction of the error and, to acertain extent, quantitatively with the optical illusion. But if, onthe other hand, they are in their origin and in their developed statereally disparate senses, each guided by a different psychologicalprinciple, the illusion in the one sense might well be the reverse ofthe corresponding illusion in the other sense. Therefore, if theresults of an empirical study should furnish evidence that theillusions are reversed in passing from one field to the other, weshould be obliged to conclude that we are here in the presence of whatpsychologists have been content to call the 'unanalyzable fact' thatthe two senses function differently under the same objectiveconditions. But if, on the contrary, it should turn out that theillusions are not reversed for the two senses, then the theory of theultimate uniformity of the psychical laws will have received animportant defence. 

These experiments were carried on in the Harvard PsychologicalLaboratory during the greater part of the years 1898-1901. In all, fifteen subjects coöperated in the work at different times. 

The experimental work in the direction of a comparison of the opticalillusions with the tactual illusions, to the time of the presentinvestigation, has been carried on chiefly with the familiar opticalillusion of the overestimation of filled space. If the distancebetween two points be divided into two equal parts by a point midwaybetween them, and the one of the halves be filled with intermediatepoints, the filled half will, to the eye, appear longer than the openhalf. James[1] says that one may easily prove that with the skin weunderestimate a filled space, 'by taking a visiting card, and cuttingone edge of it into a saw-toothed pattern, and from the opposite edgecutting out all but two corners, and then comparing the feelingsaroused by the two edges when held against the skin. ' He then remarks, 'the skin seems to obey a different law here from the eye. ' Thisexperiment has often been repeated and verified. The most extensivework on the problem, however, is that by Parrish. [2] It is doubtlessprincipally on the results of Parrish's experiments that severalauthors of text-books in psychology have based their assertions that afilled space is underestimated by the skin. The opposite conclusion, namely, that the illusion is not reversed for the skin, has beenmaintained by Thiéry, [3] and Dresslar. [4] Thiéry does not, so far as Iknow, state the statistics on which he bases his view. Dresslar'sexperiments, as Parrish has correctly observed, do not deal with theproper analogue of the optical illusion for filled space. The work ofDresslar will be criticised in detail when we come to the illusionsfor active touch. 

 [1] James, William: 'Principles of Psychology, ' New York, 1893, Vol. II. , p. 141. 

 [2] Parrish, C. S. : _Amer. Journ. Of Psy. _, 1895, Vol. VI. , p. 514. 

 [3] Thiéry, A. : _Philos. Studien_, 1896, Bd. XII. , S. 121. 

 [4] Dresslar, F. B. : _Amer. Journ. Of Psy. _, 1894, Vol. VI. , p. 332. 

At the beginning of the present investigation, the preponderance oftestimony was found to be in favor of the view that filled space isunderestimated by the skin; and this view is invariably accompanied bythe conclusion, which seems quite properly to follow from it, that theskin and the eye do not function alike in our perception of space. Ibegan my work, however, in the belief that there was lurking somewherein the earlier experiments a radical error or oversight. I may sayhere, parenthetically, that I see no reason why experimentalpsychologists should so often be reluctant to admit that they begincertain investigations with preconceptions in favor of the theorywhich they ultimately defend by the results of their experiments. Theconclusions of a critical research are in no wise vitiated becausethose conclusions were the working hypotheses with which theinvestigator entered upon his inquiry. I say frankly, therefore, thatalthough my experiments developed many surprises as they advanced, Ibegan them in the belief that the optical illusions are not reversedfor touch. The uniformity of the law of sense perception is prejudicedif two senses, when affected by the same objective conditions, shouldreport to consciousness diametrically opposite interpretations ofthese same objective facts. I may say at once, in advance of theevidence upon which I base the assertion, that the belief with which Ibegan the experiments has been crystallized into a firm conviction, namely, that neither the illusion for open or filled spaces, nor anyother optical illusion, is genuinely reversed for touch. 

II. 

I began my work on the problem in question by attempting to verifywith similar apparatus the results of some of the previousinvestigations, in the hope of discovering just where the suspectederror lay. It is unnecessary for me to give in detail the results ofthese preliminary series, which were quite in agreement with thegeneral results of Parrish's experiments. Distances of six centimetersfilled with points varying in number and position were, on the whole, underestimated in comparison with equal distances without intermediatepoint stimulations. So, too, the card with saw-toothed notches wasjudged shorter than the card of equal length with all but the endpoints cut out. 

After this preliminary verification of the previous results, I wasconvinced that to pass from these comparatively meager statistics, gathered under limited conditions in a very special case, to thegeneral statement that the optical illusion is reversed in the fieldof touch, is an altogether unwarranted procedure. When one reads thesummarized conclusions of these previous investigators, one finds itthere assumed or even openly asserted that the objective conditions ofthe tactual illusion are precisely the same as those of the opticalillusion. But I contend that it is not the real analogue of theoptical illusion with which these experiments have been concerned. The objective conditions are not the same in both. Although somethingthat is very much like the optical illusion is reversed, yet I shallattempt to prove in this part of my paper, first, that the formerexperiments have not been made with the real counterpart of theoptical illusion; second, that the optical illusion can be quiteexactly reproduced on the skin; third, that where the objectiveconditions are the same, the filled cutaneous space is overestimated, and the illusion thus exists in the same sense for both sight andtouch. 

Let me first call attention to some obvious criticisms on Parrish'sexperiments. They were all made with one distance, namely, 6. 4centimeters; and on only one region, the forearm. Furthermore, inthese experiments no attempt was made to control the factor ofpressure by any mechanical device. The experimenter relied entirely onthe facility acquired by practice to give a uniform pressure to thestimuli. The number of judgments is also relatively small. Again, theopen and filled spaces were always given successively. This, ofcourse, involves the comparison of a present impression with thememory of a somewhat remote past impression, which difficulty can notbe completely obviated by simply reversing the order of presentation. In the optical illusion, the two spaces are presented simultaneously, and they lie adjacent to each other. It is still a debated questionwhether this illusion would exist at all if the two spaces were notgiven simultaneously and adjacent. Münsterberg[5] says of the opticalillusion for the open and filled spaces, "I have the decidedimpression that the illusion does not arise from the fact of ourcomparing one half with the other, but from the fact that we grasp theline as a whole. As soon as an interval is inserted, so that theperception of the whole line as constituted of two halves vanishes, the illusion also disappears. " This is an important consideration, towhich I shall return again. 

 [5] Münsterberg, H. : 'Beiträge zur Exper. Psy. , ' Freiburg i. B. , 1889, Heft II. , S. 171. 

Now, in my experiments, I endeavored to guard against all of theseobjections. In the first place, I made a far greater number of tests. Then my apparatus enabled me, firstly, to use a very wide range ofdistances. Where the points are set in a solid block, the experimentswith long distances are practically impossible. Secondly, theapparatus enabled me to control accurately the pressure of each point. Thirdly, the contacts could be made simultaneously or successivelywith much precision. This apparatus (Fig. 1) was planned and made inthe Harvard Laboratory, and was employed not only in our study of thisparticular illusion, but also for the investigation of a number ofallied problems. 

[Illustration: FIG. 1. ]

Two ęsthesiometers, A and B, were arranged in a framework, so thatuniform stimulations could be given on both arms. The ęsthesiometerswere raised or lowered by means of the crank, C, and the cams, D andE. The contacts were made either simultaneously or successively, withany interval between them according to the position of the cams on thecrank. The height of the ęsthesiometer could be conveniently adjustedby the pins F and H. The shape of the cams was such that the descentof the ęsthesiometer was as uniform as the ascent, so that thecontacts were not made by a drop motion unless that was desired. Thesliding rules, of which there were several forms and lengths, could beeasily detached from the upright rods at _K_ and _L_. Each of thepoints by which the contacts were made moved easily along the slidingrule, and could be also raised or lowered for accommodation to theunevenness of the surface of the skin. These latter were the mostvaluable two features of the apparatus. There were two sets of points, one of hard rubber, the other of metal. This enabled me to take intoaccount, to a certain extent, the factor of temperature. A wide rangeof apparent differences in temperature was secured by employing thesetwo stimuli of such widely different conductivity. Then, as each pointwas independent of the rest in its movements, its weight could also bechanged without affecting the rest. 

In the first series of experiments I endeavored to reproduce for touchthe optical illusion in its exact form. There the open and the filledspaces are adjacent to each other, and are presented simultaneouslyfor passive functioning of the eye, which is what concerns us here inour search for the analogue of passive touch. This was by no means aneasy task, for obviously the open and the filled spaces in thisposition on the skin could not be compared directly, owing to the lackof uniformity in the sensibility of different portions of the skin. Atfirst, equivalents had to be established between two collinear openspaces for the particular region of the skin tested. Three points weretaken in a line, and one of the end points was moved until the twoadjacent open spaces were pronounced equal. Then one of the spaces wasfilled, and the process of finding another open space equivalent tothis filled space was repeated as before. This finding of twoequivalent open spaces was repeated at frequent intervals. It wasfound unsafe to determine an equivalent at the beginning of eachsitting to be used throughout the hour. 

Two sets of experiments were made with the illusion in this form. Inone the contacts were made simultaneously; the results of this seriesare given in Table I. In the second set of experiments the centralpoint which divided the open from the filled space touched the skinfirst, and then the others in various orders. The object of this wasto prevent fusion of the points, and, therefore, to enable the subjectto pronounce his judgments more rapidly and confidently. A record ofthese judgments is given in Table II. In both of these series thefilled space was always taken near the wrist and the open space in astraight line toward the elbow, on the volar side of the arm. Atpresent, I shall not undertake to give a complete interpretation ofthe results of these two tables, but simply call attention to twomanifest tendencies in the figures. First, it will be seen that theshort filled distance of four centimeters is underestimated, but thatthe long filled distance is overestimated. Second, in Table II. , whichrepresents the judgments when the contacts were made successively, thetendency to underestimate the short distance is less, and at the sametime we notice a more pronounced overestimation of the longer filleddistances. I shall give a further explanation of these results inconnection with later tables. 

TABLE I. 

 4 cm. 6 cm. 8 cm. Filled. Open. Filled. Open. Filled. Open. 

 F. 5. 3 4. 7 7. 8 7. 6 9. 3 10. 5 F. 5. 7 4. 4 6. 5 7. 3 9. 2 11. 7 F. 6. 0 5. 6 8. 2 7. 3 8. 7 10. 8 --- --- --- --- --- ---- Av. 5. 7 4. 9 7. 5 7. 4 9. 1 11. 0

 R. 5. 7 5. 1 6. 7 6. 8 9. 3 10. 2 R. 5. 4 5. 4 7. 2 7. 1 8. 5 10. 7 R. 4. 6 4. 2 8. 1 8. 1 9. 1 11. 4 --- --- --- --- --- ---- Av. 5. 2 4. 9 7. 3 7. 3 9. 0 10. 8

 K. 5. 6 5. 1 6. 8 6. 7 8. 1 9. 6 K. 5. 0 5. 1 7. 3 7. 5 8. 2 11. 2 K. 4. 9 4. 9 8. 2 8. 1 10. 1 10. 1 --- --- --- --- ---- ---- Av. 5. 2 5. 0 7. 4 7. 4 8. 8 10. 3

TABLE II. 

 4 cm. 6 cm. 8 cm. Filled. Open. Filled. Open. Filled. Open. 

 F. 5. 1 5. 0 8. 0 8. 3 9. 2 10. 3 F. 5. 8 4. 7 7. 2 7. 9 8. 7 10. 9 F. 5. 6 5. 5 6. 9 9. 1 9. 1 11. 1 --- --- --- --- --- ---- Av. 5. 5 5. 1 7. 4 8. 4 9. 0 10. 8

 R. 6. 0 4. 8 8. 2 7. 5 9. 4 10. 6 R. 5. 7 5. 4 6. 5 7. 4 10. 1 9. 4 R. 5. 0 5. 2 7. 7 7. 8 8. 6 11. 2 --- --- --- --- ---- ---- Av. 5. 6 5. 1 7. 5 7. 6 9. 4 10. 4

 K. 4. 8 4. 8 8. 2 8. 3 8. 1 9. 8 K. 5. 1 5. 3 7. 1 7. 7 10. 0 10. 8 K. 4. 7 5. 0 8. 1 8. 6 8. 6 9. 4 --- --- --- --- ---- ---- Av. 4. 9 5. 0 7. 8 8. 2 8. 9 10. 0

 The first two numbers in the first line signify that when an open distance of 4 cm. Was taken, an adjacent open distance of 4. 7 cm. Was judged equal; but when the adjacent space was filled, 5. 3 cm. Was judged equal. Each number in the column of filled distances represents an average of five judgments. All of the contacts in Table I. Were made simultaneously; in Table II. They were made successively. 

In the next series of experiments the illusion was approached from anentirely different point of view. The two points representing the openspace were given on one arm, and the filled space on a symmetricalpart of the other arm. I was now able to use a much wider range ofdistances, and made many variations in the weights of the points andthe number that were taken for the filled distance. 

However, before I began this second series, in which one of the chiefvariations was to be in the weights of the different points, I made abrief preliminary series of experiments to determine in a general waythe influence of pressure on judgments of point distances. Only threedistances were employed, four, six and twelve centimeters, and threeweights, twelve, twenty and forty grams. Table III. Shows that, forthree men who were to serve as subjects in the main experiments thatare to follow, an increase in the weight of the points was almostalways accompanied by an increase in the apparent distance. 

TABLE III. 

 Distances. 4 cm. 6 cm. 12 cm. 

 Weights (Grams). 12 20 40 12 20 40 12 20 40

 R. 3. 9 3. 2 3. 0 6. 2 5. 6 5. 3 11. 4 10. 4 9. 3 F. 4. 3 4. 0 3. 6 6. 1 5. 3 5. 5 12. 3 11. 6 10. 8 B. 4. 1 3. 6 3. 1 6. 0 5. 7 5. 8 12. 0 10. 2 9. 4 P. 4. 3 4. 1 3. 7 5. 9 5. 6 5. 6 13. 1 11. 9 10. 7

 In the standard distances the points were each weighted to 6 grams. The first three figures signify that a two-point distance of 4 cm. , each point weighing 6 grams, was judged equal to 3. 9 cm. When each point weighed 12 grams. 3. 2 cm. When each point weighed 20 grams, etc. Each figure is the average of five judgments. 

Now the application of this principle in my criticism of Parrish'sexperiments, and as anticipating the direction which the followingexperiments will take, is this: if we take a block such as Parrishused, with only two points in it, and weight it with forty grams inapplying it to the skin, it is plain that each point will receive onehalf of the whole pressure, or twenty grams. But if we put a pressureof forty grams upon a block of eight points, each point will receiveonly one eighth of the forty, or five grams. Thus, in the case of thefilled space, the end points, which play the most important part inthe judgment of the distance, have each only five grams' pressure, while the points in the open space have each twenty grams. We should, therefore, naturally expect that the open space would beoverestimated, because of the decided increase of pressure at thesesignificant points. Parrish should have subjected the blocks, not tothe same pressure, but to a pressure proportional to the number ofpoints in each block. With my apparatus, I was easily able to provethe correctness of my position here. It will be seen in Tables IV. ToVIII. That, when the sum of the weights of the two end points in theopen space was only just equal to the sum of the weights of all thepoints in the filled space, the filled space was underestimated justas Parrish has reported. But when the points were all of the sameweight, both in the filled and the open space, the filled space wasjudged longer in all but the very short distances. For this latterexception I shall offer an explanation presently. 

Having now given an account of the results of this digression intoexperiments to determine the influence of pressure upon pointdistances, I shall pass to the second series of experiments on theillusion in question. In this series, as has been already stated, thefilled space was taken on one arm and the open on the other, and thenthe process was reversed in order to eliminate any error arising froma lack of symmetry between the two regions. Without, for the present, going into a detailed explanation of the statistics of this secondseries of experiments, which are recorded in Tables IV. , V. , VI. , VII. And VIII. , I may summarize the salient results into these generalconclusions: First, the short filled distance is underestimated;second, this underestimation of the filled space gradually decreasesuntil in the case of the filled distance of 18 cm. The judgments passover into pronounced overestimations; third, an increase in the numberof points of contact in the shorter distances increases theunderestimation, while an increase in the number of points in thelonger distance increases the overestimation; fourth, an increase ofpressure causes an invariable increase in the apparent length ofspace. If a general average were made of the results given in TablesIV. , V. , VI. , VII. And VIII. , there would be a preponderance ofevidence for the conclusion that the filled spaces are overestimated. But we cannot ignore the marked tendencies in the opposite directionfor the long and the short distances. These anomalous results, which, it will be remembered, were also found in our first series, call forexplanation. Several hypotheses were framed to explain thesefluctuations in the illusion, and then some shorter series ofexperiments were made in different directions with as large a numberof variations in the conditions as possible, in the hope ofdiscovering the disturbing factors. 

TABLE IV. ¹

 4 Centimeters. 

 A B D E less = gr. Less = gr. Less = gr. Less = gr. R. (a) 7 2 1 8 1 1 6 2 2 5 1 4 (b) 7 3 0 7 1 2 6 2 2 6 1 3 F. (a) 6 3 1 7 1 2 7 0 3 6 0 4 (b) 7 0 3 9 1 0 6 1 3 5 2 3 ------- -------- -------- -------- 27 8 5 31 4 5 25 5 10 22 4 14

 ¹In columns _A_, _B_, and _C_ the filled spaces were made up of 4, 5 and 6 points, respectively. The total weight of the filled space in _A_, _B_ and _C_ was always just equal to the weight of the two points in the open space, 20 gr. In (_a_) the filled distance was given on the right arm first, in (_b_) on the left arm. It will be observed that this reversal made practically no difference in the judgments and therefore was sometimes omitted. In _D_ the filled space consisted of four points, but here the weight of each point was 10 gr. , making a total weight of 40 gr. For the filled space, as against 20 gr. For the open space. In _E_ the weight of each was 20 gr. , making the total weight of the filled space 80 gr. 

TABLE V. 

 6 Centimeters. 

 A B C D E less = gr. Less = gr. Less = gr. Less = gr. Less = gr. R. (a) 10 8 2 12 0 8 14 6 0 9 6 5 8 2 10 F. (a) 12 4 4 12 6 2 12 4 4 8 3 9 6 3 11 K. (a) 10 2 8 12 6 2 14 2 4 6 4 10 7 2 11 -------- -------- -------- -------- -------- 32 14 14 36 12 12 40 12 8 23 13 24 21 7 32

TABLE VI. 

 8 Centimeters. 

 A B C D E less = gr. Less = gr. Less = gr. Less = gr. Less = gr. R. (a) 4 1 5 5 1 4 7 0 3 4 0 6 3 0 7 (b) 4 0 6 5 1 4 6 1 3 4 1 5 2 1 7 F. (a) 5 0 5 5 0 5 6 0 4 3 0 7 4 0 6 (b) 5 1 4 6 1 3 8 0 2 4 1 5 2 3 5 K. (a) 4 1 5 6 1 3 7 1 2 3 2 5 1 3 6 (b) 4 0 6 7 0 3 6 1 3 4 0 6 3 0 7 ------- ------- ------- ------- ------- 26 3 31 34 4 22 40 3 17 22 4 34 15 7 38

TABLE VII. 

 12 Centimeters. 

 A B C D E less = gr. Less = gr. Less = gr. Less = gr. Less = gr. R. (a) 3 6 16 8 3 14 10 8 7 6 3 16 3 4 18 F. (a) 5 7 13 10 5 10 9 6 10 6 4 15 5 1 19 K. (a) 8 2 15 8 4 13 13 9 3 3 7 15 3 0 22 -------- -------- ------- -------- --------- 16 15 44 26 12 37 32 23 20 15 14 46 11 5 59

TABLE VIII. 

 18 Centimeters. 

 A B C D E less = gr. Less = gr. Less = gr. Less = gr. Less = gr. R. (a) 2 0 23 0 0 25 4 4 17 3 1 21 0 1 24 (b) 3 1 21 1 0 24 5 3 17 1 6 18 0 2 23 F. (a) 1 4 20 3 0 22 8 6 11 0 5 20 2 0 23 (b) 2 3 20 2 1 22 6 7 12 1 4 20 0 3 22 K. (a) 4 2 19 4 0 21 2 7 16 0 7 18 0 0 25 (b) 1 0 24 2 6 17 8 0 17 2 6 17 1 0 24 -------- -------- -------- -------- -------- 13 10 127 12 7 131 33 27 90 7 29 114 3 6 141

TABLES IV. -VIII. 

The first line in column _A_ (Table IV. ) signifies that out of 10judgments, comparing an open space 4 cm. , total weight 20 gr. , with afilled space of 4 points, total weight also 20 gr. , the filled spacewas judged less 7 times, equal 2 times, and greater once. 

III. 

The results of the investigation, thus far, point to the conclusionthat short filled spaces are underestimated, that long spaces areoverestimated, and that between the two there lies what might becalled an 'indifference zone. ' This unexpected outcome explains, Ithink, the divergent opinions of the earlier investigators of thisproblem. Each theory is right in what it affirms, but wrong in what itimplicitly or openly denies. 

I next set out to determine as precisely as possible how far thefactor of fusion, or what Parrish has called irradiation, enters intothe judgments. It was evident from the beginning of this wholeinvestigation that fusion or displacement of the points was verycommon. The term 'irradiation' is, however, too specific a term todescribe a process that works in these two opposite directions. Theprimary concern of these next experiments was, therefore, to devisemeans for preventing fusion among the points before the subjectpronounced his judgment. With our apparatus we were able to make anumber of experiments that show, in an interesting way, the resultsthat follow when the sensations are not permitted to fuse. It is onlythe shorter distances that concern us here. The longer distances havealready been shown to follow the law of optical illusion, that is, that filled space is overestimated. The object of the presentexperiments is to bring the shorter distances under the same law, byshowing, first, that the objective conditions as they have existed inour experiments thus far are not parallel to those which we find inthe optical illusion. Second, that when the objective conditions arethe same, the illusion for the shorter distances follows the law juststated. 

In repeating some of the experiments reported in Tables IV. -VIII. Withvarying conditions, I first tried the plan of using metallic points atthe ends of the spaces. Thus, by an apparent difference in thetemperature between the end points and the filling, the sensationsfrom the end points, which play the most important part in thejudgment of the length, were to a certain extent kept from fusing withthe rest. The figures in Table II. Have already shown what may beexpected when the points are kept from fusing. Here, also, a markedtendency in the direction of apparent lengthening of the distance wasat once observed. These short filled distances, which had before beenunderestimated, were now overestimated. The same results follow whenmetallic points are alternated with hard rubber points in the fillingitself. 

This changing of the apparent temperature of the end points has, itmust be admitted, introduced another factor; and it might be objectedthat it was not so much the prevention of fusion as the change in thetemperature that caused the judgments to drift towards overestimation. I have statistics to show that this observation is in a way just. Extremes in temperature, whether hot or cold, are interpreted as anincrease in the amount of space. This conclusion has also beenreported from a number of other laboratories. My contention at thispoint is simply that there are certain conditions under which thesedistances will be overestimated and that these are the very conditionswhich bring the phenomenon into closer correspondence with the opticalillusion, both as to the stimuli and the subjective experience. Then, aside from this, such an objection will be seen to be quite irrelevantif we bear in mind that when the end points in the filled distancewere replaced by metallic points, metallic points were also employedin the open distance. The temperature factor, therefore, entered intoboth spaces alike. By approaching the problem from still another pointof view, I obtained even more conclusive evidence that it is thefusion of the end points with the adjacent points in the shortdistances that leads to the underestimation of these. I have severalseries in which the end points were prevented from fusing into thefilling, by raising or lowering them in the apparatus, so that theycame in contact with the skin just after or before the intermediatepoints. When the contacts were arranged in this way, the tendency tounderestimate the filled spaces was very much lessened, and with somesubjects the tendency passed over into a decided overestimation. This, it will be seen, is a confirmation of the results in Table II. 

I have already stated that the two series of experiments reported inSection II. Throughout point to the conclusion that an increase ofpressure is taken to mean an increase in the distance. I now carriedon some further experiments with short filled distances, makingvariations in the place at which the pressure was increased. I found amaximum tendency to underestimate when the central points in thefilled space were weighted more than the end points. A strong drift inthe opposite direction was noticed when the end points were heavierthan the intermediate ones. It is not so much the pressure as a whole, as the place at which it is applied, that causes the variations in thejudgments of length. In these experiments the total weights of thepoints were the same in both cases. An increase of the weight on theend points with an equivalent diminution of the weights on theintervening points gave the end points greater distinctness apparentlyand rendered them less likely to disappear from the judgments. 

At this stage in the inquiry as to the cause of the underestimation ofshort distances, I began some auxiliary experiments on the problem ofthe localization of cutaneous impressions, which I hoped would throwlight on the way in which the fusion or displacement that I have justdescribed takes place. These studies in the localization of touchsensations were made partly with a modification of the Jastrowęsthesiometer and partly with an attachment to the apparatus beforedescribed (Fig. 1). In the first case, the arm upon which theimpressions were given was screened from the subject's view, and hemade a record of his judgments on a drawing of the arm. The criticismmade by Pillsbury[6] upon this method of recording the judgments inthe localization of touch sensations will not apply to my experiments, for I was concerned only with the relative, not with the absoluteposition of the points. In the case of the other experiments, a cardwith a single line of numbered points was placed as nearly as possibleover the line along which the contacts had been made on the arm. Thesubject then named those points on the card which seemed directly overthe points which had been touched. 

 [6] Pillsbury, W. B. : Amer. Journ. Of Psy. , 1895, Vol. VII. , p. 42. 

The results from these two methods were practically the same. But thesecond method, although it obviously permitted the determination ofthe displacements in one dimension only, was in the end regarded asthe more reliable method. With this apparatus I could be more certainthat the contacts were made simultaneously, which was soon seen to beof the utmost importance for these particular experiments. Then, too, by means of this ęsthesiometer, all movement of the points after thecontact was made was prevented. This also was an advantage in the useof this apparatus, here and elsewhere, which can hardly beoverestimated. With any ęsthesiometer that is operated directly by thehand, it is impossible to avoid imparting a slight motion to thepoints and thus changing altogether the character of the impression. The importance of this consideration for my work was brought forciblyto my attention in this way. One of the results of these tests wasthat when two simultaneous contacts are made differing in weight, ifonly one is recognized it is invariably located in the region of thecontact with the heavier point. But now if, while the points were incontact with the skin and before the judgment was pronounced, I gavethe lighter point a slight jar, its presence and location were therebyrevealed to the subject. Then, too, it was found to be an advantagethat the judgments were thus confined to the longitudinal displacementonly; for, as I have before insisted, it was the relative, not theabsolute position that I wished to determine, since my object in allthese experiments in localization was to determine what connection, ifany, exists between judgments upon cutaneous distances made indirectlyby means of localization, and judgments that are pronounced directlyupon the subjective experience of the distance. 

In the first of these experiments, in which two points of differentweight were used, the points were always taken safely outside of thethreshold for the discrimination between two points in the particularregion of the skin operated on. An inspection of the results shown inFigs. 2 and 3 will indicate the marked tendency of the heavier pointto attract the lighter. In Figs. 2 and 3 the heavy curves were plottedfrom judgments where both heavy and light points were given together. The dotted curve represents the localization of each point when givenalone. The height of the curves at any particular point is determinedby the number of times a contact was judged to be directly under thatpoint. The fact that the curves are higher over the heavy points showsthat, when two points were taken as one, this one was localized in thevicinity of the heavier point. When points were near the threshold forany region, it will be observed that the two points were attracted toeach other. But when the points were altogether outside the threshold, they seemed strangely to have repelled each other. As this problem laysomewhat away from my main interest here, I did not undertake toinvestigate this peculiar fluctuation exhaustively. My chief purposewas satisfied when I found that the lighter point is displaced towardthe heavier, in short distances. A further explanation of thesefigures will be given in connection with similar figures in the nextsection. 

[Illustration: FIG. 2. Back of hand. ]

[Illustration: FIG. 3. Forearm. ]

This attraction of the heavier for the lighter points is, I think, asufficient explanation for the variations in judgments upon filleddistances where changes are made in the place at which the pressure isapplied. I furthermore believe that an extension of this principleoffers an explanation for the underestimation of cutaneousline-distances, which has been frequently reported from variouslaboratories. Such a straight line gives a subjective impression ofbeing heavier at the center. I found that if the line is slightlyconcave at the center, so as to give the ends greater prominence andthereby leave the subjective impression that the line is uniformthroughout its entire length, the line will be overestimated incomparison with a point distance. Out of one hundred judgments on therelative length of two hard-rubber lines of 5 cm. When pressed againstthe skin, one of which was slightly concave, the concave line wasoverestimated eighty-four times. For sight, a line in which the shadedpart is concentrated at the center appears longer than an objectivelyequal line with the shading massed towards the ends. 

IV. 

In the last section, I gave an account of some experiments in thelocalization of touch sensations which were designed to show how, under varying pressure, the points in the filled distance aredisplaced or fused and disappear entirely from the judgment. Ourearliest experiments, it will be remembered, yielded unmistakableevidence that short, filled distances were underestimated; while allof the secondary experiments reported in the last section have pointedto the conclusion that even these shorter distances will follow thelaw of the longer distances and be overestimated under certainobjective conditions, which conditions are also more nearly parallelwith those which we find in the optical illusion. I wish now to givethe results of another and longer set of experiments in thelocalization of a manifold of touch sensations as we find them in thissame illusion for filled space, by which I hope to prove a directrelation between the function of localization and the spatialfunctioning proper. 

These experiments were made with the same apparatus and method thatwere used in the previous study in localization; but instead of twopoints of different weights, four points of uniform weight wereemployed. This series, therefore, will show from quite another pointof view that the fusion which takes place, even where there is nodifference in the weight, is a very significant factor in judgments ofdistance on the skin. 

[Illustration: Fig. 4. ]

I need hardly say that here, and in all my other experiments, thesubjects were kept as far as possible in complete ignorance of theobject of the experiment. This and the other recognized laboratoryprecautions were carefully observed throughout this work. Fourdistances were used, 4, 8, 12 and 16 cm. At frequent intervalsthroughout the tests the contact was made with only one of the pointsinstead of four. In this way there came to light again the interestingfact which we have already seen in the last section, which is of greatsignificance for my theory--that the end points are locateddifferently when given alone than when they are presentedsimultaneously with the other points. I give a graphic representationof the results obtained from a large number of judgments in Figs. 4, 5and 6. These experiments with filled spaces, like the earlierexperiments, were made on the volar side of the forearm beginning nearthe wrist. In each distance four points were used, equally distributedover the space. The shaded curve, as in the previous figures, represents the results of the attempts to localize the points when allfour were given simultaneously. In the dotted curves, the end pointswere given alone. The height of the curve at any place is determinedby the number of times a point was located immediately underneath thatparticular part of the curve. In Fig. 4 the curve which was determinedby the localization of the four points when given simultaneously, shows by its shape how the points appear massed towards the center. InFig. 5 the curve _AB_ shows, by its crests at _A_ and _B_, that theend points tended to free themselves from the rest in the judgments. But if the distance _AB_ be taken to represent the average of thejudgments upon the filled space 1, 2, 3, 4, it will be seen to beshorter than what may be regarded as the average of the judgments uponthe corresponding open space, namely, the distance _A'B'_, determinedby the localizations of the end points alone. The comparativeregularity of the curve indicates that the subject was unable todiscriminate among the points of the filling with any degree ofcertainty. The localizations were scattered quite uniformly along theline. In these short distances the subject often judged four points astwo, or even one. 

[Illustration: Fig. 5. ]

[Illustration: Fig. 6. ]

Turning to Fig. 6, we notice that the tendency is now to locate theend points in the filled distance outside of the localization of thesesame points when given without the intermediate points. It will alsobe seen from the irregularities in these two longer curves that thereis now a clear-cut tendency to single out the individual points. Thefact that the curves here are again higher over point 4 simplysignifies that at this, the wrist end, the failure to discover thepresence of the points was less frequent than towards the elbow. Butthis does not disturb the relation of the two series of judgments. AsI have before said, the first two sets of experiments described inSection II. Showed that the shorter filled distances areunderestimated, while the longer distances are overestimated, and thatbetween the two there is somewhat of an 'indifferent zone. ' In thoseexperiments the judgments were made directly on the cutaneousdistances themselves. In the experiments the results of which areplotted in these curves, the judgment of distances is indirectlyreached through the function of localization. But it will be observedthat the results are substantially the same. The longer distances areoverestimated and the shorter distances underestimated. The curves inFigs. 4, 5 and 6 were plotted on the combined results for twosubjects. But before the combination was made the two main tendencieswhich I have just mentioned were observed to be the same for bothsubjects. 

It will be remembered also that in these experiments, where thejudgment of distance was based directly on the cutaneous impression, the underestimation of the short, filled distance was lessened andeven turned into an overestimation, by giving greater distinctness tothe end points, in allowing them to come in contact with the skin justbefore or just after the filling. The results here are again the sameas before. The tendency to underestimate is lessened by this device. Whenever, then, a filled space is made up of points which aredistinctly perceived as discrete--and this is shown in the longercurves by the comparative accuracy with which the points arelocated--these spaces are overestimated. 

In all of these experiments on localization, the judgments were givenwith open eyes, by naming the visual points under which the tactualpoints seemed to lie. I have already spoken of the other method whichI also employed. This consisted in marking points on paper whichseemed to correspond in number and position to the points on the skin. During this process the eyes were kept closed. This may appear to be avery crude way of getting at the illusion, but from a large number ofjudgments which show a surprising consistency I received the emphaticconfirmation of my previous conclusion, that filled spaces wereoverestimated. These experiments were valuable also from the fact thathere the cutaneous space was estimated by the muscle sense, or activetouch, as it is called. 

In the experiments so far described the filling in of the closed spacewas always made by means of stationary points. I shall now give abrief account of some experiments which I regard as very important forthe theory that I shall advance later. Here the filling was made bymeans of a point drawn over the skin from one end of a two-pointdistance to the other. 

These experiments were made on four different parts of the skin--theforehead, the back of the hand, the abdomen, and the leg between theknee and the thigh. I here forsook the plan which I had followedalmost exclusively hitherto, that of comparing the cutaneous distanceswith each other directly. The judgments now were secured indirectlythrough the medium of visual distances. There was placed before thesubject a gray card, upon which were put a series of two-pointdistances ranging from 2 to 20 cm. The two-point distances were givenon the skin, and the subject then selected from the optical distancesthe one that appeared equal to the cutaneous distance. This processfurnished the judgments on open spaces. For the filled spaces, immediately after the two-point distance was given a blunt stylus wasdrawn from one point to the other, and the subject then again selectedthe optical distance which seemed equal to this distance filled by themoving point. 

The results from these experiments point very plainly in onedirection. I have therefore thought it unnecessary to go into anyfurther detail with them than to state that for all subjects and forall regions of the skin the filled spaces were overestimated. Thisoverestimation varied also with the rate of speed at which the styluswas moved. The overestimation is greatest where the motion is slowest. 

Vierordt[7] found the same result in his studies on the time sense, that is, that the more rapid the movement, the shorter the distanceseems. But lines drawn on the skin are, according to him, underestimated in comparison with open two-point distances. Fechner[8]also reported that a line drawn on the skin is judged shorter than thedistance between two points which are merely touched. It will benoticed, however, that my experiments differed from those of Vierordtand Fechner in one essential respect. This difference, I think, issufficient to explain the different results. In my experiments thetwo-point distance was held on the skin, while the stylus was movedfrom one point to the other. In their experiments the line was drawnwithout the points. This of course changes the objective conditions. In simply drawing a line on the skin the subject rapidly loses sightof the starting point of the movement. It follows, as it were, themoving point, and hence the entire distance is underestimated. I madea small number of tests of this kind, and found that the line seemedshorter than the point distance as Fechner and Vierordt declared. Butwhen the point distance is kept on the skin while the stylus is beingdrawn, the filling is allowed its full effect in the judgment, inasmuch as the end points are perceived as stationary landmarks. Thesubjects at first found some difficulty in withholding their judgmentsuntil the movement was completed. Some subjects declared that theyfrequently made a preliminary judgment before the filling wasinserted, but that when the moving point approached the end point, they had distinctly the experience that the distance was widening. Inthese experiments I used five sorts of motion, quick and heavy, quickand light, slow and heavy, slow and light, and interrupted. I made noattempt to determine either the exact amount of pressure or the exactrate. I aimed simply at securing pronounced extremes. The slow ratewas approximately 3, and the fast approximately 15 cm. Per second. 

 [7] 'Zeitsinn, ' Tübingen, 1858. 

 [8] Fechner, G. Th. , 'Elem. D. Psychophysik, ' Leipzig, 1889; 2. Theil, S. 328. 

I have already said that these filled spaces were invariablyoverestimated and that the slower the movement, the greater, ingeneral, is the overestimation. In addition to the facts just stated Ifound also, what Hall and Donaldson[9] discovered, that an increase inthe pressure of a moving point diminishes the apparent distance. 

 [9] Hall, G. St. , and Donaldson, H. H. , 'Motor Sensations on the Skin, ' _Mind_, 1885, X. , p. 557. 

Nichols, [10] however, says that heavy movements seem longer and lightones shorter. 

 [10] _Op. Citat. , _ p. 98. 

V. 

There are several important matters which might properly have beenmentioned in an earlier part of this paper, in connection with theexperiments to which they relate, but which I have designedly omitted, in order not to disturb the continuity in the development of thecentral object of the research. The first of these is the question ofthe influence of visualization on the judgments of cutaneousdistances. This is in many ways a most important question, andconfronts one who is making studies in tactual space everywhere. Thereader may have already noticed that I have said but little about thefactor of visualization in any of my experiments, and may haveregarded it as a serious omission. It might be offered as a criticismof my work that the fact that I found the tactual illusions to existin the same sense as the optical illusions was perhaps due to thefailure to exclude visualization. All of the subjects declare thatthey were unable to shut out the influence of visualizing entirely. Some of the subjects who were very good visualizers found the habitespecially insistent. I think, however, that not even in these lattercases does this factor at all vitiate my conclusions. 

It will be remembered that the experiments up to this time fall intotwo groups, first, those in which the judgments on the cutaneousdistances were reached by direct comparisons of the sensationsthemselves; and secondly, those in which the sensations were firstlocalized and then the judgment of the distance read from theselocalizations. Visualizing, therefore, entered very differently intothe two groups. In the first instance all of the judgments were madewith the eyes closed, while all of the localizations were made withthe eyes open. I was uncertain through the whole of the first group ofexperiments as to just how much disturbance was being caused in theestimation of the distance by visualizing. I therefore made a seriesof experiments to determine what effect was produced upon the illusionif in the one set of judgments one purposely visualized and in theother excluded visualizing as far as possible. In my own case I foundthat after some practice I could give very consistent judgments, inwhich I felt that I had abstracted from the visualized image of thearm almost entirely. I did not examine these results until the closeof the series, and then found that the illusion was greater for thosejudgments in which visualization was excluded; that is, the filledspace seemed much larger when the judgment was made without the helpof visualization. It is evident, therefore, that the tactual illusionis influenced rather in a negative direction by visualization. 

In the second group of experiments, where the judgments were obtainedthrough the localization of the points, it would seem, at first sight, that the judgments must have been very largely influenced by thedirect vision used in localizing the points. The subject, as will beremembered, looked down at a card of numbered points and named thosewhich were directly over the contacts beneath. Here it should seemthat the optical illusion of the overestimation of filled spaces, filled with points on the card, would be directly transmitted to thesensation on the skin underneath. Such criticism on this method ofgetting at the illusion has already been made orally to me. But thisis obviously a mistaken objection. The points on the card make afilled space, which of course appears larger, but as the pointsexpand, the numbers which are attached to them expand likewise, andthe optical illusion has plainly no influence whatever upon thetactual illusion. 

A really serious objection to this indirect method of approaching theillusion is, that the character of the cutaneous sensation is never sodistinctly perceived when the eyes are open as when they are closed. Several subjects often found it necessary to close their eyes first, in order to get a clear perception of the locality of the points;they then opened their eyes, to name the visual points directly above. Some subjects even complained that when they opened their eyes theylost track of the exact location of the touch points, which theyseemed to have when their eyes were closed. The tactual impressionseems to be lost in the presence of active vision. 

On the whole, then, I feel quite sure in concluding that theoverestimation of the filled cutaneous spaces is not traceable to theinfluence of visualization. Parrish has explained all sporadic casesof overestimation as due to the optical illusion carried over invisualization. I have already shown that in my experimentsvisualization has really the opposite effect. In Parrish's experimentsthe overestimation occurred in the case of those collections of pointswhich were so arranged as to allow the greatest differentiation amongthe points, and especially where the end-points were more or lessdistinct from the rest. This, according to my theory, is preciselywhat one would expect. 

Those who have made quantitative studies in the optical illusion, especially in this particular illusion for open and filled spaces, have observed and commented on the instability of the illusion. Auerbach[11] says, in his investigation of the quantitative variationsof the illusion, that concentration of attention diminishes theillusion. In the Zöllner figure, for instance, I have been able tonotice the illusion fluctuate through a wide range, withouteye-movements and without definitely attending to any point, duringthe fluctuation of the attention. My experiments with the tactualillusion have led me to the conclusion that it fluctuates even morethan the optical illusion. Any deliberation in the judgment causes theapparent size of the filled space to shrink. The judgments that aregiven most rapidly and naļvely exhibit the strongest tendency tooverestimation; and yet these judgments are so consistent as toexclude them from the category of guesses. 

 [11] Auerbach, F. , _Zeitsch. F. Psych. U. Phys. D. Sinnesorgane_, 1874, Bd. VII. , S. 152. 

In most of my experiments, however, I did not insist on rapid andnaļve judgments; but by a close observation of the subject as he wasabout to make a judgment I could tell quite plainly which judgmentswere spontaneous and which were deliberate. By keeping track of thesewith a system of marks, I was able to collect them in the end intogroups representing fairly well the different degrees of attention. The illusion is always greatest for the group of spontaneousjudgments, which points to the conclusion that all illusions, tactualas well as visual, are very largely a function of attention. 

In Section II. I told of my attempt to reproduce the optical illusionupon the skin in the same form in which we find it for sight, namely, by presenting the open and filled spaces simultaneously, so that theymight be held in a unitary grasp of consciousness and the judgmentpronounced on the relative length of these parts of a whole. However, as I have already said, the filled space appears longer, not only whengiven simultaneously, but also when given successively with the openspace. In the case of the optical illusion I am not so sure that theillusion does not exist if the two spaces are not presentedsimultaneously and adjacent, as Münsterberg asserts. Although, to besure, for me the illusion is not so strong when an interval is allowedbetween the two spaces, I was interested to know whether this was truealso in the case of a touch illusion. My previous tables did notenable me to compare the quantitative extent of the illusion forsuccessive and simultaneous presentation. But I found in two serieswhich had this point directly in view, one with the subject _F_ andone in which _G_ served as subject, that the illusion was emphaticallystronger when the open and filled spaces were presented simultaneouslyand adjacent. In this instance, the illusion was doubtless acombination of two illusions--a shrinking of the open space, on theone hand, and a lengthening of the filled space on the other hand. Binet says, in his studies on the well-known Müller-Lyer illusion, that he believes the illusion, in its highest effects at any rate, tobe due to a double contrast illusion. 

This distortion of contrasted distances I have found in more than onecase in this investigation--not only in the case of distances in whichthere is a qualitative difference, but also in the case of two opendistances. In one experiment, in which open distances on the skin werecompared with optical point distances, a distance of 10 cm. Was givenfifty times in connection with a distance of 15 cm. , and fifty timesin connection with a distance of 5 cm. In the former instance thedistance of 10 cm. Was underestimated, and in the other it wasoverestimated. 

The general conclusion of the entire investigation thus far may besummed up in the statement: _Wherever the objective conditions are thesame in the two senses, the illusion exists in the same direction forboth sight and touch. _

VI. 

Thus far all of my experiments were made with _passive_ touch. Iintend now to pursue this problem of the relation between theillusions of sight and touch into the region of _active_ touch. I haveyielded somewhat to the current fashion in thus separating the passivefrom the active touch in this discussion. I have already said that Ibelieve it would be better not to make this distinction so pronounced. Here again I have concerned myself primarily with only one illusion, the illusion which deals with open and filled spaces. This is theillusion to which Dresslar[12] devoted a considerable portion of hisessay on the 'Psychology of Touch, ' and which he erroneously thoughtto be the counterpart of the optical illusion for open and filledspaces. One of the earliest notices of this illusion is that given byJames, [13] who says, "Divide a line on paper into two equal halves, puncture the extremities, and make punctures all along one of thehalves; then, with the finger-tip on the opposite side of the paper, follow the line of punctures; the empty half will seem much longerthan the punctured half. "

 [12] Dresslar, F. B. , _Am. Journ. Of Psy. _, 1894, VI. , p. 313. 

 [13] James, W. , 'Principles of Psychology, ' New York, 1893, II. , p. 250. 

James has given no detailed account of his experiments. He does nottell us how many tests were made, nor how long the lines were, norwhether the illusion was the same when the open half was presentedfirst. Dresslar took these important questions into consideration, andarrived at a conclusion directly opposite to that of James, namely, that the filled half of the line appears larger than the open half. Dresslar's conclusion is, therefore, that sight and touch functionalike. I have already said that I think that Parrish was entirelyright in saying that this is not the analogue of the familiar opticalillusion. Nevertheless, I felt sure that it would be quite worth thewhile to make a more extensive study than that which Dresslar hasreported. Others besides James and Dresslar have experimented withthis illusion. As in the case of the illusion for passive touch, thereare not wanting champions of both opinions as to the direction inwhich this illusion lies. 

I may say in advance of the account of my experiments, that I havehere also found a ground of reconciliation for these two divergentopinions. Just as in the case of the illusion for passive touch, thereare here also certain conditions under which the filled space seemslonger, and other conditions under which it appears shorter than theopen space. I feel warranted, therefore, in giving in some detail myresearch on this illusion, which again has been an extended one. Ithink that the results of this study are equally important with thosefor passive touch, because of the further light which they throw onthe way in which our touch sense functions in the perception of thegeometrical illusions. Dresslar's experiments, like those of James, were made with cards in which one half was filled with punctures. Thenumber of punctures in each centimeter varied with the differentcards. Dresslar's conclusion was not only that the filled space isoverestimated, but also that the overestimation varies, in a generalway, with the number of punctures in the filling. Up to a certainpoint, the more holes there are in the card, the longer the spaceappears. 

I had at the onset of the present experiment the same feeling aboutDresslar's work that I had about Parrish's work, which I have alreadycriticised, namely, that a large number of experiments, in which manyvariations were introduced, would bring to light facts that wouldexplain the variety of opinion that had hitherto been expressed. I wasconfident, however, that what was most needed was a quantitativedetermination of the illusion. Then, too, inasmuch as the illusion, whatever direction it takes, is certainly due to some sort ofqualitative differences in the two kinds of touch sensations, thosefrom the punctured, and those from the smooth half, it seemedespecially desirable to introduce as many changes into the nature ofthe filling as possible. The punctured cards I found veryunsatisfactory, because they rapidly wear off, and thus change thequality of the sensations, even from judgment to judgment. 

[Illustration: FIG. 7. ]

The first piece of apparatus that I used in the investigation of theillusion for open and filled space with active touch is shown in Fig. 7. A thimble _A_, in which the finger was carried, moved freely alongthe rod _B_. The filled spaces were produced by rows of tacks on theroller _C_. By turning the roller, different kinds of fillings werebrought into contact with the finger-tip. The paper _D_, on which thejudgments were recorded by the subject, could be slowly advanced underthe roller _E_. Underneath the thimble carrier there was a pin soarranged that, by a slight depression of the finger, a mark was madeon the record paper beneath. A typical judgment was made as follows;the subject inserted his finger in the thimble, slightly depressed thecarrier to record the starting points, then brought his finger-tipinto contact with the first point in the filled space. The subjectwas, of course, all the while ignorant of the length or character ofthe filling over which he was about to pass. The finger-tip was thendrawn along the points, and out over the smooth surface of the roller, until the open space passed over was judged equal to the filled space. Another slight depression of the finger registered the judgment on thepaper below. The paper was then moved forward by turning the roller_E_, and, if desired, a different row of pins was put in place forjudgment by revolving the roller _C_. The dividing line between theopen and filled spaces was continuously recorded on the paper frombelow by a pin not shown in the illustration. 

The rollers, of which I had three, were easily removed or turnedabout, so that the open space was presented first. In one of thedistances on each roller both spaces were unfilled. This was used atfrequent intervals in each series and served somewhat the same purposeas reversing the order in which the open and filled spaces werepresented. With some subjects this was the only safe way of securingaccurate results. The absolute distances measured off were not alwaysa sure criterion as to whether the filled space was under-oroverestimated. For example, one rather erratic subject, who was, however, very constant in his erratic judgments, as an average offifty judgments declared a filled space of 4 cm. To be equal to anopen space of 3. 7 cm. This would seem, on the surface, to mean thatthe filled space had been underestimated. But with these fiftyjudgments there were alternated judgments on two open spaces, in whichthe first open space was judged equal to the second open space of 3. 2cm. From this it is obvious that the effect of the filling was tocause an overestimation--not underestimation as seemed at first sightto be the case. 

In another instance, this same subject judged a filled space of 12. 0cm. To be equal to an open space of 12. 9 cm. , which would seem toindicate an overestimation of the filled space. But an average of thejudgments on two open spaces that were given in alternation shows thatan equivalence was set up between the two at 13. 7 cm. For the secondopen space. This would show that the filling of a space reallyproduced an underestimation. 

The same results were obtained from other subjects. In my experimentson the illusion for passive touch, I pointed out that it is unsafe todraw any conclusion from a judgment of comparison between open andfilled cutaneous spaces, unless we had previously determined whatmight be called a standard judgment of comparison between two openspaces. The parts of our muscular space are quite as unsymmetrical asthe parts of our skin space. The difficulties arising from this lackof symmetry can best be eliminated by introducing at frequentintervals judgments on two open spaces. As I shall try to show later, the psychological character of the judgment is entirely changed byreversing the order in which the spaces are presented, and we cannotin this way eliminate the errors due to fluctuations of the attention. 

The apparatus which I used in these first experiments possessesseveral manifest advantages. Chief among these was the rapidity withwhich large numbers of judgments could be gathered and automaticallyrecorded. Then, in long distances, when the open space was presentedfirst, the subject found no difficulty in striking the first point ofthe filled space. Dresslar mentioned this as one reason why in hisexperiments he could not safely use long distances. His subjectscomplained of an anxious straining of the attention in their effortsto meet the first point of the filled space. 

There are two defects manifest in this apparatus. In the first place, the other tactual sensations that arise from contact with the thimbleand from the friction with the carrier moving along the sliding rodcannot be disregarded as unimportant factors in the judgments. Secondly, there is obviously a difference between a judgment that ismade by the subject's stopping when he reaches a point which seems tohim to measure off equal spaces, and a judgment that is made bysweeping the finger over a card, as in Dresslar's experiments, with auniform motion, and then, after the movement has ceased, pronouncingjudgment upon the relative lengths of the two spaces. In the formercase the subject moves his finger uniformly until he approaches theregion of equality, and then slackens his speed and slowly comes to astandstill. This of course changes the character of the judgments. Both of these defects I remedied in another apparatus which will bedescribed later. For my present purpose I may disregard theseobjections, as they affect alike all the judgments. 

In making the tests for the first series, the subject removed hisfinger after each judgment, so that the position of the apparatuscould be changed and the subject made to enter upon the new judgmentwithout knowing either the approximate length or the nature of thefilling of this new test. With this apparatus no attempt was made todiscover the effects of introducing changes in the rate of speed. Theonly requirement was that the motion should be uniform. This does notmean that I disregarded the factor of speed. On the contrary, this_time_ element I consider as of the highest consequence in the wholeof the present investigation. But I soon discovered, in theseexperiments, that the subjects themselves varied the rate of speedfrom judgment to judgment over a wide range of rates. There was nodifficulty in keeping track of these variations, by recording thejudgments under three groups, fast, slow and medium. But I found thatI could do this more conveniently with another apparatus, and willtell at a later place of the results of introducing a time element. Inthese first experiments the subject was allowed to use any rate ofspeed which was convenient to him. 

TABLE IX. 

 Subjects P R F Rr 2= 3. 8 3. 6 2. 9 2. 8 3= 4. 1 4. 1 4. 2 3. 9 4= 4. 7 5. 1 4. 3 4. 3 Filled 5= 5. 2 5. 6 5. 8 6. 0 Spaces. 6= 6. 0 6. 3 6. 4 5. 2 7= 6. 8 6. 5 6. 6 7. 0 8= 7. 5 7. 6 7. 2 7. 4 9= 8. 3 8. 1 8. 2 8. 6 10= 8. 9 9. 1 8. 7 8. 5

TABLE X. 

 Subjects P R F Rr 2= 4. 0 3. 8 3. 2 2. 6 3= 4. 3 4. 2 4. 4 3. 6 4= 4. 6 5. 6 4. 6 4. 8 Filled 5= 5. 4 6. 1 5. 6 5. 7 Spaces. 6= 6. 2 6. 4 6. 8 6. 9 7= 7. 3 6. 8 7. 9 7. 2 8= 7. 8 7. 4 7. 3 7. 8 9= 8. 6 8. 0 7. 9 8. 9 10= 9. 3 9. 1 8. 9 8. 5

TABLES IX. AND X. 

 First line reads: 'When the finger-tip was drawn over a filled distance of 2 cm. , the subject _P_ measured off 3. 8 on the open surface, the subject _R_ 3. 6, etc. ' Each number is the average of five judgments. In Table IX. The points were set at regular intervals. In Table X. The filling was made irregular by having some points rougher than the others and set at different intervals. 

I can give here only a very brief summary of the results with thisapparatus. In Tables IX. And X. I give a few of the figures which willshow the tendency of the experiments. In these tests a differentlength and a different filling were given for each judgment. Theresult of the experiments of this group is, first, that the _shorterfilled spaces are judged longer and the longer spaces shorter_ thanthey really were. Second, that an increase in the number of points inthe filled space causes no perceptible change in the apparent length. Third, that when the filling is so arranged as to produce a tactualrhythm by changing the position or size of every third point, theapparent length of the space is increased. It will be noticed, also, that this is just the reverse of the result that was obtained forpassive touch. These facts, which were completely borne out by severalother experiments with different apparatus which I shall describelater, furnish again a reason why different investigators havehitherto reported the illusion to exist, now in one direction, now inthe other. Dresslar drew the conclusion from his experiments that thefilled spaces are always overestimated, but at the same time hisfigures show an increasing tendency towards an underestimation of thefilled spaces as the distances increased in length. I shall later, inconnection with similar results from other experiments on thisillusion, endeavor to explain these anomalous facts. 

In section IV. I mentioned the fact that I found the illusion forpassive touch to be subject to large fluctuations. This is true alsoof the illusion for active touch. When the finger-tip is drawn overthe filled, and then out over the open space, the limits between whichthe stopping point varies is a much wider range than when thefinger-tip is drawn over two open spaces. In the latter case I foundthe variation to follow Weber's Law in a general way. At first Ithought these erratic judgments were mere guesses on the part of thesubject; but I soon discovered a certain consistency in the midst ofthese extreme fluctuations. To show what I mean, I have plotted somediagrams based on a few of the results for three subjects. Thesediagrams are found in Fig. 8. It will be observed that the curve whichrepresents the collection of stopping points is shorter and higherwhere the judgments were on two open spaces. This shows plainly agreater accuracy in the judgments than when the judgments were on afilled and an open space, where the curves are seen to be longer andflatter. This fluctuation in the illusion becomes important in thetheoretical part of my discussion, and, at the risk of apparentlyemphasizing unduly an insignificant matter, I have given in Fig. 9 anexact copy of a sheet of judgments as it came from the apparatus. Thisshows plainly how the illusion wears away with practice, when onedistance is given several times in succession. The subject was allowedto give his judgment on the same distance ten times before passing toanother. A glance at the diagram will show how pronounced the illusionis at first, and how it then disappears, and the judgment settles downto a uniform degree of accuracy. It will be seen that the short filledspace is at first overestimated, and then, with the succeedingjudgments, this overestimation is gradually reduced. In the case ofthe longer filled distances (which could not be convenientlyreproduced here) the spaces were at first underestimated, and thenthis underestimation slowly decreased. 

[Illustration: FIG. 8. ]

[Illustration: FIG. 9. ]

None of the qualitative studies that have hitherto been made on thisillusion have brought to light this significant wearing away of theillusion. 

VII. 

I have already spoken of the defects of the apparatus with which theexperiments of the previous chapter were made. I shall now give anaccount of some experiments that were made with an apparatus designedto overcome these difficulties. This is shown in Fig. 10. The block_C_ was clamped to a table, while the block _A_ could be moved backand forth by the lever _B_, in order to bring up different lengths offilled space for judgment. For each judgment the subject brought hisfinger back to the strip _D_, and by moving his finger up along theedge of this strip he always came into contact with the first point ofthe new distance. The lever was not used in the present experiment;but in later experiments, where the points were moved under the fingertip, which was held stationary, this lever was very useful inproducing different rates of speed. In one series of experiments withthis apparatus the filled spaces were presented first, and in anotherseries the open spaces were presented first. In the previousexperiments, so far as I have reported them, the filled spaces werealways presented first. 

[Illustration: FIG. 10. ]

In order to enable the subject to make proper connections with thefirst point in the filled space, when the open space was presentedfirst, a slight depression was put in the smooth surface. Thisdepression amounted merely to the suggestion of a groove, but itsufficed to guide the finger. 

The general results of the first series of experiments with thisapparatus were similar to those already given, but were based on avery much larger number of judgments. They show at once that the shortfilled spaces are overestimated, while the longer spaces areunderestimated. The uniformity of this law has seemed to me one of themost significant results of this entire investigation. In the resultsalready reported from the experiments with the former apparatus, Ihave mentioned the fact that the judgments upon the distancesfluctuate more widely when one is filled and the other open, than whenboth are open. This fluctuation appeared again in a pronounced way inthe present experiments. I now set about to discover the cause of thisvariation, which was so evidently outside of the limits of Weber'slaw. 

TABLE XI. 

 I. II. Subjects. R. B. A. R. B. A. 2= 3. 1 3. 2 3. 7 2. 7 2. 5 3. 1 3= 4. 5 4. 4 4. 1 4. 1 4. 0 3. 6 4= 5. 3 5. 0 4. 3 4. 2 4. 6 4. 6 5= 6. 0 5. 1 5. 8 5. 9 5. 2 4. 3 6= 6. 8 5. 6 6. 2 6. 9 5. 3 6. 0 7= 7. 4 7. 2 6. 9 7. 6 7. 3 6. 8 8= 8. 1 8. 4 7. 3 8. 3 9. 7 7. 8 9= 9. 3 9. 0 8. 5 9. 5 8. 9 8. 7 Filled 10= 10. 1 10. 0 8. 1 10. 3 10. 0 9. 2 Spaces. 11= 10. 5 9. 3 9. 7 10. 6 8. 7 9. 6 12= 11. 7 10. 6 10. 6 11. 8 9. 7 10. 2 13= 12. 3 10. 9 10. 9 11. 1 10. 2 9. 6 14= 12. 2 11. 5 12. 2 10. 4 9. 6 11. 3 15= 13. 6 12. 3 11. 9 13. 1 10. 1 9. 6 16= 14. 1 13. 5 14. 1 12. 3 13. 2 13. 3 17= 14. 9 12. 9 14. 6 14. 1 12. 6 13. 7 18= 15. 0 15. 3 14. 9 15. 0 15. 3 13. 8 19= 15. 2 14. 6 15. 2 14. 1 13. 9 14. 2 20= 17. 1 16. 5 15. 7 16. 1 16. 4 14. 7

 The first line of group I. Reads: 'When the finger-tip was passed over a filled space of 2 cm. , the subject _R_ measured off 3. 1 cm. On the open space, the subject _B_ 3. 2 cm. , and the subject _A_ 3. 7. ' In group II. , the numbers represent the distance measured off when both spaces were unfilled. 

In my search for the cause of the variations reported previously Ifirst tried the plan of obliging the subject to attend more closely tothe filled space as his finger was drawn over it. In order to do this, I held a piece of fine wire across the line of the filled space, andafter the subject had measured off the equal open space he was askedto tell whether or not he had crossed the wire. The wire was so finethat considerable attention was necessary to detect it. In some of theexperiments the wire was inserted early in the filled space, and insome near the end. When it was put in near the beginning, it wasinteresting to notice, as illustrating the amount of attention thatwas being given to the effort of finding the wire, that the subject, as soon as he had discovered it, would increase his speed, relax theattention, and continue the rest of the journey more easily. 

The general effect of this forcing of the attention was to increasethe apparent length of the filled space. This conclusion was reachedby comparing these results with those in which there was no compelledattention. When the obstacle was inserted early, the space was judgedshorter than when it came at the end of the filled space. This showsvery plainly the effect of continued concentration of attention, whenthat attention is directed intensely to the spot immediately under thefinger-tip. When the attention was focalized in this way, the subjectlost sight of the space as a whole. It rapidly faded out of memorybehind the moving finger-tip. But when this concentration of attentionwas not required, the subject was able to hold together inconsciousness the entire collection of discrete points, and heoverestimated the space occupied by them. It must be remembered herethat I mean that the filled space with the focalized attention wasjudged shorter than the filled space without such concentration ofattention, but both of these spaces were judged shorter than theadjacent open space. This latter fact I shall attempt to explainlater. Many other simple devices were employed to oblige the subjectto fix his attention on the space as it was traversed by the finger. The results were always the same: the greater the amount of attention, the longer the distance seemed. 

In another experiment, I tried the plan of tapping a bell as thesubject was passing over the filled space and asking him, after he hadmeasured off the equivalent open space, whether the sound had occurredin the first half or in the second half of the filled space. 

When the finger-tip was drawn over two adjacent open spaces, andduring the first a bell was tapped continuously, this kind of filledspace was underestimated if the distance was long and overestimated ifthe distance was short. So, too, if a disagreeable odor was held tothe nostrils while the finger-tip was being drawn over one of the twoadjacent open spaces, the space thus filled by the sensations of smellfollowed the law already stated. But if an agreeable perfume was used, the distance always seemed shorter than when an unpleasant odor wasgiven. 

In all of these experiments with spaces filled by means of other thantactual sensations, I always compared the judgment on the filled andopen spaces with judgments on two open spaces, in order to guardagainst any error due to unsymmetrical, subjective conditions for thetwo spaces. It is difficult to have the subject so seat himself beforethe apparatus as to avoid the errors arising from tension and flexion. In one experiment, a piece of plush was used for the filled space andthe finger drawn over it against the nap. This filled space was judgedlonger than a piece of silk of equal length. The sensations from theplush were very unpleasant. One subject said, even, that they made himshudder. This was of course precisely what was wanted for theexperiment. It showed that the affective tone of the sensation withinthe filled space was a most important factor in producing an illusoryjudgment of distance. 

The overestimation of these filled spaces is evidently due in a largemeasure to ęsthetic motives. The space that is filled with agreeablesensations is judged shorter than one which is filled withdisagreeable sensations. In other words, the illusions in judgments oncutaneous space are not so much dependent on the quality of sensationsthat we get from the outer world through these channels, as from theamount of inner activity that we set over against these baresense-perceptions. 

I have already spoken of the defects of this method of measuring offequivalent distances as a means of getting at the quantitative amountof the illusion. The results that have come to light thus far have, however, amply justified the method. I had no difficulty, however, inadapting my apparatus to the other way of getting the judgments. I hada short curved piece of wire inserted in the handle, which could beheld across the line traversed, and thus the end of the open spacecould be marked out. Different lengths were presented to the subjectas before, but now the subject passed his finger in a uniform motionover the spaces, after which he pronounced the judgment 'greater, ''equal, ' or 'less. ' The general result of these experiments was notdifferent from those already given. The short, filled spaces wereoverestimated, while the longer ones were underestimated. The onlydifference was found to be that now the transition from one directionto the other was at a more distant point. It was, of course, moredifficult to convert these qualitative results into a quantitativedetermination of the illusion. 

Before passing to the experiments in which the open spaces werepresented first, I wish to offer an explanation for the divergenttendencies that were exhibited through all the experiments of the lasttwo sections, namely, that the short filled spaces are overestimatedand the long spaces underestimated. Let us take two typical judgments, one in which a filled space of 3 cm. Is judged equal to an open spaceof 4. 2 cm. , and then one in which the filled space is 9 cm. , and isjudged equal to an open space of 7. 4 cm. In the case of the shorterdistance, because of its shortness, after the finger leaves it, it isheld in a present state of consciousness for some moments, and doesnot suffer the foreshortening that comes from pastness. This is, however, only a part of the reason for its overestimation. After thefinger-tip has left the filled space, and while it is traversing thefirst part of the open space, there is a dearth of sensations. Thetactual sensations are meager and faint, and muscular tensions havenot yet had time to arise. It is not until the finger has passed overseveral centimeters of the distance, that the surprise of itsbarrenness sets up the organic sensations of muscular strain. Onesubject remarked naļvely at the end of some experiments of this kind, that the process of judging was an easy and comfortable affair so longas he was passing over the filled space, but when he set out upon theopen space he had to pay far more strict attention to the experiment. 

By a careful introspection of the processes in my own case, I came tothe conclusion that it is certainly a combination of these twoillusions that causes the overestimation of the short filleddistances. In the case of the long distances, the underestimation ofthe filled space is, I think, again due to a combination of twoillusions. When the finger-tip leaves the filled space, part of it, because of its length, has already, as it were, left the speciouspresent, and has suffered the foreshortening effect of being relegatedto the past. And, on the other hand, after the short distance of theopen space has been traversed the sensations of muscular strain becomevery pronounced, and cause a premature judgment of equality. 

One subject, who was very accurate in his judgments, and for whom theillusion hardly existed, said, when asked to explain his method ofjudging, that after leaving the filled space he exerted a little morepressure with his finger as he passed over the open space, so as toget the same quantity of tactual sensations in both instances. Themuscular tension that was set up when the subject had passed out overthe open space a short way was very plainly noticeable in somesubjects, who were seen at this time to hold their breath. 

I have thus far continually spoken of the space containing the tacksas being the filled space, and the smooth surface as the open space. But now we see that in reality the name should be reversed, especiallyfor the longer distances. The smooth surface is, after the first fewcentimeters, very emphatically filled with sensations arising from theorganism which, as I have already intimated, are of the most vitalimportance in our spatial judgments. Now, according to the mostgenerally accepted psychological theories, it is these organicsensations which are the means whereby we measure time, and ourspatial judgments are, in the last analysis, I will not for thepresent say dependent on, but at any rate fundamentally related to ourtime judgments. 

VIII. 

In the last section I attempted to explain the overestimation of shortfilled spaces, and the underestimation of long filled spaces by activetouch, as the result of a double illusion arising from the differencesin the manner and amount of attention given to the two kinds ofspaces when they are held in immediate contrast. This explanation wasof course purely theoretical. I have thus far offered no experimentsto show that this double illusion of lengthening, on the one hand, andshortening, on the other, does actually exist. I next made some simpleexperiments which seemed to prove conclusively that the phenomenondoes not exist, or at least not in so important a way, when the timefactor is not permitted to enter. 

In these new experiments the filled and the open spaces were comparedseparately with optical distances. After the finger-tip was drawn overthe filled path, judgment was given on it at once by comparing itdirectly with an optical distance. In this way the foreshorteningeffect of time was excluded. In all these experiments it was seen thatthe filled space was judged longer when the judgment was pronounced onit at once than when an interval of time was allowed, either bydrawing the finger-tip out over the open space, as in the previousexperiment, or by requiring the subject to withhold his judgment untila certain signal was given. Any postponement of the judgment resultedin the disappearance of a certain amount of the illusion. Thejudgments that were made rapidly and without deliberation were subjectto the strongest illusion. I have already spoken of the unanimoustestimony which all who have made quantitative studies in thecorresponding optical illusions have given in this matter of thediminution of the illusion with the lapse of time. The judgments thatwere made without deliberation always exhibited the strongest tendencyto illusion. 

I have already said that the illusion for passive touch was greatestwhen the two spaces were presented simultaneously and adjacent. Dresslar has mentioned in his studies on the 'Psychology of Touch, 'that the time factor cannot enter into an explanation of thisillusion; but the experiments of which I have just spoken seem topoint plainly to a very intimate relation between this illusion andthe illusions in our judgments of time. We have here presented on adiminutive scale the illusions which we see in our daily experience incomparing past with present stretches of time. It is a well-knownpsychological experience that a filled time appears short in passing, but long in retrospect, while an empty time appears long in passing, but short in retrospect. Now this illusion of the open and filledspace, for the finger-tip, is at every point similar to the illusionto which our time judgment is subject. If we pronounce judgment on afilled space or filled time while we are still actually living in it, it seems shorter than it really is, because, while we pay attention tothe discrete sensations of external origin, we lose sight of thesensations of internal origin, which are the sole means whereby wemeasure lapse of time, and we consequently underestimate suchstretches of time or space. But when the sensations from the outerworld which enter into such filled spaces or times exist only inmemory, the time-measuring sensations of internal origin are allowedtheir full effect; and such spaces and times seem much longer thanwhen we are actually passing through them. 

I dwell on this illusion at a length which may seem out of proportionto its importance. My object has been to show how widely different arethe objective conditions here from what they are in the opticalillusion which has so often been called the analogue of this. James[14] has said of this tactual illusion: 'This seems to bringthings back to the unanalyzable laws, by reason of which our feelingof size is determined differently in the skin and in the retina evenwhen the objective conditions are the same. ' I think that myexperiments have shown that the objective conditions are not the same;that they differ in that most essential of all factors, namely, thetime element. Something very nearly the analogue of the opticalillusion is secured when we take very short open and filled tactualspaces, and move over them very rapidly. Here the illusion exists inthe same direction as it does for sight, as has already been stated. On the other hand, a phenomenon more nearly parallel to the tactualillusion, as reported in the experiments of James and Dresslar, isfound if we take long optical distances, and traverse the open andfilled spaces continuously, without having both parts of the lineentirely in the field of view at any one moment. I made a fewexperiments with the optical illusion in this form. The filled andopen spaces were viewed by the subject through a slot which waspassed over them. These experiments all pointed in the direction of anunderestimation of a filled space. Everywhere in this illusion, then, where the objective conditions were at all similar for sight andtouch, the resulting illusion exists in the same direction for bothsenses. 

 [14] James, William, 'Principles of Psychology, ' New York, II. , p. 250. 

Throughout the previous experiments with the illusion for active touchwe saw the direct influence of the factor of time. I have yet one setof experiments to report, which seems to me to prove beyond thepossibility of a doubt the correctness of my position. Theseexperiments were made with the apparatus shown in Fig. 10. Thesubjects proceeded precisely as before. The finger-tip was passed overthe filled space, and then out over the open space, until anequivalent distance was measured off. But while the subject wasdrawing his fingers over the spaces, the block _A_ was moved in eitherdirection by means of the lever _B_. The subjects were all the whilekept ignorant of the fact that the block was being moved. They allexpressed great surprise on being told, after the experiments wereover, that the block had been moved under the finger-tip through suchlong distances without their being able to detect it. The block alwaysremained stationary as the finger passed over one space, but was movedeither with or against the finger as it passed over the other space. 

TABLE XII. 

 A B C D E 4 7. 1 2. 6 2. 4 6. 5 5 8. 3 3. 1 3. 3 8. 7 6 8. 2 3. 3 4. 1 9. 2 7 9. 7 3. 6 3. 7 10. 1 8 10. 5 3. 7 4. 5 10. 6 9 12. 4 4. 8 5. 1 11. 5 10 13. 1 4. 7 5. 3 13. 2 11 13. 3 5. 3 6. 1 14. 6 12 13. 7 6. 9 7. 2 12. 7 13 14. 6 7. 5 8. 1 13. 2 14 15. 3 8. 2 9. 4 15. 6 15 15. 7 8. 7 10. 3 14. 9

 Column _A_ contains the filled spaces, columns _B_, _C_, _D_, _E_ the open spaces that were judged equal. In _B_ the block was moved with the finger, and in _C_ against the finger as it traversed the filled space, and in _D_ and _E_ the block was moved with and against the finger respectively as it passed over the open space. The block was always moved approximately one-half the distance of the filled space. 

I have given some of the results for one subject in Table XII. Theseresults show at a glance how potent a factor the time element is. Thequantity of tactual sensations received by the finger-tip enters intothe judgment of space to no appreciable extent. With one subject, after he had passed his finger over a filled space of 10 cm. The blockwas moved so as almost to keep pace with the finger as it passed overthe open space. In this way the subject was forced to judge a filledspace of 10 cm. Equal to only 2 cm. Of the open space. And when theblock was moved in the opposite direction he was made to judge adistance of 10 cm. Equal to an open distance of 16 cm. 

The criticism may be made on these experiments that the subject hasnot in reality been obliged to rely entirely upon the time sense, butthat he has equated the two spaces as the basis of equivalent muscleor joint sensation, which might be considered independent of thesensations which yield the notion of time. I made some experiments, however, to prove that this criticism would not be well founded. Byarranging the apparatus so that the finger-tip could be heldstationary, and the block with the open and filled spaces moved backand forth under it, the measurement by joint and muscle sensations waseliminated. 

It will be observed that no uniform motion could be secured by simplymanipulating the lever with the hand. But uniformity of motion was notnecessary for the results at which I aimed here. Dresslar has laidgreat stress on the desirability of having uniform motion in hissimilar experiments. But this, it seems to me, is precisely what isnot wanted. With my apparatus, I was able to give widely differentrates of speed to the block as it passed under the finger-tip. Bygiving a slow rate for the filled space and a much more rapid rate forthe open space, I found again that the subject relied hardly at all onthe touch sensations that came from the finger-tip, but almostentirely on the consciousness of the amount of time consumed inpassing over the spaces. The judgments were made as in the previousexperiments with this apparatus. When the subject reached the point inthe open space which he judged equal to the filled space, he slightlydepressed his finger and stopped the moving block. In this way, thesubject was deprived of any assistance from arm-movements in hisjudgments, and was obliged to rely on the tactual impressions receivedat the finger-tip, or on his time sense. That these tactual sensationsplayed here also a very minor part in the judgment of the distance wasshown by the fact that these sensations could be doubled or trebled bydoubling or trebling the amount of space traversed, withoutperceptibly changing the judgment, provided the rate of speed wasincreased proportionately. Spaces that required the same amount oftime in traversing were judged equal. 

In all these experiments the filled space was presented first. Whenthe open space was presented first, the results for four out of fivesubjects were just reversed. For short distances the filled space wasunderestimated, for long distances the filled space was overestimated. A very plausible explanation for these anomalous results is again tobe found in the influence of the time factor. The open space seemedlonger while it was being traversed, but rapidly foreshortened afterit was left for the filled space. While on the other hand, if thejudgment was pronounced while the subject was still in the midst ofthe filled space, it seemed shorter than it really was. Thecombination of these two illusions is plainly again responsible forthe underestimation of the short filled spaces. The same doubleillusion may be taken to explain the opposite tendency for the longerdistances. 

IX. 

The one generalization that I have thus far drawn from theinvestigation--namely, that the optical illusions are not reversed inpassing from the field of touch, and that we therefore have a safewarrant for the conclusion that sight and touch do function alike--hascontained no implicit or expressed assertion as to the origin of ournotion of space. I have now reached the point where I must venture anexplanation of the illusion itself. 

The favorite hypothesis for the explanation of the geometrical opticalillusions is the movement theory. The most generally acceptedexplanation of the illusion with whose tactual counterpart this paperis concerned, is that given by Wundt. [15] Wundt's explanation rests onvariation in eye movements. When the eye passes over brokendistances, the movement is made more difficult by reason of thefrequent stoppages. The fact that the space which is filled with onlyone point in the middle is underestimated, is explained by Wundt onthe theory that the eye has here the tendency to fix on the middlepoint and to estimate the distance by taking in the whole space atonce without moving from this middle point. A different explanationfor this illusion is offered by Helmholtz. [16] He makes use of theęsthetic factor of contrasts. Wundt insists that the fact that thisillusion is still present when there are no actual eye movements doesnot demonstrate that the illusion is not to be referred to a motororigin. He says, "If a phenomenon is perceived with the moving eyeonly, the influence of movement on it is undoubtedly true. But aninference cannot be drawn in the opposite direction, that movement iswithout influence on the phenomenon that persists when there is nomovement. "[17]

 [15] Wundt. , W. , 'Physiolog. Psych. , ' 4te Aufl. , Leipzig, 1893, Bd. II. , S. 144. 

 [16] v. Helmholtz, H. , 'Handbuch d. Physiol. Optik, ' 2te Aufl. , Hamburg u. Leipzig, 1896, S. 705. 

 [17] Wundt, W. , _op. Citat. _, S. 139. 

Satisfactorily as the movement hypothesis explains this and otheroptical illusions, it yet falls short of furnishing an entirelyadequate explanation. It seems to me certain that several causes existto produce this illusion, and also the illusion that is oftenassociated with it, the well-known Müller-Lyer illusion. But in whatdegree each is present has not yet been determined by any of thequantitative studies in this particular illusion. I made a number oftests of the optical illusion, with these results: that the illusionis strongest when the attention is fixed at about the middle of theopen space, that there is scarcely any illusion left when theattention is fixed on the middle of the filled space. It is strongerwhen the outer end-point of the open space is fixated than when theouter end of the filled space is fixated. For the moving eye, I findthe illusion to be much stronger when the eye passes over the filledspace first, and then over the open space, than when the process isreversed. 

Now, the movement hypothesis does not, it seems to me, sufficientlyexplain all the fluctuations in the illusion. My experiments with thetactual illusion justify the belief that the movement theory is evenless adequate to explain all of the variations there, unless themovement hypothesis is given a wider and richer interpretation than isordinarily given to it. In the explanation of the tactual illusionwhich I have here been studying two other important factors must betaken into consideration. These I shall call, for the sake ofconvenience, the ęsthetic factor and the time factor. These factorsshould not, however, be regarded as independent of the factor ofmovement. That term should be made wide enough to include these withinits meaning. The importance of the time factor in the illusion forpassive touch I have already briefly mentioned. I have also, inseveral places in the course of my experiments, called attention tothe importance of the ęsthetic element in our space judgments. I wishnow to consider these two factors more in detail. 

The foregoing discussion has pointed to the view that thespace-perceiving and the localizing functions of the skin have adeep-lying common origin in the motor sensations. My experiments showthat, even in the highly differentiated form in which we find them intheir ordinary functioning, they plainly reveal their common origin. Aformula, then, for expressing the judgments of distance by means ofthe resting skin might be put in this way. Let _P_ and _P'_ representany two points on the skin, and let _L_ and _L'_ represent the localsigns of these points, and _M_ and _M'_ the muscle sensations whichgive rise to these local signs. Then _M-M'_ will represent thedistance between _P_ and _P'_, whether that distance be judgeddirectly in terms of the localizing function of the skin or in termsof its space-perceiving function. This would be the formula for anormal judgment. In an illusory judgment, the temporal and ęstheticfactors enter as disturbing elements. Now, the point which I insist onhere is that the judgments of the extent of the voluntary movements, represented in the formula by _M_ and _M'_, do not depend alone on thesensations from the moving parts or other sensations of objectiveorigin, as Dresslar would say, nor alone on the intention or impulseor innervation as Loeb and others claim, but on the sum of all thesensory elements that enter, both those of external and those ofinternal origin. And, furthermore, these sensations of external originare important in judgments of space, only in so far as they arereferred to sensations of internal origin. Delabarre says, "Movementsare judged equal when their sensory elements are judged equal. Thesesensory elements need not all have their source in the moving parts. All sensations which are added from other parts of the body and whichare not recognized as coming from these distant sources, are mingledwith the elements from the moving member, and influence thejudgment. "[18] The importance of these sensations of inner origin wasshown in many of the experiments in sections VI. To VIII. In theinstance where the finger-tip was drawn over an open and a filledspace, in the filled half the sensations were largely of externalorigin, while in the open half they were of internal origin. Theresult was that the spaces filled with sensations of internal originwere always overestimated. 

The failure to recognize the importance of these inwardly initiatedsensations is the chief defect in Dresslar's reasoning. He hasendeavored to make our judgments in the illusion in question dependentirely on the sensations of external origin. He insists also thatthe illusion varies according to the variations in quantity of theseexternal sensations. Now my experiments have shown, I think, veryclearly that it is not the numerical or quantitative extent of theobjective sensations which disturbs the judgment of distance, but thesensation of inner origin which we set over against these outersensations. The piece of plush, because of the disagreeable sensationswhich it gives, is judged shorter than the space filled with closelycrowded tacks. Dresslar seems to have overlooked entirely the factthat the feelings and emotions can be sources of illusions in theamount of movement, and hence in our judgments of space. Theimportance of this element has been pointed out by Münsterberg[19] inhis studies of movement. 

 [18] Delabarre, E. B. , 'Ueber Bewegungsempfindungen, ' Inaug. Dissert. , Freiburg, 1891. 

 [19] Münsterberg, H. , 'Beiträge zur Experimentellen Psychol. , ' Freiburg i. B. , 1892, Heft 4. 

Dresslar says again, "The explanations heretofore given, wholly basedon the differences in the time the eye uses in passing over the twospaces, must stop short of the real truth. " My experiments, however, as I have already indicated, go to prove quite the contrary. In short, I do not think we have any means of distinguishing our tactualjudgments of time from our similar judgments of space. When thesubject is asked to measure off equal spaces, he certainly uses timeas means, because when he is asked to measure off equal times heregisters precisely the same illusion that he makes in his judgmentsof spatial distances. The fact that objectively equal times were usedby Dresslar in his experiments is no reason for supposing that thesubject also regarded these times as equal. What I have here assertedof active touch is true also of the resting skin. When a stylus isdrawn over the skin, the subject's answer to the question, How long isthe distance? is subject to precisely the same illusion as his answerto the question, How long is the time?

I can by a simple illustration show more plainly what I mean by thestatement that the blending of the inner and outer sensations isnecessary for the perception of space. I shall use the sense of sightfor the illustration, although precisely the same reasoning wouldapply to the sense of touch. Suppose that I sat in an entirely passiveposition and gazed at a spot on an otherwise blank piece of paperbefore me. I am perfectly passive so far as motion on my part isconcerned. I may be engaged in any manner of speculation or be in themidst of the so-called active attention to the spot; but I must be andfor the present remain motionless. Now, while I am in this conditionof passivity, suppose the spot be made to move slowly to one side bysome force external to myself. I am immovable all the while, and yetam conscious of this movement of the spot from the first position, which I call _A_, to the new position, _A'_, where it stops. Thesensation which I now have is qualitatively different from thesensation which I had from the spot in its original position. My worldof experience thus far has been a purely qualitative one. I might goon to eternity having experiences of the same kind, and never dream ofspace, or geometry, nor should I have the unique experience of ageometrical illusion, either optical or tactual. Now suppose I set upthe bodily movements of the eyes or the head, or of the whole body, which are necessary to follow the path of that point, until I overtakeit and once more restore the quality of the original sensation. Thiscircle, completed by the two processes of external activity andrestoration by internal activity, forms a group of sensations whichconstitutes the ultimate atom in our spatial experience. I have myfirst spatial experience when I have the thrill of satisfaction thatcomes from overtaking again, by means of my own inner activity, asensation that has escaped me through an activity not my own. A beingincapable of motion, in a world of flux, would not have the spatialexperience that we have. A being incapable of motion could not makethe distinction between an outer change that can be corrected by aninternal change, and an outer change that cannot so be restored. Suchan external change incapable of restoration by internal activity weshould have if the spot on the paper changed by a chemical processfrom black to red. 

Now such a space theory is plainly not to be confused with the theorythat makes the reversibility of the spatial series its primaryproperty. It is evident that we can have a series of sensations whichmay be reversed and yet not give the notion of space. But we shouldalways have space-perception if one half of the circular process abovedescribed comes from an outer activity, and the other half from aninner activity. This way of describing the reversibility of thespatial series makes it less possible to urge against it theobjections that Stumpf[20] has formulated against Bain's geneticspace-theory. Stumpf's famous criticism applies not only to Bain, butalso to the other English empiricists and to Wundt. Bain says: "Whenwith the hand we grasp something moving and move with it, we have asensation of one unchanged contact and pressure, and the sensation isimbedded in a movement. This is one experience. When we move the handover a fixed surface, we have with the feelings of movement asuccession of feelings of touch; if the surface is a variable one, the sensations are constantly changing, so that we can be under nomistake as to our passing through a series of tactual impressions. This is another experience, and differs from the first not in thesense of power, but in the tactile accompaniment. The difference, however, is of vital importance. In the one case, we have an objectmoving and measuring time and continuous, in the other case we havecoėxistence in space. The coėxistence is still further made apparentby our reversing the movement, and thereby meeting the tactile seriesin the inverse order. Moreover, the serial order is unchanged by therapidity of our movements. "[21]

 [20] Stumpf, K. , 'Ueber d. Psycholog. Ursprung d. Raumvorstellung, ' Leipzig, 1873, S. 54. 

 [21] Bain, A. , 'The Senses and the Intellect, ' 3d ed. , New York, 1886, p. 183. 

Stumpf maintained in his exhaustive criticism of this theory, first, that there are cases where all of the elements which Bain requires forthe perception of space are present, and yet we have no presentationof space. Secondly, there are cases where not all of these elementsare present, and where we have nevertheless space presentation. It isthe first objection that concerns me here. Stumpf gives as an example, under his first objection, the singing of a series of tones, C, G, E, F. We have here the muscle sensations from the larynx, and the seriesof the tone-sensations which are, Stumpf claims, reversed when themuscle-sensations are reversed, etc. According to Stumpf, these areall the elements that are required by Bain, and yet we have noperception of space thereby. Henri[22] has pointed out two objectionsto Stumpf's criticism of Bain's theory. He says that Bain assumes, what Stumpf does not recognize, that the muscle sensations mustcontain three elements--resistance, time, and velocity--before theycan lead to space perceptions. These three elements are not to befound in the muscle sensations of the larynx as we find them in thesensations that come from the eye or arm muscles. In addition to this, Henri claims that Bain's theory demands a still further condition. Ifwe wish to touch two objects, _A_ and _B_, with the same member, wecan get a spatial experience from the process only if we insertbetween the touching of _A_ and the touching of _B_ a continualseries of tactual sensations. In Stumpf's instance of the singing oftones, this has been overlooked. We can go from the tone C to the toneF without inserting between the two a continuous series of musicalsensations. 

 [22] Henri, V. , 'Ueber d. Raumwahrnehmungen d. Tastsinnes, ' Berlin, 1898, S. 190. 

I think that all such objections to the genetic space theories areavoided by formulating a theory in the manner in which I have juststated. When one says that there must be an outer activity producing adisplacement of sensation, and then an inner activity retaining thatsensation, it is plain that the singing of a series of tones ascendingand then descending would not be a case in point. 

 * * * * *

TACTUAL TIME ESTIMATION. 

BY KNIGHT DUNLAP. 

I. GENERAL NATURE OF THE WORK. 

The experiments comprised in this investigation were made during theyear 1900-1901 and the early part of the year 1901-1902. They wereplanned as the beginning of an attempt at the analysis of theestimation of time intervals defined by tactual stimulations. The onlypublished work in this quarter of the field so far is that ofVierordt, [1] who investigated only the constant error of timejudgment, using both auditory and tactual stimulations, and that ofMeumann, [2] who in his last published contribution to the literatureof the time sense gives the results of his experiments with 'filled'and 'empty' tactual intervals. The stimuli employed by Meumann were, however, not purely tactual, but electrical. 

 [1] Vierordt: 'Der Zeitsinn, ' Tübingen, 1868. 

 [2] Meumann, E. : 'Beiträge zur Psychologie des Zeitbewusstseins, ' III. , _Phil. Studien, _ XII. , S. 195-204. 

The limitation of time intervals by tactual stimulations offers, however, a rich field of variations, which promise assistance in theanalytical problem of the psychology of time. The variations may bethose of locality, area, intensity, rigidity, form, consecutiveness, and so on, in addition to the old comparisons of filled and emptyintervals, intervals of varying length, and intervals separated by apause and those not so separated. 

To begin with, we have selected the conditions which are mechanicallythe simplest, namely, the comparison of two empty time intervals, bothgiven objectively with no pause between them. We have employed themost easily accessible dermal areas, namely, that of the fingers ofone or both hands, and introduced the mechanically simplestvariations, namely, in locality stimulated and intensity ofstimulation. 

It was known from the results of nearly all who have studied the timesense experimentally, that there is in general a constant error ofover- or underestimation of time intervals of moderate length, andfrom the results of Meumann, [3] that variations in intensity oflimiting stimulation influenced the estimation decidedly, butapparently according to no exact law. The problem first at hand wasthen to see if variations introduced in tactual stimulations produceany regularity of effect, and if they throw any new light on thephenomena of the constant error. 

 [3] Meumaun, E. : 'Beiträge zur Psychologie des Zeitsinns, ' II. , _Phil. Studien_, IX. , S. 264. 

The stimulations employed were light blows from the cork tip of ahammer actuated by an electric current. These instruments, of whichthere were two, exactly alike in construction, were similar inprinciple to the acoustical hammers employed by Estel and Mehner. Eachconsisted essentially of a lever about ten inches in length, pivotednear one extremity, and having fastened to it near the pivot anarmature so acted upon by an electromagnet as to depress the leverduring the passage of an electric current. The lever was returned toits original position by a spring as soon as the current through theelectromagnet ceased. A clamp at the farther extremity held a smallwooden rod with a cork tip, at right angles to the pivot, and thedepression of the lever brought this tip into contact with the dermalsurface in proximity with which it had been placed. The rod was easilyremovable, so that one bearing a different tip could be substitutedwhen desired. The whole instrument was mounted on a compact baseattached to a short rod, by which it could be fastened in any desiredposition in an ordinary laboratory clamp. 

During the course of most of the experiments the current wascontrolled by a pendulum beating half seconds and making a mercurycontact at the lowest point of its arc. A condenser in parallel withthe contact obviated the spark and consequent noise of the currentinterruption. A key, inserted in the circuit through the mercury cupand tapping instrument, allowed it to be opened or closed as desired, so that an interval of any number of half seconds could be interposedbetween successive stimulations. 

In the first work, a modification of the method of right and wrongcases was followed, and found satisfactory. A series of intervals, ranging from one which was on the whole distinctly perceptible aslonger than the standard to one on the whole distinctly shorter, wasrepresented by a series of cards. Two such series were shuffledtogether, and the intervals given in the order so determined. Thus, when the pile of cards had been gone through, two complete series hadbeen given, but in an order which the subject was confident wasperfectly irregular. As he also knew that in a given series there weremore than one occurrence of each compared interval (he was notinformed that there were exactly two of each), every possibleinfluence favored the formation each time of a perfectly freshjudgment without reference to preceding judgments. The only fear waslest certain sequences of compared intervals (_e. G. _, a long comparedinterval in one test followed by a short one in the next), mightproduce unreliable results; but careful examination of the data, inwhich the order of the interval was always noted, fails to show anyinfluence of such a factor. 

To be more explicit with regard to the conditions of judgment; twointervals were presented to the subject in immediate succession. Thatis, the second stimulation marked the end of the first interval andthe beginning of the second. The first interval was always thestandard, while the second, or compared interval, varied in length, asdetermined by the series of cards, and the subject was requested tojudge whether it was equal to, or longer or shorter than the standardinterval. 

In all of the work under Group 1, and the first work under Group 2, the standard interval employed was 5. 0 seconds. This interval wasselected because the minimum variation possible with the pendulumapparatus (½ sec. ) was too great for the satisfactory operation of ashorter standard, and it was not deemed advisable to keep thesubject's attention on the strain for a longer interval, since 5. 0sec. Satisfied all the requirements of the experiment. 

In all work here reported, the cork tip on the tapping instrument wascircular in form, and 1 mm. In diameter. In all, except one experimentof the second group, the areas stimulated were on the backs of thefingers, just above the nails. In the one exception a spot on theforearm was used in conjunction with the middle finger. 

In Groups 1 and 2 the intensity of stroke used was just sufficient togive a sharp and distinct stimulation. The intensity of thestimulation was not of a high degree of constancy from day to day, onaccount of variations in the electric contacts, but within each testof three stimulations the intensity was constant enough. 

In experiments under Group 3 two intensities of strokes were employed, one somewhat stronger than the stroke employed in the otherexperiments, and one somewhat weaker--just strong enough to beperceived easily. The introduction of the two into the same test waseffected by the use of an auxiliary loop in the circuit, containing arheostat, so that the depression of the first key completed thecircuit as usual, or the second key completed it through the rheostat. 

At each test the subject was warned to prepare for the firststimulation by a signal preceding it at an exact interval. Inexperiments with the pendulum apparatus the signal was the spoken word'now, ' and the preparatory interval one second. Later, experimentswere undertaken with preparatory intervals of one second and 1-4/5seconds, to find if the estimation differed perceptibly in one casefrom that in the other. No difference was found, and in workthereafter each subject was allowed the preparatory interval whichmade the conditions subjectively most satisfactory to him. 

Ample time for rest was allowed the subject after each test in aseries, two (sometimes three) series of twenty to twenty-four testsbeing all that were usually taken in the course of the hour. Attentionto the interval was not especially fatiguing and was sustained withoutdifficulty after a few trials. 

Further details will be treated as they come up in the considerationof the work by groups, into which the experiment naturally falls. 

II. EXPERIMENTAL RESULTS. 

1. The first group of experiments was undertaken to find the directionof the constant error for the 5. 0 sec. Standard, the extent to whichdifferent subjects agree and the effects of practice. The tests weretherefore made with three taps of equal intensity on a single dermalarea. The subject sat in a comfortable position before a table uponwhich his arm rested. His hand lay palm down on a felt cushion and thetapping instrument was adjusted immediately over it, in position tostimulate a spot on the back of the finger, just above the nail. A fewtests were given on the first finger and a few on the secondalternately throughout the experiments, in order to avoid the numbingeffect of continual tapping on one spot. The records for each of thetwo fingers were however kept separately and showed no disagreement. 

The detailed results for one subject (_Mr_, ) are given in Table I. Thefirst column, under _CT_, gives the values of the different comparedintervals employed. The next three columns, under _S_, _E_ and _L_, give the number of judgments of _shorter_, _equal_ and _longer_, respectively. The fifth column, under _W_, gives the number of errorsfor each compared interval, the judgments of _equal_ being dividedequally between the categories of _longer_ and _shorter_. 

In all the succeeding discussion the standard interval will berepresented by _ST_, the compared interval by _CT_. _ET_ is that _CT_which the subject judges equal to _ST_. 

TABLE I. 

 _ST_=5. 0 SEC. SUBJECT _Mr. _ 60 SERIES. 

 _CT_ _S_ _E_ _L_ _W_ 4. 58 1 1 1. 5 4. 5 45 11 4 9. 5 5. 32 13 15 21. 5 5. 5 19 16 25 27 6. 5 4 51 7 6. 5 1 2 57 2

We can calculate the value of the average _ET_ if we assume that thedistribution of wrong judgments is in general in accordance with thelaw of error curve. We see by inspection of the first three columnsthat this value lies between 5. 0 and 5. 5, and hence the 32 cases of_S_ for _CT_ 5. 0 must be considered correct, or the principle of theerror curve will not apply. 

The method of computation may be derived in the following way: If wetake the origin so that the maximum of the error curve falls on the_Y_ axis, the equation of the curve becomes

 y = ke^{-[gamma]²x²}

and, assuming two points (x_{1} y_{1}) and (x_{2} y_{2}) on thecurve, we deduce the formula

 ____________ ±D \/ log k/y_{1} x_{1} = --------------------------------- ____________ ____________ \/ log k/y_{1} ± \/ log k/y_{2}

where D = x_{1} ± x_{2}, and k = value of y when x = 0. 

x_{1} and x_{2} must, however, not be great, since the conditionthat the curve with which we are dealing shall approximate the formdenoted by the equation is more nearly fulfilled by those portions ofthe curve lying nearest to the _Y_ axis. 

Now since for any ordinates, y_{1} and y_{2} which we may selectfrom the table, we know the value of x_{1} ± x_{2}, we can computethe value of x_{1}, which conversely gives us the amount to be addedto or subtracted from a given term in the series of _CT_'s to producethe value of the average _ET_. This latter value, we find, bycomputing by the formula given above, using the four terms whosevalues lie nearest to the _Y_ axis, is 5. 25 secs. 

In Table II are given similar computations for each of the ninesubjects employed, and from this it will be seen that in every casethe standard is overestimated. 

TABLE II. _ST_= 5. 0 SECS. 

 Subject. Average ET. No. Of Series. _A_. 5. 75 50 _B_. 5. 13 40 _Hs_. 5. 26 100 _P_. 5. 77 38 _Mn_. 6. 19 50 _Mr_. 5. 25 60 _R_. 5. 63 24 _Sh_. 5. 34 100 _Sn_. 5. 57 50

This overestimation of the 5. 0 sec. Standard agrees with the resultsof some of the experimenters on auditory time and apparently conflictswith the results of others. Mach[4] found no constant error. Höring[5]found that intervals over 0. 5 sec. Were overestimated. Vierordt, [6]Kollert, [7] Estel[8] and Glass, [9] found small intervals overestimatedand long ones underestimated, the indifference point being placed atabout 3. 0 by Vierordt, 0. 7 by Kollert and Estel and 0. 8 by Glass. Mehner[10] found underestimation from 0. 7 to 5. 0 and overestimationabove 5. 0. Schumann[11] found in one set of experiments overestimationfrom 0. 64 to 2. 75 and from 3. 5 to 5. 0, and underestimation from 2. 75to 3. 5. Stevens[12] found underestimation of small intervals andoverestimation of longer ones, placing the indifference point between0. 53 and 0. 87. 

 [4] Mach, E. : 'Untersuchungen über den Zeitsinn des Ohres, ' _Sitzungsber. D. Wiener Akad. _, Math. -Nat. Kl. , Bd. 51, Abth. 2. 

 [5] Höring: 'Versuche über das Unterscheidungsvermögen des Hörsinnes für Zeitgrössen, ' Tübingen, 1864. 

 [6] Vierordt: _op. Cit. _

 [7] Kollert, J. : 'Untersuchungen über den Zeitsinn, ' _Phil. Studien_, I. , S. 79. 

 [8] Estel, V. : 'Neue Versuche über den Zeitsinn, ' _Phil. Studien_, II. , S. 39. 

 [9] Glass R. : 'Kritisches und Experimentelles über den Zeitsinn, ' _Phil. Studien_, IV. , S. 423. 

 [10] Mehner, Max: 'Zum Lehre vom Zeitsinn, ' _Phil. Studien_, II. , S. 546. 

 [11] Schumann, F. : 'Ueber die Schätzung kleiner Zeitgrössen, ' _Zeitsch. F. Psych. _, IV. , S. 48. 

 [12] Stevens, L. T. : 'On the Time Sense, ' _Mind_, XI. , p. 393. 

The overestimation, however, is of no great significance, for datawill be introduced a little later which show definitely that theunderestimation or overestimation of a given standard is determined, among other factors, by the intensity of the stimulation employed. Theapparently anomalous results obtained in the early investigations arein part probably explicable on this basis. 

As regards the results of _practice_, the data obtained from the twosubjects on whom the greatest number of tests was made (_Hs_ and _Sh_)is sufficiently explicit. The errors for each successive group of 25series for these two subjects are given in Table III. 

TABLE III. 

 _ST_ = 5. 0 SECONDS. 

 SUBJECT _Hs_. SUBJECT _Sh_. CT (1) (2) (3) (4) (1) (2) (3) (4) 4. 2. 5 2. 5 1. 5 2. 5 0. . 5 0. . 5 4. 5 6. 0 3. 0 3. 5 7. 0 5. 0 3. 5 2. 0 . 5 5. 14. 0 11. 0 11. 0 11. 0 8. 5 11. 5 4. 0 7. 0 5. 5 11. 5 11. 5 6. 0 12. 5 11. 0 16. 0 14. 0 15. 0 6. 12. 0 9. 0 6. 5 6. 0 3. 5 2. 0 1. 5 1. 0 6. 5 4. 0 3. 5 4. 0 3. 5 4. 0 . 5 0. 0. 

No influence arising from practice is discoverable from this table, and we may safely conclude that this hypothetical factor may bedisregarded, although among the experimenters on auditory timeMehner[13] thought results gotten without a maximum of practice areworthless, while Meumann[14] thinks that unpracticed and henceunsophisticated subjects are most apt to give unbiased results, aswith more experience they tend to fall into ruts and exaggerate theirmistakes. The only stipulation we feel it necessary to make in thisconnection is that the subject be given enough preliminary tests tomake him thoroughly familiar with the conditions of the experiment. 

 [13] _op. Cit. _, S. 558, S. 595. 

 [14] _op. Cit. _ (II. ), S. 284. 

2. The second group of experiments introduced the factor of adifference between the stimulation marking the end of an interval andthat marking the beginning, in the form of a change in localitystimulated, from one finger to the other, either on the same hand oron the other hand. Two classes of series were given, in one of whichthe change was introduced in the standard interval, and in the otherclass in the compared interval. 

In the first of these experiments, which are typical of the wholegroup, both of the subject's hands were employed, and a tappinginstrument was arranged above the middle finger of each, as above theone hand in the preceding experiment, the distance between middlefingers being fifteen inches. The taps were given either two on theright hand and the third on the left, or one on the right and thesecond and third on the left, the two orders being designated as _RRL_and _RLL_ respectively. The subject was always informed of the orderin which the stimulations were to be given, so that any element ofsurprise which might arise from it was eliminated. Occasionally, however, through a lapse of memory, the subject expected the wrongorder, in which case the disturbance caused by surprise was usually sogreat as to prevent any estimation. 

The two types of series were taken under as similar conditions aspossible, four (or in some cases five) tests being taken from eachseries alternately. Other conditions were the same as in the precedingwork. The results for the six subjects employed are given in Table IV. 

TABLE IV. 

 _ST_= 5. 0 SECS. TWO HANDS. 15 INCHES. 

 Subject. Average RT. No. Of Series. RRL. RLL. * (Table II. ) _Hs. _ 4. 92 6. 55 (5. 26) 50 _Sh. _ 5. 29 5. 28 (5. 34) 50 _Mr. _ 5. 02 6. 23 (5. 25) 60 _Mn. _ 5. 71 6. 71 (6. 19) 24 _A. _ 5. 34 5. 89 (5. 75) 28 _Sn. _ 5. 62 6. 43 (5. 47) 60

 *Transcriber's Note: Original "RRL"

From Table IV. It is apparent at a glance that the new conditioninvolved introduces a marked change in the time judgment. Comparisonwith Table II. Shows that in the cases of all except _Sh_ and _Sn_ thevariation _RRL_ shortens the standard subjectively, and that _RLL_lengthens it; that is, a local change tends to lengthen the intervalin which it occurs. In the case of _Sh_ neither introduces any changeof consequence, while in the case of _Sn_ both values are higher thanwe might expect, although the difference between them is in conformitywith the rest of the results shown in the table. 

Another set of experiments was made on subject _Mr_, using taps on themiddle finger of the left hand and a spot on the forearm fifteeninches from it; giving in one case two taps on the finger and thethird on the arm, and in the other one tap on the finger and thesecond and third on the arm; designating the orders as _FFA_ and _FAA_respectively. Sixty series were taken, and the values found for theaverage _ET_ were 4. 52 secs, for _FFA_ and 6. 24 secs, for _FAA_, _ST_being 5. 0 secs. This shows 0. 5 sec. More difference than theexperiment with two hands. 

Next, experiments were made on two subjects, with conditions the sameas in the work corresponding to Table IV. , except that the distancebetween the fingers stimulated was only five inches. The results ofthis work are given in Table V. 

TABLE V. 

 _ST_= 5. 0 SECS. TWO HANDS. 5 INCHES. 

 Subject RRL. RLL. No. Of Series. _Sh. _ 5. 32 5. 32 60 _Hs. _ 4. 40 6. 80 60

It will be noticed that _Hs_ shows a slightly wider divergence thanbefore, while _Sh_ pursues the even tenor of his way as usual. 

Series were next obtained by employing the first and second fingers onone hand in exactly the same way as the middle fingers of the twohands were previously employed, the orders of stimulation being 1, 1, 2, and 1, 2, 2. The results of sixty series on Subject _Hs_ give thevalues of average _ET_ as 4. 8 secs. For 1, 1, 2, and 6. 23 sees, for 1, 2, 2, _ST_ being 5. 0 secs. , showing less divergence than in thepreceding work. 

These experiments were all made during the first year's work. Theyshow that in most cases a change in the locality stimulated influencesthe estimation of the time interval, but since the details of thatinfluence do not appear so definitely as might be desired, the groundwas gone over again in a little different way at the beginning of thepresent year. 

A somewhat more serviceable instrument for time measurements wasemployed, consisting of a disc provided with four rows of sockets inwhich pegs were inserted at appropriate angular intervals, so thattheir contact with fixed levers during the revolution of the discclosed an electric circuit at predetermined time intervals. The discwas rotated at a uniform speed by an electric motor. 

Experiments were made by stimulation of the following localities: (1)First and third fingers of right hand; (2) first and second fingers ofright hand; (3) first fingers of both hands, close together, but justescaping contact; (4) first fingers of both hands, fifteen inchesapart; (5) first fingers of both hands, thirty inches apart; (6) twopositions on middle finger of right hand, on same transverse line. 

A standard of two seconds was adopted as being easier for the subjectand more expeditious, and since qualitative and not quantitativeresults were desired, only one _CT_ was used in each case, thuspermitting the investigation to cover in a number of weeks groundwhich would otherwise have required a much longer period. The subjectswere, however, only informed that the objective variations were verysmall, and not that they were in most cases zero. Tests of the twotypes complementary to each other (_e. G. _, _RRL_ and _RRL_) were ineach case taken alternately in groups of five, as in previous work. 

TABLE VI. 

 _ST_= 2. 0 SECS. 

 _Subject W. _

 (1) CT=2. 0 (3) CT=2. 2 (5) CT=2. 0 113 133 RRL RLL RRL RLL S 3 3 9 20 5 21 E 18 19 25 16 18 14 L 24 28 16 14 17 15

 _Subject P. _

 (1) CT=2. 0 (3)CT={1. 6 (5) CT={1. 6 {2. 4 {2. 4 113 133 RRL(1. 6) RLL(2. 4) RRL(1. 6) RLL(2. 4) S 2 16 12 16 15 10 E 38 32 32 21 26 19 L 10 2 6 15 14 21

 _Subject B. _

 (1) CT=2. 0 (2) CT=2. 0 (6) CT=2. 0 113 133 112 122 aab abb S 4 21 5 20 7 6 E 23 19 22 24 40 38 L 23 10 23 6 3 6

 _Subject Hy. _

 (1) CT=2. 0 (2) CT=2. 4 (1a) CT=2. 0 113 133 112 122 113 133 S 12 46 17 40 17 31 E 9 2 14 8 9 7 L 29 2 19 2 14 2

 In the series designated as (1a) the conditions were the same as in (1), except that the subject abstracted as much as possible from the tactual nature of the stimulations and the position of the fingers. This was undertaken upon the suggestion of the subject that it would be possible to perform the abstraction, and was not repeated on any other subject. 

The results are given in Table VI. , where the numerals in theheadings indicate the localities and changes of stimulation, inaccordance with the preceding scheme, and _'S'_, _'E'_ and _'L'_designate the number of judgments of _shorter_, _equal_ and _longer_respectively. 

It will be observed that in several cases a _CT_ was introduced in oneclass which was different from the _CT_ used in the other classes withthe same subject. This was not entirely arbitrary. It was found withsubject _W_, for example, that the use of _CT_ = 2. 0 in (3) producedjudgments of shorter almost entirely in both types. Therefore a _CT_was found, by trial, which produced a diversity of judgments. Thecomparison of the different classes is not so obvious under theseconditions as it otherwise would be, but is still possible. 

The comparison gives results which at first appear quite irregular. These are shown in Table VII. Below, where the headings (1)--(3), etc. , indicate the classes compared, and in the lines beneath them'+' indicates that the interval under consideration is estimated asrelatively greater (more overestimated or less underestimated) in thesecond of the two classes than in the first, --indicating the oppositeeffect. Results for the first interval are given in the line denoted'first, ' and for the second interval in the line denoted 'second. 'Thus, the plus sign under (1)--(3) in the first line for subject _P_indicates that the variation _RLL_ caused the first interval to beoverestimated to a greater extent than did the variation 133. 

TABLE VII. 

 SUBJECT _P. _ SUBJECT _W. _ SUBJECT _B. _ SUBJECT _Hy. _ (1)--(3) (3)--(4) (1)--(3) (3)--(5) (2)--(1) (6)--(2) (2)--(1)First. + - + - - + -Sec. + + - + + + +

The comparisons of (6) and (2), and (1) and (3) confirm theprovisional deduction from Table IV. , that the introduction of a_local change_ in an interval _lengthens_ it subjectively, but thecomparisons of (3) and (5), (3) and (4), and (2) and (1) showapparently that while the _amount_ of the local change influences thelengthening of the interval, it does not vary directly with thislatter in all cases, but inversely in the first interval and directlyin the second. This is in itself sufficient to demonstrate that thechief factors of the influence of locality-change upon the timeinterval are connected with the spatial localization of the areasstimulated, but a further consideration strengthens the conclusion anddisposes of the apparent anomaly. It will be noticed that in generalthe decrease in the comparative length of the first interval producedby increasing the spatial change is less than the increase in thecomparative length of the second interval produced by a correspondingchange. In other words, the disparity between the results for the twotypes of test is greater, the greater the spatial distance introduced. 

The results seem to point to the existence of two distinct factors inthe so-called 'constant error' in these cases: first, what we may callthe _bare constant error_, or simply the constant error, which appearswhen the conditions of stimulation are objectively the same as regardsboth intervals, and which we must suppose to be present in all othercases; and second, the particular lengthening effect which a change inlocality produces upon the interval in which it occurs. These twofactors may work in conjunction or in opposition, according toconditions. The bare constant error does not remain exactly the sameat all times for any individual and is probably less regular intactual time than in auditory or in optical time, according to theirregularity actually found and for reasons which will be assignedlater. 

3. The third group of experiments introduced the factor of variationin intensity of stimulation. By the introduction of a loop in thecircuit, containing a rheostat, two strengths of current andconsequently of stimulus intensity were obtained, either of whichcould be employed as desired. One intensity, designated as _W_, wasjust strong enough to be perceived distinctly. The other intensity, designated as _S_, was somewhat stronger than the intensity used inthe preceding work. 

In the first instance, sixty series were taken from Subject _B_, withthe conditions the same as in the experiments of Group 1, except thattwo types of series were taken; the first two stimulations beingstrong and the third one weak in the first type (_SSW_), and the orderbeing reversed in the second type (_WSS_). The results gave values of_ET_ of 5. 27 secs. For _SSW_ and 5. 9 secs. For _WSS_. 

In order to get comprehensive qualitative results as rapidly aspossible, a three-second standard was adopted in the succeeding workand only one compared interval, also three seconds, was given, although the subject was ignorant of that fact--the method being thussimilar to that adopted later for the final experiments of Group 2, described above. Six types of tests were given, the order ofstimulation in the different types being _SSS, WWW, SSW, WWS, SWW_ and_WSS_, the subject always knowing which order to expect. For each ofthe six types one hundred tests were made on one subject and onehundred and five on another, in sets of five tests of each type, thesets being taken in varied order, so that possible contrast effectshould be avoided. The results were practically the same, however, inwhatever order the sets were taken, no contrast effect beingdiscernible. 

The total number of judgments of _CT_, longer, equal, and shorter, isgiven in Table VIII. The experiments on each subject consumed a numberof experiment hours, scattered through several weeks, but the relativeproportions of judgments on different days was in both cases similarto the total proportions. 

TABLE VIII. 

 _ST=CT=_ 3. 0 SECS. 

 Subject _R_, 100. Subject _P_, 105. L E S d L E S d SSS 32 56 12 + 20 SSS 16 67 22 - 9 WWW 11 53 36 - 25 WWW 19 72 14 + 5 SSW 6 27 67 - 61 SSW 17 56 32 - 15 WWS 57 36 7 + 50 WWS 37 61 7 + 30 WSS 10 45 45 - 35 WSS 9 69 27 - 18 SWW 3 31 66 - 63 SWW 3 64 33 - 25

By the above table the absolute intensity of the stimulus is clearlyshown to be an important factor in determining the constant error ofjudgment, since in both cases the change from _SSS_ to _WWW_ changedthe sign of the constant error, although in opposite directions. Butthe effect of the relative intensity is more obscure. To discover morereadily whether the introduction of a stronger or weaker stimulationpromises a definite effect upon the estimation of the interval whichprecedes or follows it, the results are so arranged in Table IX. Thatreading downward in any pair shows the effect of a decrease in theintensity of (1) the first, (2) the second, (3) the third, and (4) allthree stimulations. 

TABLE IX. 

 Subject _R. _ Subject _P. _

 (1) _SSS_ + 20 - 6 _WSS_ - 35 - 55 - 18 - 12

 _SWW_ - 63 - 25 _WWW_ - 25 - 38 + 5 + 30

 (2) _SSW_ - 61 - 15 _SWW_ - 63 - 2 - 25 + 10

 _WSS_ - 35 - 18 _WWS_ + 50 + 85 + 30 - 48

 (3) _SSS_ + 20 - 6 _SSW_ - 61 - 81 - 15 - 7

 _WWS_ + 50 + 30 _WWW_ - 25 - 75 + 5 - 25

 (4) _SSS_ + 20 - 6 _WWW_ - 15 - 35 + 5 + 11

There seems at first sight to be no uniformity about these results. Decreasing the first stimulation in the first case increases, in thesecond case diminishes, the comparative length of the first interval. We get a similar result in the decreasing of the second stimulation. In the case of the third stimulation only does the decrease produce auniform result. If, however, we neglect the first pair of (3), weobserve that in the other cases the effect of a _difference_ betweenthe two stimulations is to lengthen the interval which they limit. Thefact that both subjects make the same exception is, however, strikingand suggestive of doubt. These results were obtained in the firstyear's work, and to test their validity the experiment was repeated atthe beginning of the present year on three subjects, fifty seriesbeing taken from each, with the results given in Table X. 

TABLE X. 

_ST_ = 3. 0 secs. = _CT_. 

 Subject _Mm. _ Subject _A. _ Subject _D. _

 S E L d S E L d S E L d SSS 24 13 13 - 11 7 30 13 + 6 10 31 9 - 1 WSS 33 9 8 - 25 20 24 6 - 14 17 27 6 - 11 SSW 19 15 16 - 3 23 16 11 - 12 10 31 9* - 1 WWW 19 12 19 0 13 26 11 - 2 1 40 9 + 8 SWW 18 30 2 - 16 23 21 6* - 17 7 38 5 - 2 WWS 13 16 21 + 8 12 30 8 - 4 15 25 10 - 5

 *Transcriber's Note: Original "16" changed to "6", "19" to "9". 

Analysis of this table shows that in every case a difference betweenthe intensities of the first and second taps lengthens the firstinterval in comparative estimation. In the case of subject _Mm_ adifference in the intensities of the second and third taps lengthensthe second interval subjectively. But in the cases of the other twosubjects the difference shortens the interval in varying degrees. 

The intensity difference established for the purposes of theseexperiments was not great, being less than that established for thework on the first two subjects, and therefore the fact that theseresults are less decided than those of the first work was notunexpected. The results are, however, very clear, and show that thelengthening effect of a difference in intensity of the stimulationslimiting an interval has its general application only to the firstinterval, being sometimes reversed in the second. From the combinedresults we find, further, that a uniform change in the intensity ofthree stimulations is capable of reversing the direction of theconstant error, an intensity change in a given direction changing theerror from positive to negative for some subjects, and from negativeto positive for others. 

III. INTERPRETATION OF RESULTS. 

We may say provisionally that the _change_ from a tactual stimulationof one kind to a tactual stimulation of another kind tends to lengthensubjectively the interval which the two limit. If we apply the samegeneralization to the other sensorial realms, we discover that itagrees with the general results obtained by Meumann[15] ininvestigating the effects of intensity changes upon auditory time, andalso with the results obtained by Schumann[16] in investigations withstimulations addressed alternately to one ear and to the other. Meumann reports also that the change from stimulation of one sense tostimulation of another subjectively lengthens the correspondinginterval. 

 [15] _op. Cit. _ (II. ), S. 289-297. 

 [16] _op. Cit. _, S. 67. 

What, then, are the factors, introduced by the change, which producethis lengthening effect? The results of introspection on the part ofsome of the subjects of our experiments furnish the clue which mayenable us to construct a working hypothesis. 

Many of the subjects visualize a time line in the form of a curve. Ineach case of this kind the introduction of a change, either inintensity or location, if large enough to produce an effect on thetime estimation, produced a distortion on the part of the curvecorresponding to the interval affected. All of the subjects employedin the experiments of Group 2 were distinctly conscious of the changein attention from one point to another, as the two were stimulatedsuccessively, and three of them, _Hy_, _Hs_ and _P_, thought ofsomething passing from one point to the other, the representationbeing described as partly muscular and partly visual. Subjects _Mr_and _B_ visualized the two hands, and consciously transferred theattention from one part of the visual image to the other. Subject _Mr_had a constant tendency to make eye movements in the direction of thechange. Subject _P_ detected these eye movements a few times, butsubject _B_ was never conscious of anything of the kind. 

All of the subjects except _R_ were conscious of more or less of a_strain_, which varied during the intervals, and was by some felt tobe largely a tension of the chest and other muscles, while others feltit rather indefinitely as a 'strain of attention. ' The characteristicsof this tension feeling were almost always different in the secondinterval from those in the first, the tension being usually felt to bemore _constant_ in the second interval. In experiments of the thirdgroup a higher degree of tension was felt in awaiting a light tap thanin awaiting a heavy one. 

Evidently, in all these cases, the effect of a _difference_ betweentwo stimulations was to introduce certain changes in sensation_during_ the interval which they limited, owing to the fact that thesubject expected the difference to occur. Thus in the third group ofexperiments there were, very likely, in all cases changes fromsensations of high tension to sensations of lower, or vice versa. Itis probable that, in the experiments of the second group, there werealso changes in muscular sensations, partly those of eye muscles, partly of chest and arm muscles, introduced by the change of attentionfrom one point to another. At any rate, it is certain that there werecertain sensation changes produced during the intervals by changes oflocality. 

If, then, we assume that the introduction of additional sensationchange into an interval lengthens it, we are led to the conclusionthat psychological time (as distinguished from metaphysical, mathematical, or transcendental time) is perceived simply as thequantum of change in the sensation content. That this is a trueconclusion is seemingly supported by the fact that when we wish tomake our estimate correspond as closely as possible with externalmeasurements, we exclude from the content, to the best of our ability, the general complex of external sensations, which vary with extremeirregularity; and confine the attention to the more uniformly varyingbodily sensations. We perhaps go even further, and inhibit certainbodily sensations, corresponding to activity of the more peripherallylocated muscles, that the attention may be confined to certain others. But attention to a dermal stimulation is precisely the condition whichwould tend to some extent to prevent this inhibition. For this reasonwe might well expect to find the error in estimation more variable, the 'constant error' in general greater, and the specific effects ofvariations which would affect the peripheral muscles, more marked in'tactual' time than in either 'auditory' or 'optical' time. Certainlyall these factors appear surprisingly large in these experiments. 

It is not possible to ascertain to how great an extent subject _Sh_inhibited the more external sensations, but certainly if he succeededto an unusual degree in so doing, that fact would explain the absenceof effect of stimulation difference in his case. 

Explanation has still to be offered for the variable effect ofintensity difference upon the _second_ interval. According to allsubjects except _Sn_, there is a radical difference in attitude in thetwo intervals. In the first interval the subject is merely observant, but in the second he is more or less reproductive. That is, hemeasures off a length which seems equal to the standard, and if thestimulation does not come at that point he is prepared to judge theinterval as 'longer, ' even before the third stimulation is given. Incases, then, where the judgment with equal intensities would be'longer, ' we might expect that the actual strengthening or weakeningof the final tap would make no difference, and that it would make verylittle difference in other cases. But even here the expectation of theintensity is an important factor in determining tension changes, although naturally much less so than in the first interval. So weshould still expect the lengthening of the second interval. 

We must remember, however, that, as we noticed in discussing theexperiments of Group 2, there is complicated with the lengtheningeffect of a change the _bare constant error_, which appears even whenthe three stimulations are similar in all respects except temporallocation. Compare _WWW_ with _SSS_, and we find that with all fivesubjects the constant error is decidedly changed, being even reversedin direction with three of the subjects. 

Now, what determines the direction of the constant error, where thereis no pause between the intervals? Three subjects reported that attimes there seemed to be a slight loss of time after the secondstimulation, owing to the readjustment called for by the change ofattitude referred to above, so that the second interval was begun, notreally at the second stimulation, but a certain period after it. Thisfact, if we assume it to be such, and also assume that it is presentto a certain degree in all observations of this kind, explains theapparent overestimation of the first interval. Opposed to the factorof _loss of time_ there is the factor of _perspective_, by which aninterval, or part of an interval, seems less in quantity as it recedesinto the past. The joint effect of these two factors determines theconstant error in any case where no pause is introduced between _ST_and _CT_. It is then perfectly obvious that, as the perspective factoris decreased by diminishing the intervals compared, the constant errormust receive positive increments, _i. E. _, become algebraicallygreater; which corresponds exactly with the results obtained byVierordt, Kollert, Estel, and Glass, that under ordinary conditionslong standard intervals are comparatively underestimated, and shortones overestimated. 

On the other hand, if with a given interval we vary the loss of time, we also vary the constant error. We have seen that a change in theintensity of the stimulations, although the relative intensity of thethree remains constant, produces this variation of the constant error;and the individual differences of subjects with regard to sensibility, power of attention and inhibition, and preferences for certainintensities, lead us to the conclusion that for certain subjectscertain intensities of stimulation make the transition from thereceptive attitude to the reproductive easiest, and, therefore, mostrapid. 

Now finally, as regards the apparent failure of the change in _SSW_ tolengthen the second interval, for which we are seeking to account; thecomparatively great loss of time occurring where the change ofattitude would naturally be most difficult (that is, where it iscomplicated with a change of attention from a strong stimulation tothe higher key of a weak stimulation) is sufficient to explain whywith most subjects the lengthening effect upon the second interval ismore than neutralized. The individual differences mentioned in thepreceding paragraph as affecting the relation of the two factorsdetermining the constant error, enter here of course to modify thejudgments and cause disagreement among the results for differentsubjects. 

Briefly stated, the most important points upon which this discussionhinges are thus the following: We have shown--

 1. That the introduction of either a local difference or a difference of intensity in the tactual stimulations limiting an interval has, in general, the effect of causing the interval to appear longer than it otherwise would appear. 

 2. That the apparent exceptions to the above rule are, (_a_) that the _increase_ of the local difference in the first interval, the stimulated areas remaining unchanged, produces a slight _decrease_ in the subjective lengthening of the interval, and (_b_) that in certain cases a difference in intensity of the stimulations limiting the second interval apparently causes the interval to seem shorter than it otherwise would. 

 3. That the 'constant error' of time judgment is dependent upon the intensity of the stimulations employed, although the three stimulations limiting the two intervals remain of equal intensity. 

To harmonize these results we have found it necessary to assume:

 1. That the length of a time interval is perceived as the amount of change in the sensation-complex corresponding to that interval. 

 2. That the so-called 'constant error' of time estimation is determined by two mutually opposing factors, of which the first is the _loss of time_ occasioned by the change of attitude at the division between the two intervals, and the second is the diminishing effect of _perspective_. 

 It is evident, however, that this last assumption applies only to the conditions under which the results were obtained, namely, the comparison of two intervals marked off by three brief stimulations. 

 * * * * *

PERCEPTION OF NUMBER THROUGH TOUCH. 

BY J. FRANKLIN MESSENGER. 

The investigation which I am now reporting began as a study of thefusion of touch sensations when more than two contacts were possible. As the work proceeded new questions came up and the inquiry broadenedso much that it seemed more appropriate to call it a study in theperception of number. 

The experiments are intended to have reference chiefly to threequestions: the space-threshold, fusion of touch sensations, and theperception of number. I shall deny the validity of a threshold, anddeny that there is fusion, and then offer a theory which attempts toexplain the phenomena connected with the determination of a thresholdand the problem of fusion and diffusion of touch sensations. 

The first apparatus used for the research was made as follows: Twouprights were fastened to a table. These supported a cross-bar aboutten inches from the table. To this bar was fastened a row of steelsprings which could be pressed down in the manner of piano keys. Toeach of these springs was fastened a thread which held a bullet. Thebullets, which were wrapped in silk to obviate temperature sensations, were thus suspended just above the fingers, two over each finger. Eachthread passed through a small ring which was held just a little abovethe fingers. These rings could be moved in any direction toaccommodate the bullet to the position of the finger. Any number ofthe bullets could be let down at once. The main object at first was tolearn something about the fusion of sensations when more than twocontacts were given. 

Special attention was given to the relation of the errors made whenthe fingers were near together to those made when the fingers werespread. For this purpose a series of experiments was made with thefingers close together, and then the series was repeated with thefingers spread as far as possible without the subject's feeling anystrain. Each subject was experimented on one hour a week for aboutthree months. The same kind of stimulation was given when the fingerswere near together as was given when they were spread. The figuresgiven below represent the average percentage of errors for foursubjects. 

Of the total number of answers given by all subjects when the fingerswere close together, 70 per cent. Were wrong. An answer was calledwrong whenever the subject failed to judge the number correctly. Inmaking out the figures I did not take into account the nature of theerrors. Whether involving too many or too few the answer was calledwrong. Counting up the number of wrong answers when the fingers werespread, I found that 28 per cent. Of the total number of answers werewrong. This means simply that when the fingers were near togetherthere were more than twice as many errors as there were when they werespread, in spite of the fact that each finger was stimulated in thesame way in each case. 

A similar experiment was tried using the two middle fingers only. Inthis case not more than four contacts could be made at once, and hencewe should expect a smaller number of errors, but we should expectstill to find more of them when the fingers are near together thanwhen they are spread. I found that 49 per cent. Of the answers werewrong when the fingers were near together and 20 per cent. Were wrongwhen they were spread. It happens that this ratio is approximately thesame as the former one, but I do not regard this fact as verysignificant. I state only that it is easier to judge in one case thanin the other; how much easier may depend on various factors. 

To carry the point still further I took only two bullets, one over thesecond phalanx of each middle finger. When the fingers were spread thetwo were never felt as one. When the fingers were together they wereoften felt as one. 

The next step was to investigate the effect of bringing together thefingers of opposite hands. I asked the subject to clasp his hands insuch a way that the second phalanges would be about even. I could notuse the same apparatus conveniently with the hands in this position, but in order to have the contacts as similar as possible to those Ihad been using, I took four of the same kind of bullets and fastenedthem to the ends of two ęsthesiometers. This enabled me to give fourcontacts at once. However, only two were necessary to show thatcontacts on fingers of opposite hands could be made to 'fuse' byputting the fingers together. If two contacts are given on contiguousfingers, they are quite as likely to be perceived as one when thefingers are fingers of opposite hands, as when they are contiguousfingers of the same hand. 

These results seem to show that one of the important elements offusion is the actual space relations of the points stimulated. Thereports of the subjects also showed that generally and perhaps alwaysthey located the points in space and then remembered what fingeroccupied that place. It was not uncommon for a subject to report acontact on each of two adjacent fingers and one in between where hehad no finger. A moment's reflection would usually tell him it must bean illusion, but the sensation of this illusory finger was as definiteas that of any of his real fingers. In such cases the subject seemedto perceive the relation of the points to each other, but failed toconnect them with the right fingers. For instance, if contacts weremade on the first, second and third fingers, the first might belocated on the first finger, the third on the second finger, and thenthe second would be located in between. 

So far my attention had been given almost entirely to fusion, but thetendency on the part of all subjects to report more contacts than wereactually given was so noticeable that I concluded that diffusion wasnearly as common as fusion and about as easy to produce. It alsoseemed that the element of weight might play some part, but just whateffect it had I was uncertain. I felt, too, that knowledge of theapparatus gained through sight was giving the subjects too much help. The subjects saw the apparatus every day and knew partly what toexpect, even though the eyes were closed when the contacts were made. A more efficient apparatus seemed necessary, and, therefore, beforetaking up the work again in 1900, I made a new apparatus. 

Not wishing the subjects to know anything about the nature of themachine or what could be done with it, I enclosed it in a box with anopening in one end large enough to allow the subject's hand to passthrough, and a door in the other end through which I could operate. Onthe inside were movable wooden levers, adjustable to hands ofdifferent width. These were fastened by pivotal connection at theproximal end. At the outer end of each of these was an upright stripwith a slot, through which was passed another strip which extendedback over the hand. This latter strip could be raised or lowered bymeans of adjusting screws in the upright strip. On the horizontalstrip were pieces of wood made so as to slide back and forth. Throughholes in these pieces plungers were passed. At the bottom of eachplunger was a small square piece of wood held and adjusted by screws. From this piece was suspended a small thimble filled with shot andparaffine. The thimbles were all equally weighted. Through a hole inthe plunger ran a thread holding a piece of lead of exactly the weightof the thimble. By touching a pin at the top this weight could bedropped into the thimble, thus doubling its weight. A screw at the topof the piece through which the plunger passed regulated the stop ofthe plunger. This apparatus had three important advantages. It wasentirely out of sight, it admitted of rapid and accurate adjustment, and it allowed the weights to be doubled quickly and withoutconspicuous effort. 

For the purpose of studying the influence of weight on the judgmentsof number I began a series of experiments to train the subjects tojudge one, two, three, or four contacts at once. For this the baremetal thimbles were used, because it was found that when they werecovered with chamois skin the touch was so soft that the subjectscould not perceive more than one or two with any degree of accuracy, and I thought it would take entirely too long to train them toperceive four. The metal thimbles, of course, gave some temperaturesensation, but the subject needed the help and it seemed best to usethe more distinct metal contacts. 

In this work I had seven subjects, all of whom had had some experiencein a laboratory, most of them several years. Each one took part onehour a week. The work was intended merely for training, but a fewrecords were taken each day to see how the subjects progressed. Theobject was to train them to perceive one, two, three, and fourcorrectly, and not only to distinguish four from three but todistinguish four from more than four. Hence five, six, seven, andeight at a time were often given. When the subject had learned to dothis fairly well the plan was to give him one, two, three, and four inorder, then to double the weight of the four and give them again tosee if he would interpret the additional weight as increase in number. This was done and the results were entirely negative. The subjectseither noticed no difference at all or else merely noticed that thesecond four were a little more distinct than the first. 

The next step was to give a number of light contacts to be comparedwith the same number of heavy ones--the subject, not trying to tellthe exact number but only which group contained the greater number. Adifference was sometimes noticed, and the subject, thinking that theonly variations possible were variations of number and position, ofteninterpreted the difference as difference in number; but the lightweights were as often called more as were the heavy ones. 

So far as the primary object of this part of the experiment isconcerned the results are negative, but incidentally the process oftraining brought out some facts of a more positive nature. It wasearly noticed that some groups of four were much more readilyrecognized than others, and that some of them were either judgedcorrectly or underestimated while others were either judged correctlyor overestimated. For convenience the fingers were indicated by theletters _A B C D_, _A_ being the index finger. The thumb was not used. Two weights were over each finger. The one near the base was called 1, the one toward the end 2. Thus _A12 B1 C2_ means two contacts on theindex finger, one near the base of the second finger, and one near theend of the third finger. The possible arrangements of four may bedivided into three types: (1) Two weights on each of two fingers, as_A12 B12, C12 D12_, etc. , (2) four in a line across the fingers, _A1B1 C1 D1_ or _A2 B2 C2 D2_, (3) unsymmetrical arrangements, as _A1 B2C1 D2_, etc. Arrangements of the first type were practically neveroverestimated. _B12 C12_ was overestimated once and _B12 D12_ wasoverestimated once, but these two isolated cases need hardly be takeninto account. Arrangements of the second type were but rarelyoverestimated--_A2 B2 C2 D2_ practically never, _A1 B1 C1 D1_ a fewtimes. Once the latter was called eight. Apparently the subjectperceived the line across the hand and thought there were two weightson each finger instead of one. Arrangements of the third type werepractically never underestimated, but were overestimated in 68 percent. Of the cases. 

These facts in themselves are suggestive, but equally so was thebehavior of the subject while making the answers. It would have hardlydone to ask the person if certain combinations were hard to judge, forthe question would serve as a suggestion to him; but it was easy totell when a combination was difficult without asking questions. When asymmetrical arrangement was given, the subject was usually composedand answered without much hesitation. When an unsymmetricalarrangement was given he often hesitated and knit his brows or perhapsused an exclamation of perplexity before answering, and after givinghis answer he often fidgeted in his chair, drew a long breath, or insome way indicated that he had put forth more effort than usual. Itmight be expected that the same attitude would be taken when six oreight contacts were made at once, but in these cases the subject waslikely either to fail to recognize that a large number was given or, if he did, he seemed to feel that it was too large for him to perceiveat all and would guess at it as well as he could. But when only fourwere given, in a zigzag arrangement, he seemed to feel that he oughtto be able to judge the number but to find it hard to do so, andknowing from experience that the larger the number the harder it is tojudge he seemed to reason conversely that the more effort it takes tojudge the more points there are, and hence he would overestimate thenumber. 

The comments of the subjects are of especial value. One subject (Mr. Dunlap) reports that he easily loses the sense of location of hisfingers, and the spaces in between them seem to belong to him as muchas do his fingers themselves. When given one touch at a time and toldto raise the finger touched he can do so readily, but he says he doesnot know which finger it is until he moves it. He feels as if hewilled to move the place touched without reference to the fingeroccupying it. He sometimes hesitates in telling which finger it is, and sometimes he finds out when he moves a finger that it is not theone he thought it was. 

Another subject (Dr. MacDougall) says that his fingers seem to himlike a continuous surface, the same as the back of his hand. Heusually named the outside points first. When asked about the order inwhich he named them, he said he named the most distinct ones first. Once he reported that he felt six things, but that two of them were inthe same places as two others, and hence he concluded there were butfour. This feeling in a less careful observer might lead tooverestimation of number and be called diffusion, but all cases ofoverestimation cannot be explained that way, for it does not explainwhy certain combinations are so much more likely to lead to it thanothers. 

In one subject (Mr. Swift) there was a marked tendency to locatepoints on the same fingers. He made many mistakes about fingers _B_and _C_ even when he reported the number correctly. When _B_ and _D_were touched at the same time he would often call it _C_ and _D_, andwhen _C_ and _D_ were given immediately afterward he seemed to noticeno difference. With various combinations he would report _C_ when _B_was given, although _C_ had not been touched at the same time. If _B_and _C_ were touched at the same time he could perceive them wellenough. 

The next part of the research was an attempt to discover whether aperson can perceive any difference between one point and two pointswhich feel like one. A simple little experiment was tried with theęsthesiometer. The subjects did not know what was being used, and wereasked to compare the relative size of two objects placed on the backof the hand in succession. One of these objects was one knob of theęsthesiometer and the other was two knobs near enough together to liewithin the threshold. The distance of the points was varied from 10 to15 mm. Part of the time the one was given first and part of the timeboth were given together. The one, whether given first or second, wasalways given about midway between the points touched by the two. Ifthe subject is not told to look for some specific difference he willnot notice any difference between the two knobs and the one, and hewill say they are alike; but if he is told to give particularattention to the size there seems to be a slight tendency to perceivea difference. The subjects seem to feel very uncertain about theiranswers, and it looks very much like guess-work, but something causedthe guesses to go more in one direction than in the other. 

 Two were called less than one . . . . 16% of the times given. " " " equal to . . . . 48% " " " " " greater than . . . . 36% " "

Approximately half of the time two were called equal to one, and ifthere had been no difference in the sensations half of the remainingjudgments should have been that two was smaller than one, but two werecalled larger than one more than twice as many times as one was calledlarger than two. There was such uniformity in the reports of thedifferent subjects that no one varied much from this average ratio. 

This experiment seems to indicate a very slight power ofdiscrimination of stimulations within the threshold. In strikingcontrast to this is the power to perceive variations of distancebetween two points outside the threshold. To test this theęsthesiometer was spread enough to bring the points outside thethreshold. The back of the hand was then stimulated with the twopoints and then the distance varied slightly, the hand touched and thesubject asked to tell which time the points were farther apart. Adifference of 2 mm. Was usually noticed, and one of from 3 to 5 mm. Was noticed always very clearly. 

I wondered then what would be the result if small cards set parallelto each other were used in place of the knobs of the ęsthesiometer. Imade an ęsthesiometer with cards 4 mm. Long in place of knobs. Thesecards could be set at any angle to each other. I set them at first 10mm. Apart and parallel to each other and asked the subjects to comparethe contact made by them with a contact by one card of the same size. The point touched by the one card was always between the pointstouched by the two cards, and the one card was put down so that itsedge would run in the same direction as the edges of the other cards. The result of this was that:

 Two were called less, 14 per cent. " " " equal, 36 " " " " " greater, 50 " "

I then increased the distance of the two cards to 15 mm. , the otherconditions remaining the same, and found that:

 Two were called less, 11 per cent. " " " equal, 50 " " " " " greater, 39 " "

It will be noticed that the ratio in this last series is notmaterially different from the ratio found when the two knobs of theęsthesiometer were compared with one knob. The ratio found when thedistance was 10 mm. , however, is somewhat different. At that distancetwo were called greater half of the time, while at 15 mm. Two werecalled equal to one half of the time. The explanation of thedifference, I think, is found in the comments of one of my subjects. Idid not ask them to tell in what way one object was larger than theother--whether longer or larger all around or what--but simply toanswer 'equal, ' 'greater, ' or 'less. ' One subject, however, frequentlyadded more to his answers. He would often say 'larger crosswise' or'larger lengthwise' of his hand. And a good deal of the time hereported two larger than one, not in the direction in which it reallywas larger, but the other way. It seems to me that when the two cardswere only 10 mm. Apart the effect was somewhat as it would be if asolid object 4 mm. Wide and 10 mm. Long had been placed on the hand. Such an object would be recognized as having greater mass than a line4 mm. Long. But when the distance is 15 mm. The impression is lesslike that of a solid body but still not ordinarily like two objects. 

In connection with the subject of diffusion the _Vexirfehler_ is ofinterest. An attempt was made to develop the _Vexirfehler_ with theęsthesiometer. Various methods were tried, but the following was mostsuccessful. I would tell the subject that I was going to use theęsthesiometer and ask him to close his eyes and answer simply 'one' or'two. ' He would naturally expect that he would be given part of thetime one, and part of the time two. I carefully avoided any suggestionother than that which could be given by the ęsthesiometer itself. Iwould begin on the back of the hand near the wrist with the points asnear the threshold as they could be and still be felt as two. At eachsuccessive putting down of the instrument I would bring the points alittle nearer together and a little lower down on the hand. By thetime a dozen or more stimulations had been given I would be workingdown near the knuckles, and the points would be right together. Fromthat on I would use only one point. It might be necessary to repeatthis a few times before the illusion would persist. A great deal seemsto depend on the skill of the operator. It would be noticed that thefirst impression was of two points, and that each stimulation was sonearly like the one immediately preceding that no difference could benoticed. The subject has been led to call a thing two which ordinarilyhe would call one, and apparently he loses the distinction between thesensation of one and the sensation of two. After going through theprocedure just mentioned I put one knob of the ęsthesiometer down onehundred times in succession, and one subject (Mr. Meakin) called ittwo seventy-seven times and called it one twenty-three times. Four ofthe times that he called it one he expressed doubt about his answerand said it might be two, but as he was not certain he called it one. Another subject (Mr. George) called it two sixty-two times and onethirty-eight times. A third subject (Dr. Hylan) called it twoseventy-seven times and one twenty-three times. At the end of theseries he was told what had been done and he said that most of hissensations of two were perfectly distinct and he believed that he wasmore likely to call what seemed somewhat like two one, than to callwhat seemed somewhat like one two. With the fourth subject (Mr. Dunlap) I was unable to do what I had done with the others. I couldget him to call one two for four or five times, but the idea of twowould not persist through a series of any length. He would call it twowhen two points very close together were used. I could bring the knobswithin two or three millimeters of each other and he would report two, but when only one point was used he would find out after a very fewstimulations were given that it was only one. After I had given up theattempt I told him what I had been trying to do and he gave what seemsto me a very satisfactory explanation of his own case. He says theearly sensations keep coming up in his mind, and when he feels likecalling a sensation two he remembers how the first sensation felt andsees that this one is not like that, and hence he calls it one. I passnow to a brief discussion of what these experiments suggest. 

It has long been known that two points near together on the skin areoften perceived as one. It has been held that in order to be felt astwo they must be far enough apart to have a spatial character, andhence the distance necessary for two points to be perceived has beencalled the 'space-threshold. ' This threshold is usually determinedeither by the method of minimal changes or by the method of right andwrong cases. 

If, in determining a threshold by the method of minimal changes--onthe back of the hand, for example, we assume that we can begin theascending series and find that two are perceived as one always untilthe distance of twenty millimeters is reached, and that in thedescending series two are perceived as two until the distance of tenmillimeters is reached, we might then say that the threshold issomewhere between ten and twenty millimeters. But if the results werealways the same and always as simple as this, still we could not saythat there is any probability in regard to the answer which would bereceived if two contacts 12, 15, or 18 millimeters apart were given bythemselves. All we should know is that if they form part of anascending series the answer will be 'one, ' if part of a descendingseries 'two. '

The method of right and wrong cases is also subject to seriousobjections. There is no lower limit, for no matter how close togethertwo points are they are often called two. If there is any upper limitat all, it is so great that it is entirely useless. It might be arguedthat by this method a distance could be found at which a givenpercentage of answers would be correct. This is quite true, but ofwhat value is it? It enables one to obtain what one arbitrarily callsa threshold, but it can go no further than that. When the experimentchanges the conditions change. The space may remain the same, but itis only one of the elements which assist in forming the judgment, andits importance is very much overestimated when it is made the basisfor determining the threshold. 

Different observers have found that subjects sometimes describe asensation as 'more than one, but less than two. ' I had a subject whohabitually described this feeling as 'one and a half. ' This does notmean that he has one and a half sensations. That is obviouslyimpossible. It must mean that the sensation seems just as much liketwo as it does like one, and he therefore describes it as half waybetween. If we could discover any law governing this feeling ofhalf-way-between-ness, that might well indicate the threshold. Butsuch feelings are not common. Sensations which seem between one andtwo usually call forth the answer 'doubtful, ' and have a negativerather than a positive character. This negative character cannot bedue to the stimulus; it must be due to the fluctuating attitudes ofthe subject. However, if the doubtful cases could be classed with the'more than one but less than two' cases and a law be found governingthem, we might have a threshold mark. But such a law has not beenformulated, and if it had been an analysis of the 'doubtful' caseswould invalidate it. For, since we cannot have half of a sensation orhalf of a place as we might have half of an area, the subject regardseach stimulation as produced by one or by two points as the case maybe. Occasionally he is stimulated in such a way that he can regard theobject as two or as one with equal ease. In order to describe thisfeeling he is likely to use one or the other of the methods justmentioned. 

We might say that when the sum of conditions is such that the subjectperceives two points, the points are above the threshold, and when thesubject perceives one point when two are given they are below thethreshold. This might answer the purpose very well if it were not forthe _Vexirfehler_. According to this definition, when the_Vexirfehler_ appears we should have to say that one point is abovethe threshold for twoness, which is a queer contradiction, to say theleast. It follows that all of the elaborate and painstakingexperiments to determine a threshold are useless. That is, thethreshold determinations do not lead us beyond the determinationsthemselves. 

In order to explain the fact that a person sometimes fails todistinguish between one point and two points near together, it hasbeen suggested that the sensations fuse. This, I suppose, means eitherthat the peripheral processes coalesce and go to the center as asingle neural process, or that the process produced by each stimulusgoes separately to the brain and there the two set up a singleactivity. Somewhat definite 'sensory circles, ' even, were oncebelieved in. 

If the only fact we had to explain was that two points are oftenthought to be one when they are near together, 'fusion' might be agood hypothesis, but we have other facts to consider. If this one isexplained by fusion, then the mistaking of one point for two must bedue to diffusion of sensations. Even that might be admissible if the_Vexirfehler_ were the only phenomenon of this class which we met. Butit is also true that several contacts are often judged to be more thanthey actually are, and that hypothesis will not explain why certainarrangements of the stimulating objects are more likely to bring aboutthat result than others. Still more conclusive evidence againstfusion, it seems to me, is found in the fact that two points, one oneach hand, may be perceived as one when the hands are broughttogether. Another argument against fusion is the fact that two pointspressed lightly may be perceived as one, and when the pressure isincreased they are perceived as two. Strong pressures should fusebetter than weak ones, and therefore fusion would imply the oppositeresults. Brückner[1] has found that two sensations, each too weak tobe perceived by itself, may be perceived when the two are givensimultaneously and sufficiently near together. This reėnforcement ofsensations he attributes to fusion. But we have a similar phenomenonin vision when a group of small dots is perceived, though each dot byitself is imperceptible. No one, I think, would say this is due tofusion. It does not seem to me that we need to regard reėnforcement asan indication of fusion. 

 [1] Brückner, A. : 'Die Raumschwelle bei Simultanreizung, ' _Zeitschrift für Psychologie_, 1901, Bd. 26, S. 33. 

My contention is that the effects sometimes attributed to fusion anddiffusion of sensations are not two different kinds of phenomena, butare identical in character and are to be explained in the same way. 

Turning now to the explanation of the special experiments, we maybegin with the _Vexirfehler_. [2] It seems to me that the _Vexirfehler_is a very simple phenomenon. When a person is stimulated with twoobjects near together he attends first to one and then to the otherand calls it two; then when he is stimulated with one object heattends to it, and expecting another one near by he hunts for it andhits upon the same one he felt before but fails to remember that it isthe same one, and hence thinks it is another and says he has felt twoobjects. Observers agree that the expectation of two tends to bringout the _Vexirfehler_. This is quite natural. A person who expects twoand receives one immediately looks about for the other without waitingto fixate the first, and therefore when he finds it again he is lesslikely to recognize it and more likely to think it another point andto call it two. Some observers[3] have found that the apparentdistance of the two points when the _Vexirfehler_ appears never muchexceeds the threshold distance. Furthermore, there being no distinctline of demarcation between one and two, there must be many sensationswhich are just about as much like one as they are like two, and hencethey must be lumped off with one or the other group. To themathematician one and two are far apart in the series because he hasfractions in between, but we perceive only in terms of whole numbers;hence all sensations which might more accurately be represented byfractions must be classed with the nearest whole number. A sensationis due to a combination of factors. In case of the _Vexirfehler_ oneof these factors, viz. , the stimulating object, is such as to suggestone, but some of the other conditions--expectation, precedingsensation, perhaps blood pressure, etc. --suggest two, so that thesensation as a whole suggests _one-plus_, if we may describe it thatway, and hence the inference that the sensation was produced by twoobjects. 

 [2] Tawney, Guy A. : 'Ueber die Wahrnehmung zweier Punkte mittelst des Tastsinnes mit Rücksicht auf die Frage der Uebung und die Entstehung der Vexirfehler, ' _Philos. Stud. _, 1897, Bd. XIII. , S. 163. 

 [3] See Nichols: 'Number and Space, ' p. 161. Henri, V. , and Tawney, G. : _Philos. Stud. _, Bd. XI. , S. 400. 

This, it seems to me, may account for the appearance of the_Vexirfehler_, but why should not the subject discover his error bystudying the sensation more carefully? He cannot attend to two thingsat once, nor can he attend to one thing continuously, even for a fewseconds. What we may call continuous attention is only a succession ofattentive impulses. If he could attend to the one object continuouslyand at the same time hunt for the other, I see no reason why he shouldnot discover that there is only one. But if he can have only onesensation at a time, then all he can do is to associate thatparticular sensation with some idea. In the case before us heassociates it with the idea of the number two. He cannot conceive oftwo objects unless he conceives them as located in two differentplaces. Sometimes a person does find that the two objects of hisperception are both in the same place, and when he does so heconcludes at once that there is but one object. At other times hecannot locate them so accurately, and he has no way of finding out thedifference, and since he has associated the sensation with the idea oftwo he still continues to call it two. If he is asked to locate thepoints on paper he fills out the figure just as he fills out theblind-spot, and he can draw them in just the same way that he can drawlines which he thinks he _sees_ with the blind-spot, but which reallyhe only _infers_. 

Any sensation, whether produced by one or by many objects, is one, butthere may be a difference in the quality of a sensation produced byone object and that of a sensation produced by more than one object. If this difference is clear and distinct, the person assigns to eachsensation the number he has associated with it. He gives it the nametwo when it has the quality he has associated with that idea. But thequalities of a sensation from which the number of objects producing itis inferred are not always clear and distinct. The quality of thesensation must not be confused with any quality of the object. If wehad to depend entirely on the sense of touch and always remainedpassive and received sensations only when we were touched bysomething, there is no reason why we should not associate the idea ofone with the sensation produced by two objects and the idea of twowith that produced by one object--assuming that we could have any ideaof number under such circumstances. The quality of a sensation fromwhich number is inferred depends on several factors. The number itselfis determined by the attitude of the subject, but the attitude isdetermined largely by association. A number of facts show this. When aperson is being experimented on, it is very easy to confuse him andmake him forget how two feel and how one feels. I have often had asubject tell me that he had forgotten and ask me to give him twodistinctly that he might see how it felt. In other words, he hadforgotten how to associate his ideas and sensations. In developing the_Vexirfehler_ I found it much better, after sufficient training hadbeen given, not to give two at all, for it only helped the subject toperceive the difference between two and one by contrast. But when onewas given continually he had no such means of contrast, and havingassociated the idea of two with a sensation he continued to do so. Theone subject with whom I did not succeed in developing the_Vexirfehler_ to any great extent perceived the difference bycomparing the sensation with one he had had some time before. I couldget him, for a few times, to answer two when only one was given, buthe would soon discover the difference, and he said he did it bycomparing it with a sensation which he had had some time before andwhich he knew was two. By this means he was able to make correctassociations when otherwise he would not have done so. It has beendiscovered that when a subject is being touched part of the time withtwo and part of the time with one, and the time it takes him to makehis judgments is being recorded, he will recognize two more quicklythan he will one if there is a larger number of twos in the seriesthan there is of ones. I do not see how this could be if the sensationof two is any more complex than that of one. But if both sensationsare units and all the subject needs to do is to associate thesensation with an idea, then we should expect that the association hehad made most frequently would be made the most quickly. 

If the feeling of twoness or of oneness is anything but an inference, why is it that a person can perceive two objects on two fingers whichare some distance apart, but perceives the same two objects as onewhen the fingers are brought near together and touched in the sameway? It is difficult to see how bringing the fingers together couldmake a sensation any less complex, but it would naturally lead aperson to infer one object, because of his previous associations. Hehas learned to call that _one_ which seems to occupy one place. If twocontacts are made in succession he will perceive them as two becausethey are separated for him by the time interval and he can perceivethat they occupy different places. 

When two exactly similar contacts are given and are perceived as one, we cannot be sure whether the subject feels only one of the contactsand does not feel the other at all, or feels both contacts and thinksthey are in the same place, which is only another way of saying hefeels both as one. It is true that when asked to locate the point heoften locates it between the two points actually touched, but eventhis he might do if he felt but one of the points. To test the matterof errors of localization I have made a few experiments in theColumbia University laboratory. In order to be sure that the subjectfelt both contacts I took two brass rods about four inches long, sharpened one end and rounded off the other. The subject sat with thepalm of his right hand on the back of his left and his fingersinterlaced. I stimulated the back of his fingers on the secondphalanges with the sharp end of one rod and the blunt end of the otherand asked him to tell whether the sharp point was to the right or tothe left of the other. I will not give the results in detail here, butonly wish to mention a few things for the purpose of illustrating thepoint in question. Many of the answers were wrong. Frequently thesubject would say both were on the same finger, when really they wereon fingers of opposite hands, which, however, in this position wereadjacent fingers. Sometimes when this happened I would ask him whichfinger they were on, and after he had answered I would leave the pointon the finger on which he said both points were and move the otherpoint over to the same finger, then move it back to its originalposition, then again over to the finger on which the other point wasresting, and so on, several times. The subject would tell me that Iwas raising one point and putting it down again in the same place allof the time. Often a subject would tell me he felt both points on thesame finger, but that he could not tell to which hand the fingerbelonged. When two or more fingers intervened between the fingerstouched no subject ever had any difficulty in telling which was thesharp and which the blunt point, but when adjacent fingers weretouched it was very common for the subject to say he could not tellwhich was which. This cannot be because there is more difference inthe quality of the contacts in one case than in the other. If theywere on the same finger it might be said that they were stimulatingthe same general area, but since one is on one hand and one on theother this is impossible. The subject does not think the two pointsare in the same place, because he feels two qualities and hence heinfers two things, and he knows two things cannot be in the same placeat the same time. If the two contacts were of the same qualityprobably they would be perceived as one on account of the absence ofdifference, for the absence of difference is precisely the quality ofoneness. 

These facts, together with those mentioned before, seem to me toindicate that errors of localization are largely responsible forjudgments which seem to be due to fusion or diffusion of sensations. But they are responsible only in this way, they prevent the correctionof the first impression. I do not mean that a person never changes hisjudgment after having once made it, but a change of judgment is notnecessarily a correction. Often it is just the contrary. But where awrong judgment is made and cannot be corrected inability to localizeis a prominent factor. This, however, is only a secondary factor inthe perception of number. The cardinal point seems to me thefollowing:

Any touch sensation, no matter by how many objects it is produced, isone, and number is an inference based on a temporal series ofsensations. It may be that we can learn by association to infer numberimmediately from the quality of a sensation, but that means only thatwe recognize the sensation as one we have had before and have found itconvenient to separate into parts and regard one part after the other, and we remember into how many parts we separated it. This separatinginto parts is a time process. What we shall regard as _one_ is a merematter of convenience. Continuity sometimes affords a convenient basisfor unity and sometimes it does not. There is no standard of onenessin the objective world. We separate things as far as convenience ortime permits and then stop and call that _one_ which our own attitudehas determined shall be one. 

That we do associate a sensation with whatever idea we have previouslyconnected it with, even though that idea be that of the number ofobjects producing it, is clearly shown by some experiments which Iperformed in the laboratory of Columbia University. I took threelittle round pieces of wood and set them in the form of a triangle. Iasked the subject to pass his right hand through a screen and told himI wanted to train him to perceive one, two, three and four contacts ata time on the back of his hand, and that I would tell him always howmany I gave him until he learned to do it. When it came to three Igave him two points near the knuckles and one toward the wrist andtold him that was three. Then I turned the instrument around and gavehim one point near the knuckles and two toward the wrist and told himthat was four. As soon as he was sure he distinguished all of thepoints I stopped telling him and asked him to answer the number. I hadfour subjects, and each one learned very soon to recognize the fourcontacts when three were given in the manner mentioned above. I thenrepeated the same thing on the left hand, except that I did not tellhim anything, but merely asked him to answer the number of contacts hefelt. In every case the idea of four was so firmly associated withthat particular kind of a sensation that it was still called four whengiven on the hand which had not been trained. I gave each subject adiagram of his hand and asked him to indicate the position of thepoints when three were given and when four were given. This was donewithout difficulty. Two subjects said they perceived the four contactsmore distinctly than the three, and two said they perceived the threemore distinctly than the four. 

It seems very evident that the sensation produced by three contacts isno more complex when interpreted as four than when interpreted asthree. If that is true, then it must also be evident that thesensation produced by one contact is no more complex when interpretedas two than when interpreted as one. The converse should also be true, that the sensation produced by two contacts is no less complex wheninterpreted as one than when interpreted as two. Difference in numberdoes not indicate difference in complexity. The sensation of four isnot made up of four sensations of one. It is a unit as much as thesensation of one is. 

There remains but one point to be elaborated. If number is not aquality of objects, but is merely a matter of attitude of the subject, we should not expect to find a very clear-cut line of demarcationbetween the different numbers except with regard to those things whichwe constantly consider in terms of number. Some of our associationsare so firmly established and so uniform that we are likely to regardthem as necessary. It is not so with our associations of number andtouch sensations. We have there only a vague, general notion of whatthe sensation of one or two is, because usually it does not make muchdifference to us, yet some sensations are so well established in ourminds that we call them one, two or four as the case may be withouthesitation. Other sensations are not so, and it is difficult to tellto which class they belong. Just so it is easy to tell a pure yellowcolor from a pure orange, yet they shade into each other, so that itis impossible to tell where one leaves off and the other begins. If wecould speak of a one-two sensation as we speak of a yellow-orangecolor we might be better able to describe our sensations. It would, indeed, be convenient if we could call a sensation which seems likeone with a suggestion of two about it a two-one sensation, and onethat seems nearly like two but yet suggests one a one-two sensation. Since we cannot do this, we must do the best we can and describe asensation in terms of the number it most strongly suggests. Subjectsvery often, as has been mentioned before, describe a sensation as'more than one but less than two, ' but when pressed for an answer willsay whichever number it most resembles. A person would do the samething if he were shown spectral colors from orange to yellow and toldto name each one either orange or yellow. At one end he would be sureto say orange and at the other yellow, but in the middle of the serieshis answers would likely depend upon the order in which the colorswere shown, just as in determining the threshold for the perception oftwo points by the method of minimal changes the answers in theascending series are not the same as those in the descending series. The experiments have shown that the sensation produced by two points, even when they are called one, is not the same as that produced byonly one point, but the difference is not great enough to suggest adifferent number. 

If the difference between one and two were determined by the distance, then the substitution of lines for knobs of the ęsthesiometer ought tomake no difference. And if the sensations produced by two objects fusewhen near together, then the sensations produced by lines ought tofuse as easily as those produced by knobs. 

In regard to the higher numbers difficulties will arise unless we takethe same point of view and say that number is an inference from asensation which is in itself a unit. It has been shown that fourpoints across the ends of the fingers will be called four or less, andthat four points, one on the end of each alternate finger and one atthe base of each of the others, will be called four or more--usuallymore. In either case each contact is on a separate finger, and it ishardly reasonable to suppose there is no diffusion when they are in astraight row, but that when they are in irregular shape there isdiffusion. It is more probable that the subject regards the sensationproduced by the irregular arrangement as a novelty, and tries toseparate it into parts. He finds both proximal and distal ends of hisfingers concerned. He may discover that the area covered extends fromhis index to his little finger. He naturally infers, judging from pastexperience, that it would take a good many points to do that, andhence he overestimates the number. When a novel arrangement was given, such as moving some of the weights back on the wrist and scatteringothers over the fingers, very little idea of number could be gotten, yet they were certainly far enough apart to be felt one by one if aperson could ever feel them that way, and the number was not so greatas to be entirely unrecognizable. 

 * * * * *

THE SUBJECTIVE HORIZON. 

BY ROBERT MACDOUGALL. 

I. 

The general nature of the factors which enter into the orientation ofthe main axes of our bodies, under normal and abnormal conditions, hasbeen of much interest to the psychologist in connection with theproblem of the development of space and movement perception. Thespecial points of attack in this general investigation have comprised, firstly, the separation of resident, or organic, from transient, orobjective, factors; secondly, the determination of the special organicfactors which enter into the mechanism of judgment and their severalvalues; and thirdly, within this latter field, the resolution of theproblem of a special mechanism of spatial orientation, the organ ofthe static sense. 

The special problem with which we are here concerned relates to thegroup of factors upon which depends one's judgment that any specifiedobject within the visual field lies within the horizontal plane of theeyes, or above or below that plane, and the several functions andvalues of these components. The method of procedure has been suggestedby the results of preceding investigations in this general field. 

The first aim of the experiments was to separate the factors ofresident and transient sensation, and to determine the part played bythe presence of a diversified visual field. To do so it was necessaryto ascertain, for each member of the experimental group, the locationof the subjective visual horizon, and the range of uncertainty in theobserver's location of points within that plane. Twelve observers inall took part in the investigation. In the first set of experiments noattempt was made to change the ordinary surroundings of the observer, except in a single point, namely, the provision that there should beno extended object within range of the subject's vision havinghorizontal lines on a level with his eyes. 

The arrangements for experimentation were as follows: A black woodenscreen, six inches wide and seven feet high, was mounted between twovertical standards at right angles to the axis of vision of theobserver. Vertically along the center of this screen and over pulleysat its top and bottom passed a silk cord carrying a disc of whitecardboard, 1 cm. In diameter, which rested against the black surfaceof the screen. From the double pulley at the bottom of the frame thetwo ends of the cord passed outward to the observer, who, by pullingone or the other, could adjust the disc to any desired position. Onthe opposite side of the screen from the observer was mounted avertical scale graduated in millimeters, over which passed a lightindex-point attached to the silk cord, by means of which the positionof the cardboard disc in front was read off. The observer was seatedin an adjustable chair with chin and head rests, and a lateralsighting-tube by which the position of the eyeball could be verticallyand horizontally aligned. The distance from the center of the eyeballto the surface of the screen opposite was so arranged that, neglectingthe radial deflection, a displacement of 1 mm. In either direction wasequal to a departure of one minute of arc from the plane of the eyes'horizon. 

The observer sat with the light at his back, and by manipulation ofthe cords adjusted the position of the white disc freely up and downthe screen until its center was judged to be on a level with the eye. Its position was then read off the vertical scale by the conductor(who sat hidden by an interposed screen), and the error of judgmentwas recorded in degrees and fractions as a positive (upward) ornegative (downward) displacement. The disc was then displacedalternately upward and downward, and the judgment repeated. From thetime of signalling that the point had been located until thisdisplacement the observer sat with closed eyes. These determinationswere made in series of ten, and the individual averages are in generalbased upon five such series, which included regularly the results ofsittings on different days. In some cases twice this number ofjudgments were taken, and on a few occasions less. The number ofjudgments is attached to each series of figures in the tables. In thatwhich follows the individual values and their general averages aregiven as minutes of arc for (_a_) the constant error or position ofthe subjective horizon, (_b_) the average deviation from the objectivehorizon, and (_c_) the mean variation of the series of judgments. 

TABLE I. 

 Observer. Constant Error. Average Deviation. Mean Variation. _A_ (100) -19. 74 38. 78 10. 67 _C_ (90) -18. 18 23. 89 10. 82 _D_ (100) -19. 84 33. 98 7. 95 _E_ (50) - 4. 28 72. 84 6. 90 _F_ (100) +46. 29 46. 29 2. 05 _G_ (50) +14. 96 35. 40 8. 40 _H_ (50) -27. 22 27. 46 5. 78 _I_ (50) + 6. 62 53. 34 7. 45 _K_ (50) + 1. 08 30. 26 6. 59 _L_ (20) -56. 70 56. 70 10. 39

 Average: -7. 70 41. 89 7. 69

The average subjective horizon shows a negative displacement, theexceptional minority being large. No special facts could be connectedwith this characteristic, either in method of judgment or in the pasthabits of the reactor. The average constant error is less than aneighth of a degree, and in neither direction does the extreme reachthe magnitude of a single degree of arc. Since the mean variation islikewise relatively small, there is indicated in one's ordinaryjudgments of this kind a highly refined sense of bodily orientation inspace. 

II. 

In order to separate the resident organic factors from those presentedby the fixed relations of the external world, an adaptation of themechanism was made for the purpose of carrying on the observations ina darkened room. For the cardboard disc was substituted a lightcarriage, riding upon rigid parallel vertical wires and bearing aminiature ground-glass bulb enclosing an incandescent electric lightof 0. 5 c. P. This was encased in a chamber with blackened surfaces, having at its center an aperture one centimeter in diameter, which wascovered with white tissue paper. The subdued illumination of thisdisc presented as nearly as possible the appearance of that used inthe preceding series of experiments. No other object than this spot ofmoving light was visible to the observer. Adjustment and record weremade as before. The results for the same set of observers as in thepreceding case are given in the following table:

TABLE II. 

 Subject. Constant Error. Average Deviation. Mean Variation. _A_ (50) - 52. 76 55. 16 30. 08 _C_ (30) - 7. 40 42. 00 35. 31 _D_ (50) - 14. 24 38. 60 30. 98 _E_ (50) - 43. 12 86. 44 30. 19 _F_ (100) - 2. 01 72. 33 20. 27 _G_ (100) - 21. 89 47. 47 32. 83 _H_ (50) - 1. 62 59. 10 29. 95 _I_ (50) - 32. 76 41. 60 24. 40 _K_ (50) - 61. 70 100. 02 52. 44 _L_ (40) -128. 70 128. 90 27. 83

 Average: - 36. 62 67. 16 31. 43

Changes in two directions may be looked for in the results as theexperimental conditions are thus varied. The first is a decrease inthe certainty of judgment due to the simple elimination of certainfactors upon which the judgment depends. The second is the appearanceof definite types of error due to the withdrawal of certaincorrectives of organic tendencies which distort the judgment inspecific directions. The loss in accuracy is great; the mean variationincreases from 7. 69 to 31. 43, or more than 400 per cent. This largeincrease must not, however, be understood as indicating a simplereduction in the observer's capacity to locate points in thehorizontal plane of the eyes. The two series are not directlycomparable; for in the case of the lighted room, since the wholevisual background remained unchanged, each determination must beconceived to influence the succeeding judgment, which becomes really acorrection of the preceding. To make the two series strictly parallelthe scenery should have been completely changed after each act ofjudgment. Nevertheless, a very large increase of uncertainty mayfairly be granted in passing from a field of visual objects to asingle illuminated point in an otherwise dark field. It is probablethat this change is largely due to the elimination of those elementsof sensation depending upon the relation of the sagittal axis to theplane against which the object is viewed. 

The change presented by the constant error can here be interpretedonly speculatively. I believe it is a frequently noted fact that thelights in a distant house or other familiar illuminated object onland, and especially the signal lights on a vessel at sea appearhigher than their respective positions by day, to the degree at timesof creating the illusion that they hang suspended above the earth orwater. This falls in with the experimental results set forth in thepreceding table. It cannot be attributed to an uncomplicated tendencyof the eyes of a person seated in such a position to seek a lowerdirection than the objective horizon, when freed from the correctiverestraint of a visual field, as will be seen when the results ofjudgments made in complete darkness are cited, in which case thedirection of displacement is reversed. The single illuminated spotwhich appears in the surrounding region of darkness, and upon whichthe eye of the observer is directed as he makes his judgment, in theformer case restricts unconscious wanderings of the eye, and sets up aprocess of continuous and effortful fixation which accompanies eachact of determination. I attribute the depression of the eyes to thisprocess of binocular adjustment. The experience of strain in the actof fixation increases and decreases with the distance of the objectregarded. In a condition of rest the axes of vision of the eyes tendto become parallel; and from this point onward the intensity of theeffort accompanying the process of fixation increases until, when theobject has passed the near-point of vision, binocular adjustment is nolonger possible. In the general distribution of objects in the visualfield the nearer, for the human being, is characteristically thelower, the more distant the higher, as one looks in succession fromthe things at his feet to the horizon and _vice versa_. We should, therefore, expect to find, when the eyes are free to move inindependence of a determinate visual field, that increased convergenceis accompanied by a depression of the line of sight, decreasedconvergence by an elevation of it. Here such freedom was permitted, and though the fixed distance of the point of regard eliminated alllarge fluctuations in convergence, yet all the secondarycharacteristics of intense convergence were present. Those concernedin the experiment report that the whole process of visual adjustmenthad increased in difficulty, and that the sense of effort wasdistinctly greater. To this sharp rise in the general sense of strain, in coöperation with the absence of a corrective field of objects, Iattribute the large negative displacement of the subjective horizon inthis series of experiments. 

III. 

In the next set of experiments the room was made completely dark. Themethod of experimentation was adapted to these new conditions bysubstituting for the wooden screen one of black-surfaced cardboard, which was perforated at vertical distances of five millimeters bynarrow horizontal slits and circular holes alternately, making a scalewhich was distinctly readable at the distance of the observer. Opposite the end of one of these slits an additional hole was punched, constituting a fixed point from which distances were reckoned on thescale. As the whole screen was movable vertically and the observerknew that displacements were made from time to time, the succession ofjudgments afforded no objective criterion of the range of variation inthe series of determinations, nor of the relation of any individualreaction to the preceding. The method of experimentation was asfollows: The observer sat as before facing the screen, the directionof which was given at the beginning of each series by a momentaryillumination of the scale. In the darkness which followed the observerbrought the direction of sight, with open eyes, as satisfactorily asmight be into the plane of the horizontal, when, upon a simple signal, the perforated scale was instantly and noiselessly illuminated by thepressure of an electrical button, and the location of the point ofregard was read off the vertical scale by the observer himself, interms of its distance from the fixed point of origin described above. The individual and general averages for this set of experiments aregiven in the following table:

TABLE III. 

 Observer. Constant Error. Average Deviation. Mean Variation. _A_ (50) + 7. 75 20. 07 19. 45 _C_ " + 14. 41 25. 05 2. 94 _D_ " + 14. 42 34. 54 29. 16 _E_ " +108. 97 108. 97 23. 13 _F_ " - 5. 12 23. 00 2. 02 _G_ " + 20. 72 34. 80 10. 23 _H_ " + 35. 07 53. 60 33. 95 _I_ " + 25. 52 30. 68 22. 49 _K_ " - 8. 50 40. 65 21. 07

 Average: + 23. 69 41. 26 17. 16

The point at which the eyes rest when seeking the plane of the horizonin total darkness is above its actual position, the positivedisplacement involved being of relatively large amount. 

In addition to the removal of the whole diversified visual field therehas now been eliminated the final point of regard toward which, in thepreceding set of experiments, the sight was strained; and the factorof refined visual adjustment ceases longer to play a part in thephenomenon. The result of this release is manifested in a tendency ofthe eyes to turn unconsciously upward. This is their natural positionwhen closed in sleep. But this upward roll is not an uncomplicatedmovement. There takes place at the same time a relaxation of binocularconvergence, which in sleep may be replaced by a slight divergence. This tendency of the axes of vision to diverge as the eyes are raisedis undoubtedly connected biologically with the distribution ofdistances in the higher and lower parts of the field of vision, ofwhich mention has already been made. Its persistence is takenadvantage of in the artificial device of assisting the process ofstereoscopic vision without instruments by holding the figures to beviewed slightly above the primary position, so that the eyes must beraised in order to look at them and their convergence therebydecreased. It is by the concomitance of these two variables that thephenomena of both this and the preceding series of experiments are tobe explained. In the present case the elimination of a fixed point ofregard is followed by a release of the mechanism of convergence, witha consequent approximation to parallelism in the axes of vision andits concomitant elevation of the line of sight. 

The second fact to be noted is the reduction in amount of the meanvariation. The series of values under the three sets of experimentalconditions hitherto described is as follows: I. 7'. 69; II. 31'. 42;III. 17'. 16. This increase of regularity I take to be due, as in thecase of the lighted room, to the presence of a factor of constancywhich is not strictly an element in the judgment of horizontality. This is a system of sensory data, which in the former case weretransient--the vision of familiar objects; and in the latterresident--the recognition of specific experiences of strain in themechanism of the eye. The latter sensations exist under all three setsof conditions, but they are of secondary importance in those caseswhich include the presence of an objective point of regard, while inthe case of judgments made in total darkness the observer dependssolely upon resident experiences. Attention is thus directedspecifically toward these immediate sensational elements of judgment, and there arises a tendency to reproduce the preceding set ofeye-strains, instead of determining the horizon plane afresh at eachact of judgment upon more general data of body position. 

If the act of judgment be based chiefly upon sensory data connectedwith the reinstatement of the preceding set of strains, progressionsshould appear in these series of judgments, provided a constant factorof error be incorporated in the process. This deflection should bemost marked under conditions of complete darkness, least in the midstof full illumination. Such a progression would be shown at once by thedistribution of positive and negative values of the individualjudgments about the indifference point of constant error. As instancesof its occurrence all cases have been counted in which the first halfof the series of ten judgments was uniformly of one sign (four to sixbeing counted as half) and the second half of the opposite sign. Thepercentages of cases in which the series presented such a progressionare as follows: In diffused light, 7. 6%; in darkness, point of regardilluminated, 18. 3%; in complete darkness, 26. 1%. The element ofconstant error upon which such progressions depend is the tendency ofthe eye to come to rest under determinate mechanical conditions ofequilibrium of muscular strain. 

The relation of the successive judgments of a series to thereinstatement of specific eye-strains and to the presence of an errorof constant tendency becomes clearer when the distribution of thoseseries which show progression is analyzed simultaneously withreference to conditions of light and darkness and to binocular andmonocular vision respectively. Their quantitative relations arepresented in the following table:

TABLE IV. 

 Illumination. Per Cent. Showing Progress. Binocular. Monocular. 

 In light. 7. 6 % 50 % 50 % In darkness. 18. 3 34. 2 65. 8

Among judgments made in daylight those series which presentprogression are equally distributed between binocular and monocularvision. When, however, the determinations are of a luminous point inan otherwise dark field, the preponderance in monocular vision of thetendency to a progression becomes pronounced. That this is not aprogressive rectification of the judgment, is made evident by thedistribution of the directions of change in the several experimentalconditions shown in the following table:

TABLE V. Light. Darkness. Direction of Change. Binocular. Monocular. Binocular. Monocular. Upward. 50 % 100 % 38. 4 % 65. 0 % Downward. 50 00. 0 61. 6 35. 0 Const. Err. -7. 70 +11. 66 -36. 62 -3. 38

When the visual field is illuminated the occurrence of progression inbinocular vision is accidental, the percentages being equallydistributed between upward and downward directions. In monocularvision, on the contrary, the movement is uniformly upward and involvesa progressive increase in error. When the illuminated point is exposedin an otherwise dark field the progression is preponderatinglydownward in binocular vision and upward in vision with the single eye. The relation of these changes to phenomena of convergence, and thetendency to upward rotation in the eyeball has already been stated. There is indicated, then, in these figures the complication of theprocess of relocating the ideal horizon by reference to the sense ofgeneral body position with tendencies to reinstate simply the set ofeye-muscle strains which accompanied the preceding judgment, and theprogressive distortion of the latter by a factor of constant error dueto the mechanical conditions of muscular equilibrium in the restingeye. 

IV. 

The influence of this factor is also exhibited when judgments madewith both eyes are compared with those made under conditions ofmonocular vision. The latter experiments were carried on in alternateseries with those already described. The figures are given in thefollowing tables:

TABLE VI. 

 JUDGMENTS MADE IN DIFFUSED LIGHT. 

 Observer. Constant Error. Average Deviation. Mean Variation. _A_ (50) - 28. 46 29. 04 8. 87 _C_ " + 7. 54 14. 86 8. 01 _D_ " + 39. 32 43. 28 13. 83 _E_ " + 50. 46 65. 26 9. 86 _F_ " + 62. 30 62. 30 1. 60 _G_ " 0. 00 45. 28 9. 66 _H_ " + 22. 92 79. 12 5. 07 _I_ " + 14. 36 51. 96 8. 02 _K_ " + 9. 26 38. 10 9. 55 _L_ " - 61. 10 61. 10 6. 36 Average: + 11. 66 49. 03 8. 18

TABLE VII. 

 JUDGMENTS IN ILLUMINATED POINT. 

 Observer. Constant Error. Average Deviation. Mean Variation. _A_ (50) - 38. 42 51. 96 32. 64 _C_ (30) - 29. 03 41. 23 35. 75 _D_ (20) - 30. 87 34. 07 17. 24 _E_ (50) + 65. 30 75. 86 29. 98 _F_ " + 50. 74 50. 74 5. 89 _G_ " + 66. 38 88. 10 44. 98 _H_ " + 65. 40 80. 76 42. 93 _I_ " - 0. 02 80. 22 47. 53 _K_ " - 44. 60 52. 56 32. 93 _L_ " - 71. 06 73. 30 31. 86 Average: - 3. 38 62. 88 32. 17

The plane of vision in judgments made with the right eye alone isdeflected upward from the true horizon to a greater degree than it isdepressed below it in those made with binocular vision, the respectivevalues of the constant errors being -7'. 70 and +11'. 66, a differenceof 19'. 36. When the field of vision is darkened except for the singleilluminated disc, a similar reversion of sign takes place in theconstant error. With binocular vision the plane of the subjectivehorizon is deflected downward through 36'. 62 of arc; with monocularvision it is elevated 3'. 38, a difference of 40'. 00, or greater thanin the case of judgments made in the lighted room by 20'. 64. Thisincrease is to be expected in consequence of the elimination of thosecorrective criteria which the figured visual field presents. The twoeyes do not, of course, function separately in such a case, and thedifference in the two sets of results is undoubtedly due to theinfluence of movements in the closed eye upon that which is open; orrather, to the difference in binocular functioning caused by shuttingoff the visual field from one eye. The former expression is justifiedin so far as we conceive that the tendency of the closed eye to turnslightly upward in its socket affects also the direction of regard inthe open eye by attracting toward itself its plane of vision. But if, as has been pointed out, this elevation of the line of sight in theclosed eye is accompanied by a characteristic change in the process ofbinocular convergence, the result cannot be interpreted as a simplesympathetic response in the open eye to changes taking place in thatwhich is closed, but is the consequence of a release of convergencestrain secondarily due to this act of closing the eye. 

Several points of comparison between judgments made with binocular andwith monocular vision remain to be stated. In general, the process oflocation is more uncertain when one eye only is used than when bothare employed, but this loss in accuracy is very slight and in manycases disappears. The loss in accuracy is perhaps also indicated bythe range of variation in the two cases, its limits being forbinocular vision +46'. 29 to -56'. 70, and for monocular +62'. 30 to-61'. 10, an increase of 20'. 41. In the darkened room similar relationsare presented. The mean variations are as follows: binocular vision, 31'. 42; monocular, 32'. 17. Its limits in individual judgments are:binocular, -1'. 62 to -128'. 70, monocular, +66'. 38 to -71'. 06, anincrease of 10'. 36. In all ways, then, the difference in accuracybetween the two forms of judgment is extremely small, and theconclusion may be drawn that those significant factors of judgmentwhich are independent of the figuration of the visual field are notconnected with the stereoscopic functioning of the two eyes, but suchas are afforded by adjustment in the single eye and its results. 

VI. 

The experimental conditions were next complicated by the introductionof abnormal positions of the eyes, head and whole body. The results oftipping the chin sharply upward or downward and keeping it so fixedduring the process of location are given in the following table, whichis complete for only three observers:

TABLE VIII. 

 Observer. Upward Rotation. Downward Rotation. C. E. A. D. M. V. C. E. A. D. M. V. _L_ (50) +43. 98 43. 98 5. 62 +28. 32 28. 32 5. 02 _K_ (50) -33. 72 33. 72 71. 33 +19. 49 19. 49 55. 22 _L_ (20) -39. 10 45. 90 33. 60 -68. 65 69. 25 25. 20 Average: - 9. 61 41. 20 36. 85 -19. 94 39. 02 28. 48 Normal: -64. 14 67. 08 33. 51

The results of rotating the whole body backward through forty-five andninety degrees are given in the following table:

TABLE IX. 

 Observer. Rotation of 45°. Rotation of 90°. C. E. A. D. M. V. C. E. A. D. M. V. _B_ (30) + 4. 10 24. 57 18. 56 _D_ (30) +291. 03 291. 03 61. 86 _G_ (50) +266. 78 266. 78 22. 83 +200. 16 200. 16 11. 00 _F_ (60) +116. 45 116. 45 17. 14 - 36. 06 36. 30 6. 29 _J_ (20) +174. 30 174. 63 30. 94 Average: +170. 53 174. 69 30. 66

The errors which appear in these tables are not consistently of thetype presented in the well-known rotation of visual planessubjectively determined under conditions of abnormal relations of thehead or body in space. When the head is rotated upward on its lateralhorizontal axis the average location of the subjective horizon, though still depressed below the true objective, is higher than whenrotation takes place in the opposite direction. When the whole body isrotated backward through 45° a positive displacement of large amounttakes place in the case of all observers. When the rotation extends to90°, the body now reclining horizontally but with the head supportedin a raised position to allow of free vision, an upward displacementoccurs in the case of one of the two observers, and in that of theother a displacement in the opposite direction. When change ofposition takes place in the head only, the mean variation is decidedlygreater if the rotation be upward than if it be downward, its value inthe former case being above, in the latter below that of the normal. When the whole body is rotated backward through 45° the mean variationis but slightly greater than under normal conditions; when therotation is through 90° it is much less. A part of this reduction isprobably due to training. In general, it may be said that thedisturbance of the normal body relations affects the location of thesubjective horizon, but the specific nature and extent of thisinfluence is left obscure by these experiments. The ordinary movementsof eyes and head are largely independent of one another, and even whenclosed the movements of the eyes do not always symmetrically followthose of the head. The variations in the two processes have beenmeasured by Münsterberg and Campbell[1] in reference to a singlecondition, namely, the relation of attention to and interest in theobjects observed to the direction of sight in the closed eyes aftermovement of the head. But apart from the influence of such secondaryelements of ideational origin, there is reason to believe that themere movement of the head from its normal position on the shoulders upor down, to one side or the other, is accompanied by compensatorymotion of the eyes in an opposite direction, which tends to keep theaxis of vision nearer to the primary position. When the chin iselevated or depressed, this negative reflex adjustment is morepronounced and constant than when the movement is from side to side. In the majority of cases the retrograde movement of the eyes does notequal the head movement in extent, especially if the latter beextreme. 

 [1] Münsterberg, H. , and Campbell, W. W. : PSYCHOLOGICAL REVIEW, I. , 1894, p. 441. 

The origin of such compensatory reactions is connected with thepermanent relations of the whole bodily organism to the importantobjects which surround it. The relations of the body to the landscapeare fairly fixed. The objects which it is important to watch lie in abelt which is roughly on a horizontal plane with the observing eye. They move or are moved about over the surface of the ground and do notundergo any large vertical displacement. It is of high importance, therefore, that the eye should be capable of continuous observation ofsuch objects through facile response to the stimulus of their visualappearance and movements, in independence of the orientation of thehead. There are no such determinate spatial relations between bodyposition and the world of important visual objects in the case ofthose animals which are immersed in a free medium; and in theorganization of the fish and the bird, therefore, one should notexpect the development of such free sensory reflexes of the eye inindependence of head movements as we know to be characteristic of thehigher land vertebrates. In both of the former types the eye is fixedin its socket, movements of the whole head or body becoming themechanism of adjustment to new objects of observation. In theadjustment of the human eye the reflex determination through sensorystimuli is so facile as to counteract all ordinary movements of thehead, the gaze remaining fixed upon the object through a series ofminute and rapidly repeated sensory reflexes. When the eyes are closedand no such visual stimuli are presented, similar reflexes take placein response to the movements of the head, mediated possibly bysensations connected with changes in position of the planes of thesemicircular canals. 

VII. 

If eye-strain be a significant element in the process of determiningthe subjective horizon, the induction of a new center of muscularequilibrium by training the eyes to become accustomed to unusualpositions should result in the appearance of characteristic errors ofdisplacement. In the case of two observers, _A_ and _H_, the eyes weresharply raised or lowered for eight seconds before giving judgment asto the position of the illuminated spot, which was exposed at themoment when the eyes were brought back to the primary position. Theeffect of any such vertical rotation is to stretch the antagonisticset of muscles. It follows that when the eye is rotated in thecontrary direction the condition of equilibrium appears sooner than innormal vision. In the case of both observers the subjective horizonwas located higher when judgment was made after keeping the eyesraised, and lower when the line of sight had been depressed. In thecase of only one observer was a quantitative estimation of the errormade, as follows: With preliminary raising of the eyes the locationwas +36'. 4; with preliminary lowering, -11'. 4. 

When the illuminated button is exposed in a darkened room and isfixated by the observer, it undergoes a variety of changes in apparentposition due to unconscious shifting of the point of regard, thechange in local relations of the retinal stimulation being erroneouslyattributed to movements in the object. These movements were not offrequent enough occurrence to form the basis of conclusions as to theposition at which the eyes tended to come to a state of rest. Thenumber reported was forty-two, and the movement observed was rather awandering than an approximation toward a definite position ofequilibrium. The spot very rarely presented the appearance of sidewisefloating, but this may have been the result of a preconception on thepart of the observer rather than an indication of a lessened liabilityto movements in a horizontal plane. Objective movements in the latterdirection the observer knew to be impossible, while verticaldisplacements were expected. Any violent movement of the head or eyesdispelled the impression of floating at once. The phenomenon appearedonly when the illuminated spot had been fixated for an appreciableperiod of time. Its occurrence appears to be due to a fatigue processin consequence of which the mechanism becomes insensible to slightchanges resulting from releases among the tensions upon which constantfixation depends. When the insensitiveness of fatigue is avoided by aslow continuous change in the position of the illuminated spot, nosuch wandering of the eye from its original point of regard occurs, and the spot does not float. The rate at which such objectivemovements may take place without awareness on the part of the observeris surprisingly great. Here the fatigue due to sustained fixation isobviated by the series of rapid and slight sensory reflexes which takeplace; these have the effect of keeping unchanged the retinalrelations of the image cast by the illuminated spot, and beingundiscriminated in the consciousness of the observer the position ofthe point of regard is apprehended by him as stationary. Thebiological importance of such facile and unconscious adjustment of themechanism of vision to the moving object needs no emphasis; but therelation of these obscure movements of the eyes to the process ofdetermining the plane of the subjective horizon should be pointed out. The sense of horizontality in the axes of vision is a transientexperience, inner conviction being at its highest in the first momentsof perception and declining so characteristically from this maximumthat in almost every case the individual judgment long dwelt upon isunsatisfactory to the observer. This change I conceive to be asecondary phenomenon due to the appearance of the visual wanderingsalready described. 

VIII. 

The influence of sensory reflexes in the eye upon the process ofvisual orientation was next taken up in connection with two specifictypes of stimulation. At top and bottom of the vertical screen werearranged dark lanterns consisting of electric bulbs enclosed inblackened boxes, the fronts of which were covered with a series ofsheets of white tissue-paper, by which the light was decentralized andreduced in intensity, and of blue glass, by which the yellow qualityof the light was neutralized. Either of these lanterns could beilluminated at will by the pressure of a button. All otherexperimental conditions remained unchanged. The observers weredirected to pay no special regard to these lights, and the reportsshow that in almost every case they had no conscious relation to thejudgment. The results are presented in the following table:

TABLE X. 

 Light Below. Light Above. Observer. Const. Err. Av. Dev. M. Var. Const. Err. Av. Dev. M. Var. _C_ (40) +156. 37 156. 37 19. 67 +169. 85 169. 85 19. 22 _D_ (20) + 39. 30 43. 30 17. 95 + 46. 65 47. 35 15. 41 _F_ (30) + 19. 47 19. 47 8. 83 + 58. 37 58. 37 7. 83 _G_ (50) + 66. 11 112. 76 14. 65 +117. 86 117. 86 13. 10 _H_ (30) -147. 63 147. 63 21. 07 -105. 30 105. 30 30. 31 _J_ (20) + 1. 90 31. 95 22. 33 + 44. 40 44. 40 20. 55 Average: + 22. 59 85. 28 17. 42 + 55. 30 90. 52 17. 74

The eye is uniformly attracted toward the light and the location ofthe disk correspondingly elevated or depressed. The amount ofdisplacement which appears is relatively large. It will be found tovary with the intensity, extent and distance of the illuminatedsurfaces introduced. There can be little doubt that the practicaljudgments of life are likewise affected by the distribution of lightintensities, and possibly also of significant objects, above and belowthe horizon belt. Every brilliant object attracts the eye towarditself; and the horizon beneath a low sun or moon will be found to belocated higher than in a clouded sky. The upper half of the ordinaryfield of view--the clear sky--is undiversified and unimportant; thelower half is full of objects and has significance. We should probablybe right in attributing to these characteristic differences a share inthe production of the negative error of judgment which appears injudgments made in daylight. The introduction of such supplementarystimuli appears to have little effect upon the regularity of theseries of judgments, the values of the mean variations beingrelatively low: 17'. 42 with light below, 17'. 74 with it above. 

IX. 

In the final series of experiments the influence of limiting visualplanes upon the determination of the subjective horizon was taken up. It had been noticed by Dr. Münsterberg in the course of travel in hillcountry that a curious negative displacement of the subjective horizontook place when one looked across a downward slope to a distant cliff, the altitude (in relation to the observer's own standpoint) ofspecific points on the wall of rock being largely overestimated. Attributing the illusion to a reconstruction of the sensory data uponan erroneous interpretation of the objective relations of thetemporary plane of the landscape, Dr. Münsterberg later made a seriesof rough experiments by stretching an inclined cord from the eyedownward to a lower point on an opposite wall and estimating theheight above its termination of that point which appeared to be on alevel with the observing eye. He found an illusion present similar tothe case of an extended slope of country. 

The first experiments of this group repeated those just described. Theprevious mechanical conditions were varied only by the introduction ofa slender cord which was stretched from just below the eyes to thebottom of the vertical screen. Full results were obtained from onlytwo observers, which are given in the following table:

TABLE XI. 

 Observer. Const. Err. Av. Dev. Mean Var. Exp. Conds. 

 _C_ (30) +123. 92 123. 92 11. 94 Cord present and _G_ (30) +66. 47 66. 47 15. 56 consciously referred to. _C_ (30) +126. 90 126. 90 6. 31 Cord not present. _G_ (30) +83. 20 83. 20 6. 31 _C_ (30) +126. 93 126. 93 6. 39 Cord present but not _G_ (30) +86. 63 86. 63 9. 40 consciously referred to. 

 Averages. I +95. 19 95. 19 13. 75 " II +105. 05 105. 05 6. 31 " III +106. 78 106. 78 7. 89

The effect of introducing such an objective plane of reference istwofold: the mean variation is increased, and the plane of thesubjective horizon is displaced downwards. First, then, it acts as asimple factor of disturbance; it distracts from those habitualadjustments upon which the accuracy of the judgment depends. Secondly, it enters as a source of constant error into the determination of thesubjective horizon, which is attracted toward this new objectiveplane. In the third section of the table are given the results ofjudgments made in the presence of such a plane but without consciousreference to it. [2] The figures here are of intermediate value in thecase of the mean variation and of slightly greater value than thefirst in that of the constant error. In other words, the introductionof such a plane cannot be wholly overlooked, though it may be greatlyabstracted from. 

[2] In the preceding experiments the cord was definitely to be takeninto account in making the judgment. The method of so doing was byrunning the eye back and forth over the cord preliminary todetermining the location of the point. 

The single cord was next replaced by a plane of blackened wood sixinches wide and extending from the observer to the vertical screen. This strip was arranged in two ways: first, from the observer's chinto the bottom of the screen, and secondly, from the feet of theobserver to a point on the screen a short distance below the plane ofthe objective horizon. The individual and average results are given inthe following table:

TABLE XII. 

 Observer. Descending Plane. Ascending Plane. 

 _A. _ (10) +18. 80 18. 80 5. 24 +35. 10 35. 10 8. 27 _E. _ (20) +79. 30 79. 30 11. 56 +131. 67 131. 67 12. 07 _H. _ (10) -37. 50 37. 50 16. 80 -46. 90 46. 90 7. 90 _K. _ (30) +71. 40 71. 40 12. 85 +48. 05 48. 05 5. 11 Average: +33. 00 51. 75 11. 61 +41. 95 65. 43 8. 34

The introduction of a descending plane lowers the apparent horizon;that of an ascending plane elevates it. The general disturbance ofjudgment appears distinctly greater in the case of a downward than inthat of an upward incline. 

The results of a third variation of the experimental conditions may bepresented at once. In it the location of the subjective horizon undernormal conditions was compared with the results of adjustments madewhen the screen bearing the white disc was rotated backward from theobserver through an angle of varying magnitude. The averages for eachof the two subjects are as follows:

TABLE XIII. 

 Observer Const. Err. Av. Dev. Mean Var. Rotation. _F_ (20) +130. 50 130. 50 3. 20 20° " " +115. 50 115. 50 1. 10 50° _J_ (20) +443. 10 443. 10 9. 47 45°

These experiments were carried on in the presence of the definitelyfigured visual field of the lighted room, and the observers wereconscious of taking these permanent features into account ascorrectives in making their judgments. Before proceeding, this defectwas remedied as far as possible by enclosing the apparatus ofexperimentation, including the observer, between two walls of blackfabric. Nothing was to be seen but these two walls, and the inclinedplane which terminated the observer's view. The position of the screenremained constant at an inclination of 45°. The upper bounding linesof the enclosing walls, on the contrary, were adjusted in threedifferent relations to the plane of the gravity horizon. In the firstarrangement these lines were horizontal; in the second the ends nextto the observer were depressed five degrees; while in the finalarrangement these ends were elevated through a like angular distance. 

The inclined position of the screen was of course observed by everyreactor, but of the changes in the enclosing walls no subject wasinformed, and none discerned them on any occasion. Each observer wasquestioned as to alterations in the experimental conditions after theuse of each arrangement, and at the close of the whole series inquirywas made of each as to the planes of the upper boundaries of thewalls. On various occasions, but not customarily, the observer wasaware of a change of some kind in the whole set of conditions, but theparticular feature altered was not suspected. The results for allthree arrangements are given in the following table; of the sectionsof this table the third is incomplete, full results having beenreached in the cases of only three observers:

TABLE XV. 

 Ascending Planes. Descending Planes. Observer Const. Err. Av. Dev. M. Var. Const. Err. Av. Dev. M. V. _C_ (50) - 8. 02 11. 82 9. 47 - 48. 14 48. 14 9. 52 _F_ (50) + 78. 88 78. 88 2. 89 + 25. 54 25. 54 1. 98 _G_ (50) - 22. 56 24. 64 6. 58 -101. 20 101. 20 7. 39 _H_ (50) - 83. 84 83. 84 11. 78 -230. 20 230. 20 11. 88 _J_ (50) +315. 64 315. 64 18. 16 +120. 12 120. 12 9. 01 Average: + 55. 96 102. 96 9. 78 -44. 98 104. 84 7. 96

 Horizontal Planes. Observer. Const. Err. Av. Dev. Mean Var. _C_ (50) - 27. 86 27. 86 9. 58 _G_ (50) - 73. 84 73. 84 7. 59 _J_ (50) +243. 72 243. 72 18. 52

For every individual observer, the position of the disc on the screenhas been affected by each change in the direction of these visiblelines. In every case, also, its location when these boundaries lay ina horizontal plane was intermediate between the other two. Theimportance of such relations in the objects of the visual field asfactors in our ordinary determination of the subjective horizon ismade evident by these experimental results. They become constructionlines having assumed permanence in the world of visual-motorexperience. The conception of unchanging spatial relations in thefundamental lines of perspective vision receives constantreinforcement from the facts of daily experience. The influence of theabove-described changes in experimental conditions is mediated throughtheir effect upon the location of the focus of the limiting andperspective lines of vision. As the plane of the upper boundaries ofthe enclosing walls was elevated and depressed the intersection of thetwo systems of lines was correspondingly raised and lowered, and independence upon the location of this imaginary point the determinationof the position of the white disc was made, and the plane ofperspective positively or negatively rotated. 

Why such perspective lines should enter into the process of judgmentit is not difficult to infer. The plane of perspective for humanbeings is characteristically horizontal, in consequence of thedistribution of important objects within the field of visualperception. Roughly, the belt of the earth's horizon contains the lociof all human perspective planes. Both natural and artificialarrangements of lines converge there. The systems of visual objects onthe earth and in the sky are there broken sharply off in virtue oftheir practically vast differences in quality and significance for theobserver. The latter perspective probably never extends downwardillusorily to points on the earth's surface; and the former system ofobjects is carried continuously upward to skyey points only onrelatively rare occasions, as when one mistakes clouds for mountainsor the upper edge of a fog-belt on the horizon for the rim of sea andsky. The point of convergence of the fundamental lines of perspectivethus becomes assimilated with the idea of the visual horizon, as thatconcept has fused with the notion of a subjective horizon. There canbe little doubt that the disposition of such lines enters constantlyinto our bodily orientation in space along with sensations arisingfrom the general body position and from those organs more speciallyconcerned with the static sense. 

Upon the misinterpretation of such objective planes depends theillusion of underestimation of the height or incline of a hill one isbreasting, and of the converse overestimation of one seen across adescending slope or intervening valley. The latter illusion isespecially striking, and in driving over forest roads (in which casethe correction of a wider range of view is excluded) the stretch oflevel ground at the foot of a hill one is descending is constantlymistaken for an opposing rise. This illusion is put into picturesquewords by Stevenson when he describes the world, seen from the summitof a mountain upon which one stands, as rising about him on every sideas toward the rim of a great cup. The fitness of the image may beproved by climbing the nearest hill. In all such cases areconstruction of the sensory data of judgment takes place, in whichthe most significant factor is the plane determined by the positionsof the observing eye and the perspective focus. In these judgments ofspatial relationship, as they follow one another from moment tomoment, this plane becomes a temporary subjective horizon, andaccording as it is positively or negatively rotated do correspondingillusions of perception appear. 

 * * * * *

THE ILLUSION OF RESOLUTION-STRIPES ON THE COLOR-WHEEL. 

BY EDWIN B. HOLT. 

If a small rod is passed slowly before a rotating disc composed of twodifferently colored sectors, the rod appears to leave behind it on thedisc a number of parallel bands of about the width of the rod and ofabout the colors, alternately arranged, of the two sectors. Theseappear not to move, but gradually to fade away. 

This phenomenon was first observed by Münsterberg, and by him shown toJastrow, [1] who, with Moorehouse, has printed a study, without, however, offering an adequate explanation of it. 

 [1] Jastrow, J. , and Moorehouse, G. W. : 'A Novel Optical Illusion, ' _Amer. Jour. Of Psychology_, 1891, IV. , p. 201. 

I. APPARATUS FOR PRODUCING THE ILLUSION. 

Any form of color-wheel may be used, but preferably one which isdriven by electricity or clock-work, so that a fairly constant speedis assured. Several pairs of paper discs are needed, of the ordinaryinterpenetrating kind which permit a ready readjustment of the ratiosbetween the two sectors, as follows: one pair consisting of a whiteand a black disc, one of a light-and a dark-colored disc (light greenand dark red have been found admirably suited to the purpose), and apair of discs distinctly different in color, but equal in luminosity. 

The rod should be black and not more than a quarter of an inch broad. It may be passed before the rotating disc by hand. For the sake ofmore careful study, however, the rod should be moved at a constantrate by some mechanical device, such as the pendulum and works of aMaelzel metronome removed from their case. The pendulum is fixed justin front of the color-disc. A further commendable simplification ofthe conditions consists in arranging the pendulum and disc to moveconcentrically, and attaching to the pendulum an isosceles-triangularshield, so cut that it forms a true radial sector of the disc behindit. All the colored bands of the illusion then appear as radialsectors. The radial shields should be made in several sizes (from 3 to50 degrees of arc) in black, but the smallest size should also beprepared in colors matching the several discs. Such a disposition, then, presents a disc of fused color, rotating at a uniform rate, andin front of this a radial sector oscillating from side to sideconcentrically with the disc, and likewise at a uniform rate. Severalvariations of this apparatus will be described as the need and purposeof them become clear. 

II. PREVIOUS DISCUSSION OF THE ILLUSION. 

Although Jastrow and Moorehouse (_op. Cit. _) have published a somewhatdetailed study of these illusion-bands, and cleared up certain points, they have not explained them. Indeed, no explanation of the bands hasas yet been given. The authors mentioned (_ibid. _, p. 204) write ofproducing the illusion by another method. "This consists in slidingtwo half discs of the same color over one another leaving an opensector of any desired size up to 180 degrees and rotating this againsta background of a markedly different color, in other words wesubstitute for the disc composed of a large amount of one color, whichfor brevity we may call the 'majority color, ' and a small amount ofanother, the 'minority color, ' one in which the second color is in thebackground and is viewed through an opening in the first. With such anarrangement we find that we get the series of bands both when the wireis passed in front of the disc and when passed in back between discand background; and further experimentation shows that the timerelations of the two are the same. (There is, of course, no essentialdifference between the two methods when the wire is passed in front ofthe disc. )" That is true, but it is to be borne in mind that there isa difference when the wire is passed behind the disc, as these authorsthemselves state (_loc. Cit. _, note):--"The time-relations in the twocases are the same, but the _color-phenomena_ considerably_different_. " However, "these facts enable us to formulate our firstgeneralization, viz. , that for all purposes here relevant [_i. E. _, toa study of the _time-relations_] the seeing of a wire now against onebackground and then immediately against another is the same as its nowappearing and then disappearing; a rapid succession of changedappearances is equivalent to a rapid alternation of appearance anddisappearance. Why this is so we are unable to say, " etc. Theseauthors now take the first step toward explaining the illusion. Intheir words (_op. Cit. _, p. 205), "the suggestion is natural that weare dealing with the phenomena of after-images. . . . If this is the trueexplanation of the fact that several rods are seen, then we should, with different rotation rates of disc and rod, see as many rods asmultiplied by the time of one rotation of the disc would yield aconstant, _i. E. _, the time of an after image of the kind underconsideration. " For two subjects, J. J. And G. M. , the followingtabulation was made. 

 J. J. G. M. Av. Time of rot. Of disc when 2 images of rod were seen . 0812 sec. . 0750 sec. " " " " 3 " " " " . 0571 " . 0505 " " " " " 4 " " " " . 0450 " . 0357 " " " " " 5 " " " " . 0350 " . 0293 " " " " " 6 " " " " . 0302 " . 0262 "

"Multiplying the number of rods by the rotation rate we get for J. J. An average time of after image of . 1740 sec. (a little over 1/6 sec. )with an average deviation of . 0057 (3. 2%); for G. M. . 1492 (a littleover 1/7 sec. ) with an average deviation of . 0036 (2. 6%). Anindependent test of the time of after-image of J. J. And G. M. Byobserving when a black dot on a rotating white disc just failed toform a ring resulted in showing in every instance a longer time forthe former than for the latter. " That this constant product of thenumber of 'rods' seen by the time of one rotation of the disc equalsthe duration of after-image of the rod is established, then, only byinference. More indubitable, since directly measured on two subjects, is the statement that that person will see more 'rods' whoseafter-image persists longer. This result the present writer fullyconfirms. What relation the 'constant product' bears to the durationof after-image will be spoken of later. But aside from allmeasurement, a little consideration of the conditions obtaining whenthe rod is passed _behind_ the disc will convince any observer thatthe bands are indeed after-images somehow dependent on the rod. We mayaccount it established that _the bands are after-images_. 

From this beginning one might have expected to find in the paper ofJastrow and Moorehouse a complete explanation of the illusion. Onother points, however, these authors are less explicit. The changes inwidth of the bands corresponding to different sizes of the sectors anddifferent rates of movement for the rod and disc, are not explained, nor yet, what is more important, the color-phenomena. In particularthe fact needs to be explained, that the moving rod analyzes theapparently homogeneous color of the disc; or, as Jastrow andMoorehouse state it (_op. Cit. _, p. 202): "If two rotating discs werepresented to us, the one pure white in color, and the other of ideallyperfect spectral colors in proper proportion, so as to give aprecisely similar white, we could not distinguish between the two; butby simply passing a rod in front of them and observing in the one casebut not in the other the parallel rows of colored bands, we could atonce pronounce the former to be composite, and the latter simple. Inthe indefinitely brief moment during which the rod interrupts thevision of the disc, the eye obtains an impression sufficient toanalyze to some extent into its elements this rapid mixture ofstimuli. " The very question is as to _how_ the eye obtains the'impression sufficient to analyze' the mixture. 

It may be shown at this point that the mistake of these authors liesin their recognition of but one set of bands, namely (_ibid. _, p. 201), 'bands of a color similar to that present in greater proportion'on the disc. But, on the other hand, it is to be emphasized that thosebands are separated from one another, not by the fused color of thedisc, as one should infer from the article, but by _other bands_, which are, for their part, of a color similar to that present in_lesser_ proportion. Thus, bands of the two colors alternate; andeither color of band is with equal ease to be distinguished from thefused color of the main portion of the disc. 

Why our authors make this mistake is also clear. They first studiedthe illusion with the smaller sector of the disc open, and the rodmoving behind it; and since in this case the bands are separated bystrips not of the minority but of the fused color, and are of aboutthe width of the rod itself, these authors came to recognize bands ofbut one sort, and to call these 'images of the rod. ' But now, with therod moving in front of the disc, there appear bands of two colorsalternately disposed, and neither of these colors is the fused colorof the disc. Rather are these two colors approximately the majorityand minority colors of the disc as seen at rest. Thus, the recognitionof but one set of bands and the conclusion (_ibid. _, p. 208) that 'thebands originate during the vision of the minority color, ' are whollyerroneous. The bands originate as well during the vision of themajority color, and, as will later be shown, the process iscontinuous. 

Again, it is incorrect, even in the case of those bands seen behindthe open sector, to call the bands 'images of the rod, ' for images ofthe rod would be of the color of the rod, whereas, as our authorsthemselves say (_ibid. _, p. 201), the bands 'are of a color similar tothat present in greater proportion' on the disc. Moreover the 'imagesof the rod' are of the most diverse widths. In fact, we shall findthat the width of the rod is but one of several factors whichdetermine the width of its 'images, ' the bands. 

Prejudiced by the same error is the following statement (_ibid. _, p. 208): "With the majority color darker than the minority color thebands are darker than the resulting mixture, and lighter when themajority color is the lighter. " If this is to be true, one must readfor 'the bands, ' 'the narrower bands. '

Another observation found in this article must be criticised. It isasserted that difference of shade between the two sectors of the disc, as well as difference of color, is essential to the illusion. Tosupport this, four cases are given: two in which the sectors were sosimilar in luminosity as to bring out the illusion but faintly; two inwhich like luminosities yielded no illusion at all. The present writeragrees that if the two sectors are closely similar in luminosity, theillusion is fainter. He also selected a red and a green so near eachother in brightness that when a rod 4 mm. Broad (which is the largestrod that Jastrow and Moorehouse mention having used) was passed byhand before the disc, no trace of a band could be seen. The pendulum, however, bearing a shield considerably wider than 4 mm. (say of 15degrees) and moving before the very same red and green shades, mixedin the same proportions, yielded the illusion with the utmostclearness. Colors of like luminosities yield the illusion lessstrikingly, nevertheless they yield it. 

Again (_op. Cit. _, p. 205), these authors say: "It has been alreadyobserved that the distance between the bands diminishes as therotation rate and the rate of movement of the rod increases. " But whathad been said before is (_ibid. _, p. 203) that 'the bands areseparated by smaller and smaller spaces as the rate of movement of therod becomes slower and slower'; and this is equivalent to saying thatthe distance between the bands diminishes as the rate of movement ofthe rod decreases. The statements are contradictory. But there is nodoubt as to which is the wrong one--it is the first. What theseauthors have called 'distance between the bands' has here been shownto be itself a band. Now, no point about this illusion can be morereadily observed than that the widths of both kinds of band varydirectly with the speed of the rod, inversely, however (as Jastrow andMoorehouse have noted), with the speed of the disc. 

Perhaps least satisfactory of all is their statement (_ibid. _, p. 206)that "A brief acquaintance with the illusion sufficed to convince usthat its appearance was due to contrast of some form, though theprecise nature of this contrast is the most difficult point of all. "The present discussion undertakes to explain with considerableminuteness every factor of the illusion, yet the writer does not seehow in any essential sense contrast could be said to be involved. 

With the other observations of these authors, as that the generaleffect of an increase in the width of the interrupting rod was torender the illusion less distinct and the bands wider, etc. , theobservations of the present writer fully coincide. These willsystematically be given later, and we may now drop the discussion ofthis paper. 

The only other mention to be found of these resolution-bands is one bySanford, [2] who says, apparently merely reiterating the results ofJastrow and Moorehouse, that the illusion is probably produced by thesudden appearance, by contrast, of the rod as the lighter sectorpasses behind it, and by its relative disappearance as the dark sectorcomes behind. He thus compares the appearance of several rods to theappearance of several dots in intermittent illumination of the strobicwheel. If this were the correct explanation, the bands could not beseen when both sectors were equal in luminosity; for if both weredark, the rod could never appear, and if both were light, it couldnever disappear. The bands can, however, be seen, as was stated above, when both the sectors are light or both are dark. Furthermore, thisexplanation would make the bands to be of the same color as the rod. But they are of other colors. Therefore Sanford's explanation cannotbe admitted. 

 [2] Sanford, E. C. : 'A Course in Experimental Psychology, ' Boston, 1898, Part I. , p. 167. 

And finally, the suggestions toward explanation, whether of Sanford, or of Jastrow and Moorehouse, are once for all disproved by theobservation that if the moving rod is fairly broad (say three quartersof an inch) and moves _slowly_, the bands are seen nowhere so well as_on the rod itself_. One sees the rod vaguely through the bands, ascould scarcely happen if the bands were images of the rod, orcontrast-effects of the rod against the sectors. 

The case when the rod is broad and moves slowly is to be accounted aspecial case. The following observations, up to No. 8, were made witha narrow rod about five degrees in width (narrower will do), moved bya metronome at less than sixty beats per minute. 

III. OUTLINE OF THE FACTS OBSERVED. 

A careful study of the illusion yields the following points:

1. If the two sectors of the disc are unequal in arc, the bands areunequal in width, and the narrower bands correspond in color to thelarger sector. Equal sectors give equally broad bands. 

2. The faster the rod moves, the broader become the bands, but not inlike proportions; broad bands widen relatively more than narrow ones;equal bands widen equally. As the bands widen out it necessarilyfollows that the alternate bands come to be farther apart. 

3. The width of the bands increases if the speed of the revolving discdecreases, but varies directly, as was before noted, with the speed ofthe pendulating rod. 

4. Adjacent bands are not sharply separated from each other, thetransition from one color to the other being gradual. The sharpestdefinition is obtained when the rod is very narrow. It is appropriateto name the regions where one band shades over into the next'transition-bands. ' These transition-bands, then, partake of thecolors of both the sectors on the disc. It is extremely difficult todistinguish in observation between vagueness of the illusion due tofeebleness in the after-image depending on faint illumination, dark-colored discs or lack of the desirable difference in luminositybetween the sectors (cf. P. 171) and the indefiniteness which is dueto broad transition-bands existing between the (relatively) pure-colorbands. Thus much, however, seems certain (Jastrow and Moorehouse havereported the same, _op. Cit. _, p. 203): the wider the rod, the widerthe transition-bands. It is to be noticed, moreover, that, for ratherswift movements of the rod, the bands are more sharply defined if thismovement is contrary to that of the disc than if it is in likedirection with that of the disc. That is, the transition-bands arebroader when rod and disc move in the same, than when in oppositedirections. 

5. The total number of bands seen (the two colors being alternatelyarranged and with transition-bands between) at any one time isapproximately constant, howsoever the widths of the sectors and thewidth and rate of the rod may vary. But the number of bands isinversely proportional, as Jastrow and Moorehouse have shown (seeabove, p. 169), to the time of rotation of the disc; that is, thefaster the disc, the more bands. Wherefore, if the bands are broad(No. 2), they extend over a large part of the disc; but if narrow, they cover only a small strip lying immediately behind the rod. 

6. The colors of the bands approximate those of the two sectors; thetransition-bands present the adjacent 'pure colors' merging into eachother. But _all_ the bands are modified in favor of the color of themoving rod. If, now, the rod is itself the same in color as one of thesectors, the bands which should have been of the _other_ color are notto be distinguished from the fused color of the disc when no rod movesbefore it. 

7. The bands are more strikingly visible when the two sectors differconsiderably in luminosity. But Jastrow's observation, that adifference in luminosity is _necessary_, could not be confirmed. Rather, on the contrary, sectors of the closest obtainable luminositystill yielded the illusion, although faintly. 

8. A _broad_ but slowly moving rod shows the bands overlying itself. Other bands can be seen left behind it on the disc. 

9. But a case of a rod which is broad, or slowly-moving, or both, is aspecial complication which involves several other and _seemingly_quite contradictory phenomena to those already noted. Since thesesuffice to show the principles by which the illusion is to beexplained, enumeration of the special variations is deferred. 

IV. THE GEOMETRICAL RELATIONS BETWEEN THE ROD AND THE SECTORS OF THEDISC. 

It should seem that any attempt to explain the illusion-bands ought tobegin with a consideration of the purely geometrical relations holdingbetween the slowly-moving rod and the swiftly-revolving disc. First ofall, then, it is evident that the rod lies in front of each sectorsuccessively. 

Let Fig. 1 represent the upper portion of a color-wheel, with centerat _O_, and with equal sectors _A_ and _B_, in front of which a rod_P_ oscillates to right and left on the same axis as that of thewheel. Let the disc rotate clockwise, and let _P_ be observed in itsrightward oscillation. Since the disc moves faster than the rod, thefront of the sector _A_ will at some point come up to and pass behindthe rod _P_, say at _p^{A}. P_ now hides a part of _A_ and both aremoving in the same direction. Since the disc still moves the faster, the front of _A_ will presently emerge from behind _P_, then more andmore of _A_ will emerge, until finally no part of it is hidden by _P_. If, now, _P_ were merely a line (having no width) and were notmoving, the last of _A_ would emerge just where its front edge hadgone behind _P_, namely at _p^{A}_. But _P_ has a certain width and acertain rate of motion, so that _A_ will wholly emerge from behind _P_at some point to the right, say _p^{B}_. How far to the right thiswill be depends on the speed and width of _A_, and on the speed andwidth of _P_. 

Now, similarly, at _p^{B}_ the sector _B_ has come around and beginsto pass behind _P_. It in turn will emerge at some point to the right, say _p^{C}_. And so the process will continue. From _p^{A}_ to _p^{B}_the pendulum covers some part of the sector _A_; from _p^{B}_ to_p^{C}_ some part of sector _B_; from _p^{C}_ to _P^{D}_ some part of_A_ again, and so on. 

[Illustration: Fig. 1. ]

If, now, the eye which watches this process is kept from moving, theserelations will be reproduced on the retina. For the retinal areacorresponding to the triangle _p^{A}Op^{B}_, there will be lessstimulation from the sector _A_ than there would have been if thependulum had not partly hidden it. That is, the triangle in questionwill not be seen of the fused color of _A_ and _B_, but will lose apart of its _A_-component. In the same way the triangle _p^{B}OpC_will lose a part of its _B_-component; and so on alternately. And byas much as either component is lost, by so much will the color of theintercepting pendulum (in this case, black) be present to make up thedeficiency. 

We see, then, that the purely geometrical relations of disc andpendulum necessarily involve for vision a certain banded appearance ofthe area which is swept by the pendulum, if the eye is held at rest. We have now to ask, Are these the bands which we set out to study?Clearly enough these geometrically inevitable bands can be exactlycalculated, and their necessary changes formulated for any givenchange in the speed or width of _A_, _B_, or _P_. If it can be shownthat they must always vary just as the bands we set out to study are_observed_ to vary, it will be certain that the bands of the illusionhave no other cause than the interception of retinal stimulation bythe sectors of the disc, due to the purely geometrical relationsbetween the sectors and the pendulum which hides them. 

And exactly this will be found to be the case. The widths of the bandsof the illusion depend on the speed and widths of the sectors and ofthe pendulum used; the colors and intensities of the bands depend onthe colors and intensities of the sectors (and of the pendulum); whilethe total number of bands seen at one time depends on all thesefactors. 

V. GEOMETRICAL DEDUCTION OF THE BANDS. 

In the first place, it is to be noted that if the pendulum proceedsfrom left to right, for instance, before the disc, that portion of thelatter which lies in front of the advancing rod will as yet not havebeen hidden by it, and will therefore be seen of the unmodified, fusedcolor. Only behind the pendulum, where rotating sectors have beenhidden, can the bands appear. And this accords with the firstobservation (p. 167), that "The rod appears to leave behind it on thedisc a number of parallel bands. " It is as if the rod, as it passes, painted them on the disc. 

Clearly the bands are not formed simultaneously, but one after anotheras the pendulum passes through successive positions. And of course thenewest bands are those which lie immediately behind the pendulum. Itmust now be asked, Why, if these bands are produced successively, arethey seen simultaneously? To this, Jastrow and Moorehouse have giventhe answer, "We are dealing with the phenomena of after-images. " Thebands persist as after-images while new ones are being generated. Thevery oldest, however, disappear _pari-passu_ with the generation ofthe new. We have already seen (p. 169) how well these authors haveshown this, in proving that the number of bands seen, multiplied bythe rate of rotation of the disc, is a constant bearing some relationto the duration of a retinal image of similar brightness to the bands. It is to be noted now, however, that as soon as the rod has produced aband and passed on, the after-image of that band on the retina isexposed to the same stimulation from the rotating disc as before, thatis, is exposed to the fused color; and this would tend to obliteratethe after-images. Thus the oldest bands would have to disappear morequickly than an unmolested after-image of the same originalbrightness. We ought, then, to see somewhat fewer bands than theformula of Jastrow and Moorehouse would indicate. In other words, weshould find on applying the formula that the 'duration of theafter-image' must be decreased by a small amount before the numericalrelations would hold. Since Jastrow and Moorehouse did not determinethe relation of the after-image by an independent measurement, theirwork neither confirms nor refutes this conjecture. 

What they failed to emphasize is that the real origin of the bands isnot the intermittent appearances of the rod opposite the _lighter_sector, as they seem to believe, but the successive eclipse by the rodof _each_ sector in turn. 

If, in Fig. 2, we have a disc (composed of a green and a red sector)and a pendulum, moving to the right, and if _P_ represents thependulum at the instant when the green sector _AOB_ is beginning topass behind it, it follows that some other position farther to theright, as _P'_, will represent the pendulum just as the last part ofthe sector is passing out from behind it. Some part at least of thesector has been hidden during the entire interval in which thependulum was passing from _P_ to _P'_. Clearly the arc _BA'_ measuresthe band _BOA'_, in which the green stimulation from the sector _AOB_is thus at least partially suppressed, that is, on which a relativelyred band is being produced. If the illusion really depends on thesuccessive eclipse of the sectors by the pendulum, as has beendescribed, it will be possible to express BA', that is, the width ofa band, in terms of the widths and rates of movement of the twosectors and of the pendulum. This expression will be an equation, andfrom this it will be possible to derive the phenomena which the bandsof the illusion actually present as the speeds of disc and rod, andthe widths of sectors and rod, are varied. 

[Illustration: Fig 2. ]

Now in Fig. 2 let the width of the band (_i. E. _, the arc BA') = Z speed of pendulum = r degrees per second; speed of disc = r' degrees per second; width of sector AOB (_i. E. _, the arc AB) = s degrees of arc; width of pendulum (_i. E. _, the arc BC) = p degrees of arc; time in which the pendulum moves from P to P' = t seconds. 

Now arc CA' t = -------; r

but, since in the same time the green sector AOB moves from _B_ to B', we know also that arc BB' t = -------; r'then arc CA' arc BB' ------- = -------, r r'

or, omitting the word "arc" and clearing of fractions, r'(CA') = r(BB'). But now CA' = BA' - BC, while BA' = Z and BC = p;therefore CA' = Z-p. Similarly BB' = BA' + A'B' = Z + s. 

Substituting for _CA'_ and _BB'_ their values, we get

 r'(Z-p) = r(Z+s), or Z(r' - r) = rs + pr', or Z = rs + pr' / r' - r. 

It is to be remembered that _s_ is the width of the sector whichundergoes eclipse, and that it is the color of that same sector whichis subtracted from the band _Z_ in question. Therefore, whether _Z_represents a green or a red band, _s_ of the formula must refer to the_oppositely colored_ sector, _i. E. _, the one which is at that timebeing hidden. 

We have now to take cognizance of an item thus far neglected. When thegreen sector has reached the position _A'B'_, that is, is justemerging wholly from behind the pendulum, the front of the red sectormust already be in eclipse. The generation of a green band (red sectorin eclipse) will have commenced somewhat before the generation of thered band (green sector in eclipse) has ended. For a moment thependulum will lie over parts of both sectors, and while the red bandends at point _A'_, the green band will have already commenced at apoint somewhat to the left (and, indeed, to the left by a trifle morethan the width of the pendulum). In other words, the two bands_overlap_. 

This area of overlapping may itself be accounted a band, since herethe pendulum hides partly red and partly green, and obviously theresult for sensation will not be the same as for those areas where redor green alone is hidden. We may call the overlapped area a'transition-band, ' and we must then ask if it corresponds to the'transition-bands' spoken of in the observations. 

Now the formula obtained for Z includes two such transition-bands, onegenerated in the vicinity of OB and one near OA'. To find the formulafor a band produced while the pendulum conceals solely one, theoppositely colored sector (we may call this a 'pure-color' band andlet its width = W), we must find the formula for the width (w) of atransition-band, multiply it by two, and subtract the product from thevalue for Z already found. 

The formula for an overlapping or transition-band can be readily foundby considering it to be a band formed by the passage behind P of asector whose width is zero. Thus if, in the expression for Z alreadyfound, we substitute zero for s, we shall get w; that is, o + pr' pr' w = ------- = ------ r' - r r' - rSince W = Z - 2w, we have rs + pr' pr' W = -------- = 2 ------, r' - r r' - ror rs - pr' W = -------- (1) r' - r

[Illustration: Fig 3. ]

Fig. 3 shows how to derive _W_ directly (as _Z_ was derived) from thegeometrical relations of pendulum and sectors. Let _r, r', s, p_, and_t_, be as before, but now let

 width of the band (_i. E. _, the arc _BA') = W_;

that is, the band, instead of extending as before from where _P_begins to hide the green sector to where _P_ ceases to hide the same, is now to extend from the point at which _P_ ceases to hide _anypart_ of the red sector to the point where it _just commences_ again tohide the same. 

Then W + p t = -------, rand W + s t = -------, r'

therefore W + p W + s ------- = -------, r r'

 r'(W + p) = r(W + s), W (r' - r) = rs - pr', and, again, rs - pr' W = -------- . R' - r

Before asking if this pure-color band _W_ can be identified with thebands observed in the illusion, we have to remember that the valuewhich we have found for _W_ is true only if disc and pendulum aremoving in the same direction; whereas the illusion-bands are observedindifferently as disc and pendulum move in the same or in oppositedirections. Nor is any difference in their width easily observable inthe two cases, although it is to be borne in mind that there may be adifference too small to be noticed unless some measuring device isused. 

From Fig. 4 we can find the width of a pure-color band (_W_) whenpendulum and disc move in opposite directions. The letters are used asin the preceding case, and _W_ will include no transition-band. 

[Illustration: Fig. 4]

We have

 W + p t = -----, rand s - W t = -----, r'

 r'(W + p) = r(s - W), W(r' + r) = rs - pr', rs - pr' W = -------- . (2) r' + r

Now when pendulum and disc move in the same direction, rs - pr' W = ---------, (1) r' - r

so that to include both cases we may say that

 rs - pr' W = -------- . (3) r' ± r

The width (W) of the transition-bands can be found, similarly, fromthe geometrical relations between pendulum and disc, as shown in Figs. 5 and 6. In Fig. 5 rod and disc are moving in the same direction, and

 w = BB'. 

Now W - p t = -------, r'

 w t = ---, r'

 r'(w-p) = rw, w(r'-r) = pr', pr' w = ------- . (4) r'-r

[Illustration: Fig. 5]

[Illustration: Fig. 6]

In Fig. 6 rod and disc are moving in opposite directions, and

 w = BB', p - w t = -------, r

 w t = ---, r'

 r'(p - w) = rw, w(r' + r) = pr', pr' w = -------- . R' + r (5)

So that to include both cases (of movement in the same or in oppositedirections), we have that

 pr' w = -------- . R' ± r (6)

VI. APPLICATION OF THE FORMULAS TO THE BANDS OF THE ILLUSION. 

Will these formulas, now, explain the phenomena which the bands of theillusion actually present in respect to their width?

1. The first phenomenon noticed (p. 173, No. 1) is that "If the twosectors of the disc are unequal in arc, the bands are unequal inwidth; and the narrower bands correspond in color to the largersector. Equal sectors give equally broad bands. "

In formula 3, _W_ represents the width of a band, and _s_ the width ofthe _oppositely colored_ sector. Therefore, if a disc is composed, forexample, of a red and a green sector, then

 rs(green) - pr' W(red) = ------------------, r' ± rand rs(red) - pr' W(green) = ------------------, r' ± r

therefore, by dividing, W(red) rs(green) - pr' --------- = ------------------- . W(green) rs(red) - pr'

From this last equation it is clear that unless _s_(green) = _s_(red), _W_(red) cannot equal _W_(green). That is, if the two sectors areunequal in width, the bands are also unequal. This was the firstfeature of the illusion above noted. 

Again, if one sector is larger, the oppositely colored bands will belarger, that is, the light-colored bands will be narrower; or, inother words, 'the narrower bands correspond in color to the largersector. '

Finally, if the sectors are equal, the bands must also be equal. 

So far, then, the bands geometrically deduced present the samevariations as the bands observed in the illusion. 

2. Secondly (p. 174, No. 2), "The faster the rod moves the broaderbecome the bands, but not in like proportions; broad bands widenrelatively more than narrow ones. " The speed of the rod or pendulum, in degrees per second, equals _r_. Now if _W_ increases when _r_increases, _D_{[tau]}W_ must be positive or greater than zero for allvalues of _r_ which lie in question. 

Now rs - pr' W = ---------, r' ± rand (r' ± r)s [±] (rs - pr') D_{[tau]}W = --------------------------, (r ± r')

or reduced, r'(s ± p) = ----------- (r' ± r)²

Since _r'_ (the speed of the disc) is always positive, and _s_ isalways greater than _p_ (cf. P. 173), and since the denominator is asquare and therefore positive, it follows that

 D_{[tau]}W > 0

or that _W_ increases if _r_ increases. 

Furthermore, if _W_ is a wide band, _s_ is the wider sector. The rateof increase of _W_ as _r_ increases is

 r'(s ± p) D_{[tau]}W = ----------- (r' ± r)²

which is larger if _s_ is larger (_s_ and _r_ being always positive). That is, as _r_ increases, 'broad bands widen relatively more thannarrow ones. '

3. Thirdly (p. 174, No. 3), "The width of The bands increases if thespeed of the revolving disc decreases. " This speed is _r'_. That theobserved fact is equally true of the geometrical bands is clear frominspection, since in

 rs - pr' W = ---------, r' ± r

as _r'_ decreases, the denominator of the right-hand member decreaseswhile the numerator increases. 

4. We now come to the transition-bands, where one color shades overinto the other. It was observed (p. 174, No. 4) that, "These partakeof the colors of both the sectors on the disc. The wider the rod thewider the transition-bands. "

We have already seen (p. 180) that at intervals the pendulum concealsa portion of both the sectors, so that at those points the color ofthe band will be found not by deducting either color alone from thefused color, but by deducting a small amount of both colors indefinite proportions. The locus of the positions where both colors areto be thus deducted we have provisionally called (in the geometricalsection) 'transition-bands. ' Just as for pure-color bands, this locusis a radial sector, and we have found its width to be (formula 6, p. 184) pr' W = ---------, r' ± r

Now, are these bands of bi-color deduction identical with thetransition-bands observed in the illusion? Since the total concealingcapacity of the pendulum for any given speed is fixed, less of_either_ color can be deducted for a transition-band than is deductedof one color for a pure-color band. Therefore, a transition-band willnever be so different from the original fusion-color as will either'pure-color' band; that is, compared with the pure color-bands, thetransition-bands will 'partake of the colors of both the sectors onthe disc. ' Since pr' W = ---------, r' ± r

it is clear that an increase of _p_ will give an increase of _w_;_i. E. _, 'the wider the rod, the wider the transition-bands. '

Since _r_ is the rate of the rod and is always less than _r'_, themore rapidly the rod moves, the wider will be the transition-bandswhen rod and disc move in the same direction, that is, when

 pr' W = ---------, r' - r

But the contrary will be true when they move in opposite directions, for then

 pr' W = ---------, r' + r

that is, the larger _r_ is, the narrower is _w_. 

The present writer could not be sure whether or not the width oftransition-bands varied with _r_. He did observe, however (page 174)that 'the transition-bands are broader when rod and disc move in thesame, than when in opposite directions. ' This will be true likewisefor the geometrical bands, for, whatever _r_ (up to and including _r_= _r'_), pr' pr' ---- > ---- r'-r r'+r

In the observation, of course, _r_, the rate of the rod, was never solarge as _r'_, the rate of the disc. 

5. We next come to an observation (p. 174, No. 5) concerning thenumber of bands seen at any one time. The 'geometrical deduction ofthe bands, ' it is remembered, was concerned solely with the amount ofcolor which was to be deducted from the fused color of the disc. _W_and _w_ represented the widths of the areas whereon such deduction wasto be made. In observation 5 we come on new considerations, _i. E. _, asto the color from which the deduction is to be made, and the fate ofthe momentarily hidden area which suffers deduction, _after_ thependulum has passed on. 

We shall best consider these matters in terms of a concept of whichMarbe[3] has made admirable use: the 'characteristic effect. ' TheTalbot-Plateau law states that when two or more periodicallyalternating stimulations are given to the retina, there is a certainminimal rate of alternation required to produce a just constantsensation. This minimal speed of succession is called the criticalperiod. Now, Marbe calls the effect on the retina of a light-stimulationwhich lasts for the unit of time, the 'photo-chemical unit-effect. 'And he says (_op. Cit. _, S. 387): "If we call the unit of time1[sigma], the sensation for each point on the retina in each unit oftime is a function of the simultaneous and the few immediatelypreceding unit-effects; this is the characteristic effect. "

 [3] 'Marbe, K. : 'Die stroboskopischen Erscheinungen, ' _Phil. Studien. _, 1898, XIV. , S. 376. 

We may now think of the illusion-bands as being so and so manydifferent 'characteristic effects' given simultaneously in so and somany contiguous positions on the retina. But so also may we think ofthe geometrical interception-bands, and for these we can deduce anumber of further properties. So far the observed illusion-bands andthe interception-bands have been found identical, that is, in so faras their widths under various conditions are concerned. We have now tosee if they present further points of identity. 

As to the characteristic effects incident to the interception-bands;in Fig. 7 (Plate V. ), let _A'C'_ represent at a given moment _M_, thetotal circumference of a color-disc, _A'B'_ represent a green sectorof 90°, and _B'C'_ a red complementary sector of 270°. If the disc issupposed to rotate from left to right, it is clear that a momentprevious to _M_ the two sectors and their intersection _B_ will haveoccupied a position slightly to the left. If distance perpendicularlyabove _A'C'_ is conceived to represent time previous to _M_, thecorresponding previous positions of the sectors will be represented bythe oblique bands of the figure. The narrow bands (_GG_, _GG_) are theloci of the successive positions of the green sector; the broaderbands (_RR_, _RR_), of the red sector. 

In the figure, 0. 25 mm. Vertically = the unit of time = 1[sigma]. Thesuccessive stimulations given to the retina by the disc _A'C'_, say ata point _A'_, during the interval preceding the moment _M_ will be

 green 10[sigma], red 30[sigma], green 10[sigma], red 30[sigma], etc. 

Now a certain number of these stimulations which immediately precede_M_ will determine the characteristic effect, the fusion color, forthe point _A'_ at the moment _M_. We do not know the number ofunit-stimulations which contribute to this characteristic effect, nordo we need to, but it will be a constant, and can be represented by adistance _x_ = _A'A_ above the line _A'C'_. Then _A'A_ will representthe total stimulus which determines the characteristic effect at _A'_. Stimuli earlier than _A_ are no longer represented in the after-image. _AC_ is parallel to _A'C'_, and the characteristic effect for anypoint is found by drawing the perpendicular at that point between thetwo lines _A'C_ and _AC_. 

Just as the movement of the disc, so can that of the concealingpendulum be represented. The only difference is that the pendulum isnarrower, and moves more slowly. The slower rate is represented by asteeper locus-band, _PP'_, than those of the swifter sectors. 

We are now able to consider geometrically deduced bands as'characteristic effects, ' and we have a graphic representation of thecolor-deduction determined by the interception of the pendulum. Thededuction-value of the pendulum is the distance (_xy_) which itintercepts on a line drawn perpendicular to _A'C'_. 

Lines drawn perpendicular to _A'C'_ through the points of intersectionof the locus-band of the pendulum with those of the sectors will givea 'plot' on _A'C'_ of the deduction-bands. Thus from 1 to 2 thededuction is red and the band green; from 2 to 3 the deduction isdecreasingly red and increasingly green, a transition-band; from 3 to4 the deduction is green and the band red; and so forth. 

We are now prepared to continue our identification of thesegeometrical interception-bands with the bands observed in theillusion. It is to be noted in passing that this graphicrepresentation of the interception-bands as characteristic effects(Fig. 7) is in every way consistent with the previous equationaltreatment of the same bands. A little consideration of the figure willshow that variations of the widths and rates of sectors and pendulumwill modify the widths of the bands exactly as has been shown in theequations. 

The observation next at hand (p. 174, No. 5) is that "The total numberof bands seen at any one time is approximately constant, howsoever thewidths of the sectors and the width and rate of the rod may vary. Butthe number of bands is inversely proportional (Jastrow and Moorehouse)to the time of rotation of the disc; that is, the faster the disc, themore bands. "

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE V. Fig. 7. Fig. 8. Fig. 9. ]

This is true, point for point, of the interception-bands of Fig. 7. Itis clear that the number of bands depends on the number ofintersections of _PP'_ with the several locus-bands _RR_, _GG_, _RR_, etc. Since the two sectors are complementary, having a constant sum of360°, their relative widths will not affect the number of suchintersections. Nor yet will the width of the rod _P_ affect it. As tothe speed of _P_, if the locus-bands are parallel to the line _A'C'_, that is, of the disc moved _infinitely_ rapidly, there would be thesame number of intersections, no matter what the rate of _P_, that is, whatever the obliqueness of _PP'_. But although the disc does notrotate with infinite speed, it is still true that for a considerablerange of values for the speed of the pendulum the number ofintersections is constant. The observations of Jastrow and Moorehousewere probably made within such a range of values of _r_. For whiletheir disc varied in speed from 12 to 33 revolutions per second, thatis, 4, 320 to 11, 880 degrees per second, the rod was merely passed toand fro by hand through an excursion of six inches (J. And M. , _op. Cit. _, pp. 203-5), a method which could have given no speed of the rodcomparable to that of the disc. Indeed, their fastest speed for therod, to calculate from certain of their data, was less than 19 inchesper second. 

The present writer used about the same rates, except that for the discno rate below 24 revolutions per second was employed. This is aboutthe rate which v. Helmholtz[4] gives as the slowest which will yieldfusion from a bi-sectored disc in good illumination. It is hard toimagine how, amid the confusing flicker of a disc revolving but 12times in the second, Jastrow succeeded in taking any reliableobservations at all of the bands. Now if, in Fig. 8 (Plate V. ), 0. 25mm. On the base-line equals one degree, and in the vertical directionequals 1[sigma], the locus-bands of the sectors (here equal to eachother in width), make such an angle with _A'C'_ as represents the discto be rotating exactly 36 times in a second. It will be seen that thespeed of the rod may vary from that shown by the locus _P'P_ to thatshown by _P'A_; and the speeds represented are respectively 68. 96 and1, 482. 64 degrees per second; and throughout this range of speeds thelocus-band of _P_ intercepts the loci of the sectors always the samenumber of times. Thus, if the disc revolves 36 times a second, thependulum may move anywhere from 69 to 1, 483 degrees per second withoutchanging the number of bands seen at a time. 

 [4] v. Helmholtz, H. : 'Handbuch d. Physiolog. Optik, ' Hamburg u. Leipzig, 1896, S. 489. 

And from the figure it will be seen that this is true whether thependulum moves in the same direction as the disc, or in the oppositedirection. This range of speed is far greater than the concentricallyswinging metronome of the present writer would give. The rate ofJastrow's rod, of 19 inches per second, cannot of course be exactlytranslated into degrees, but it probably did not exceed the limit of1, 483. Therefore, although beyond certain wide limits the rate of thependulum will change the total number of deduction-bands seen, yet theobservations were, in all probability (and those of the presentwriter, surely), taken within the aforesaid limits. So that as theobservations have it, "The total number of bands seen at any one timeis approximately constant, howsoever . . . The rate of the rod mayvary. " On this score, also, the illusion-bands and the deduction-bandspresent no differences. 

But outside of this range it can indeed be _observed_ that the numberof bands does vary with the rate of the rod. If this rate (_r_) isincreased beyond the limits of the previous observations, it willapproach the rate of the disc (_r'_). Let us increase _r_ until _r_ =_r'_. To observe the resulting bands, we have but to attach the rod orpendulum to the front of the disc and let both rotate together. Nobands are seen, _i. E. _, the number of bands has become zero. And this, of course, is just what should have been expected from a considerationof the deduction-bands in Fig. 8. 

One other point in regard to the total number of bands seen: it wasobserved (page 174, No. 5) that, "The faster the disc, the morebands. " This too would hold of the deduction-bands, for the faster thedisc and sectors move, the narrower and more nearly parallel to _A'C'_(Fig. 7) will be their locus-bands, and the more of these bands willbe contained within the vertical distance _A'A_ (or _C'C_), which, itis remembered, represents the age of the oldest after-image whichstill contributes to the characteristic effect. _PP'_ will thereforeintercept more loci of sectors, and more deduction-bands will begenerated. 

6. "The colors of the bands (page 175, No. 6) approximate those of thetwo sectors; the transition-bands present the adjacent 'pure colors'merging into each other. But _all_ the bands are modified in favor ofthe moving rod. If, now, the rod is itself the same in color as one ofthe sectors, the bands which should have been of the other color arenot to be distinguished from the fused color of the disc when no rodmoves before it. "

These items are equally true of the deduction-bands, since a deductionof a part of one of the components from a fused color must leave anapproximation to the other component. And clearly, too, by as much aseither color is deducted, by so much must the color of the pendulumitself be added. So that, if the pendulum is like one of the sectorsin color, whenever that sector is hidden the deduction for concealmentwill exactly equal the added allowance for the color of the pendulum, and there will be no bands of the other color distinguishable from thefused color of the disc. 

It is clear from Fig. 7 why a transition-band shades gradually fromone pure-color band over into the other. Let us consider thetransition-band 2-3 (Fig. 7). Next it on the right is a green band, onthe left a red. Now at the right-hand edge of the transition-band itis seen that the deduction is mostly red and very little green, aratio which changes toward the left to one of mostly green and verylittle red. Thus, next to the red band the transition-band will bemostly red, and it will shade continuously over into green on the sideadjacent to the green band. 

7. The next observation given (page 175, No. 7) was that, "The bandsare more strikingly visible when the two sectors differ considerablyin luminosity. " This is to be expected, since the greater thecontrast, whether in regard to color, saturation, or intensity, between the sectors, the greater will be such contrast between the twodeductions, and hence the greater will it be between the resultingbands. And, therefore, the bands will be more strikinglydistinguishable from each other, that is, 'visible. '

8. "A _broad_ but slowly-moving rod shows the bands lying over itself. Other bands can also be seen behind it on the disc. "

In Fig. 9 (Plate V. ) are shown the characteristic effects produced bya broad and slowly-moving rod. Suppose it to be black. It can be sobroad and move so slowly that for a space the characteristic effect islargely black (Fig. 9 on both sides of _x_). Specially will this betrue between _x_ and _y_, for here, while the pendulum contributes no_more_ photo-chemical unit-effects, it will contribute the newer one, and howsoever many unit-effects go to make up the characteristiceffect, the newer units are undoubtedly the more potent elements indetermining this effect. The old units have partly faded. One may saythat the newest units are 'weighted. '

Black will predominate, then, on both sides of _x_, but speciallybetween _x_ and _y_. For a space, then, the characteristic effect willcontain enough black to yield a 'perception of the rod. ' The width ofthis region depends on the width and speed of the rod, but in Fig. 9it will be roughly coincident with _xy_, though somewhat behind (tothe left of) it. The characteristic will be either wholly black, asjust at _x_, or else largely black with the yet contributoryafter-images (shown in the triangle _aby_). Some bands will thus beseen overlying the rod (1-8), and others lying back of it (9-16). 

We have now reviewed all the phenomena so far enumerated of theillusion-bands, and for every case we have identified these bands withthe bands which must be generated on the retina by the mereconcealment of the rotating sectors by the moving rod. It has beenmore feasible thus far to treat these deduction-bands as if possiblythey were other than the bands of the illusion; for although theformer must certainly appear on the retina, yet it was not clear thatthe illusion-bands did not involve additional and complicated retinalor central processes. The showing that the two sets of bands have inevery case identical properties, shows that they are themselvesidentical. The illusion-bands are thus explained to be due merely tothe successive concealment of the sectors of the disc as each passesin turn behind the moving pendulum. The only physiological phenomenainvolved in this explanation have been the persistence as after-imagesof retinal stimulations, and the summation of these persisting imagesinto characteristic effects--both familiar phenomena. 

From this point on it is permissible to simplify the point of view byaccounting the deduction-bands and the bands of the illusion fullyidentified, and by referring to them under either name indifferently. Figs. 1 to 9, then, are diagrams of the bands which we actuallyobserve on the rotating disc. We have next briefly to consider a fewspecial complications produced by a greater breadth or slower movementof the rod, or by both together. These conditions are called'complicating' not arbitrarily, but because in fact they yield thebands in confusing form. If the rod is broad, the bands appear tooverlap; and if the rod moves back and forth, at first rapidly butwith decreasing speed, periods of mere confusion occur which defydescription; but the bands of the minor color may be broader or _maybe narrower_ than those of the other color. 

VII. FURTHER COMPLICATIONS OF THE ILLUSION. 

9. If the rod is broad and moves slowly, the narrower bands are likecolored, not with the broader, as before, but with the narrowersector. 

The conditions are shown in Fig. 9. From 1 to 2 the deduction isincreasingly green, and yet the remainder of the characteristic effectis also mostly green at 1, decreasingly so to the right, and at 2 ispreponderantly red; and so on to 8; while a like considerationnecessitates bands from _x_ to 16. All the bands are in a sensetransition-bands, but 1-2 will be mostly green, 2-3 mostly red, and soforth. Clearly the widths of the bands will be here proportional tothe widths of the like-colored sectors, and not as before to theoppositely colored. 

It may reasonably be objected that there should be here no bands atall, since the same considerations would give an increasingly red bandfrom _B'_ to _A'_, whereas by hypothesis the disc rotates so fast asto give an entirely uniform color. It is true that when thecharacteristic effect is _A' A_ entire, the fusion-color is so wellestablished as to assimilate a fresh stimulus of either of thecomponent colors, without itself being modified. But on the area from1 to 16 the case is different, for here the fusion-color is less wellestablished, a part of the essential colored units having beenreplaced by black, the color of the rod; and black is no stimulation. So that the same increment of component color, before ineffective, isnow able to modify the enfeebled fusion-color. 

Observation confirms this interpretation, in that band _y-1_ is notred, but merely the fusion-color slightly darkened by an increment ofblack. Furthermore, if the rod is broad and slow in motion, but whiteinstead of black, no bands can be seen overlying the rod. For here thesmall successive increments which would otherwise produce the bands1-2, 2-3, etc. , have no effect on the remainder of the fusion-colorplus the relatively intense increment of white. 

It may be said here that the bands 1-2, 2-3, etc. , are less intensethan the bands _x_-9, 9-10, etc. , because there the recent or weightedunit-effects are black, while here they are the respective colors. Also the bands grow dimmer from _x_-9 to 15-16, that is, as theybecome older, for the small increment of one color which would giveband 15-16 is almost wholly overridden by the larger and fresher massof stimulation which makes for mere fusion. This last is true of thebands always, whatever the rate or width of the rod. 

10. In general, equal sectors give equal bands, but if one sector isconsiderably more intense than the other, the bands of the brightercolor will, for a broad and swiftly-moving rod, be the broader. Thebrighter sector, though equal in width to the other, contributes moretoward determining the fusion-color; and this fact is represented byan intrusion of the stronger color into the transition-bands, at theexpense of the weaker. For in these, even the decreased amount of thestronger color, on the side next a strong-color band, is yet morepotent than the increased amount of the feebler color. In order toobserve this fact one must have the rod broad, so as to give a broadtransition-band on which the encroachment of the stronger color may beevident. The process is the same with a narrow rod and narrowtransition-bands, but, being more limited in extent, it is less easilyobserved. The rod must also move rapidly, for otherwise the bandsoverlap and become obscure, as will be seen in the next paragraph. 

11. If the disc consists of a broad and narrow sector, and if the rodis broad and moves at first rapidly but more slowly with each newstroke, there are seen at first broad, faint bands of theminority-color, and narrow bands of the majority-color. The formergrow continuously more intense as the rod moves more slowly, and grownarrower in width down to zero; whereupon the other bands seem tooverlap, the overlapped part being doubly deep in color, while thenon-overlapped part has come to be more nearly the color of the minorsector. The overlapped portion grows in width. As the rate of the rodnow further decreases, a confused state ensues which cannot bedescribed. When, finally, the rod is moving very slowly, the phenomenadescribed above in paragraph 9 occur. 

The successive changes in appearance as the rod moves more and moreslowly, are due to the factors previously mentioned, and to one otherwhich follows necessarily from the given conditions but has not yetbeen considered. This is the last new principle in the illusion whichwe shall have to take up. Just as the transition-bands are regionswhere two pure-color bands overlap, so, when the rod is broad andmoves slowly, other overlappings occur to produce more complicatedarrangements. 

These can be more compactly shown by diagram than by words. Fig. 10, _a_, _b_ and _c_ (Plate VI. ), show successively slower speeds of therod, while all the other factors are the same. In practice thetendency is to perceive the transition-bands as parts of the broadfaint band of the minor color, which lies between them. It can beseen, then, how the narrow major-color bands grow only slightly wider(Fig. 10, _a_, _b_) until they overlap (_c_); how the broadminor-color bands grow very narrow and more intense in color, therebeing always more of the major color deducted (in _b_ they are reducedexactly to zero, _z_, _z_, _z_). In _c_ the major-color bands overlap(_o_, _o_, _o_) to give a narrow but doubly intense major-color bandsince, although with one major, two minor locus-bands are deducted. The other bands also overlap to give complicated combinations betweenthe _o_-bands. These mixed bands will be, in part at least, minor-color bands (_q_, _q_, _q_), since, although a minor locus-bandis here deducted, yet nearly two major locus-bands are also taken, leaving the minor color to predominate. This corresponds with theobservation above, that, '. . . The non-overlapped part has come to bemore nearly the color of the minor sector. '

A slightly slower speed of the rod would give an irreducible confusionof bands, since the order in which they overlap becomes verycomplicated. Finally, when the rod comes to move very slowly, as inFig. 9, the appearance suffers no further change, except for a gradualnarrowing of all the bands, up to the moment when the rod comes torest. 

It is clear that this last principle adduced, of the multipleoverlapping of bands when the rod is broad and moves slowly, can givefor varying speeds of the rod the greatest variety of combinations ofthe bands. Among these is to be included that of no bands at all, aswill be understood from Fig. 11 (Plate VII). And in fact, a littlepractice will enable the observer so to adjust the rate of the (broad)rod to that of the disc that no bands are observable. But care must betaken here that the eye is rigidly fixated and not attracted intomovement by the rod, since of course if the eye moves with the rod, nobands can be seen, whatever the rate of movement may be. 

Thus, all the phenomena of these illusion-bands have been explained asthe result solely of the hiding by the rod of successive sectors ofthe disc. The only physiological principles involved are those (1) ofthe duration of after-images, and (2) of their summation into acharacteristic effect. It may have seemed to the reader tedious andunnecessary so minutely to study the bands, especially the detailslast mentioned; yet it was necessary to show how _all_ the possibleobservable phenomena arise from the purely geometrical fact thatsectors are successively hidden. Otherwise the assertions of previousstudents of the illusion, that more intricate physiological processesare involved, could not have been refuted. The present writer does notassert that no processes like contrast, induction, etc. , come intoplay to modify somewhat the saturation, etc. , of the colors in thebands. It must be here as in every other case of vision. But it is nowdemonstrated that these remoter physiological processes contributenothing _essential_ to the illusion. For these could be dispensed withand the illusion would still remain. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VI. Fig. 10. ]

If any reader still suspects that more is involved than thepersistence of after-images, and their summation into a characteristiceffect, he will find it interesting to study the illusion with acamera. The 'physiological' functions referred to belong as well tothe dry-plate as to the retina, while the former exhibits, presumably, neither contrast nor induction. The illusion-bands can be easilyphotographed in a strong light, if white and black sectors are used inplace of colored ones. It is best to arrange the other variablefactors so as to make the transition-bands as narrow as possible (p. 174, No. 4). The writer has two negatives which show the bands verywell, although so delicately that it is not feasible to try toreproduce them. 

VIII. SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION. 

The influence of the width of sector is prettily shown by a specialdisc like that shown in Fig. 12 (Plate VII. ), where the colors aredark-red and light-green, the shaded being the darker sector. A narrowrod passed before such a disc by hand at a moderate rate will giveover the outer ring equally wide green and red bands; but on the innerrings the red bands grow narrower, the green broader. 

The fact that the bands are not 'images of the rod' can be shown byanother disc (Fig. 13, Plate VII. ). In all three rings the lighter(green) sector is 60° wide, but disposed on the disc as shown. Thebands are broken into zigzags. The parts over the outer ring lagbehind those over the middle, and these behind those over the innerring--'behind, ' that is, farther behind the rod. 

Another effective variation is to use rods alike in color with one orthe other of the sectors. Here it is clear that when the rod hides theoppositely-colored sector, the deduction of that color is replaced(not by black, as happens if the rod is black) but by the very colorwhich is already characteristic of that band. But when the rod hidesthe sector of its own color, the deduction is replaced by the verysame color. Thus, bands like colored with the rod gain in depth oftone, while the other pure-color bands present simply thefusion-color. 

IX. A STROBOSCOPE WHICH DEPENDS ON THE SAME PRINCIPLE. 

If one produce the illusion by using for rod, not the pendulum of ametronome, but a black cardboard sector on a second color-mixer placedin front of the first and rotating concentrically with it, that is, with the color-disc, one will observe with the higher speeds of therod which are now obtainable several further phenomena, all of whichfollow simply from the geometrical relations of disc and rod (now arotating sector), as discussed above. The color-mixer in front, whichbears the sector (let it still be called a 'rod'), should rotate byhand and independently of the disc behind, whose two sectors are togive the bands. The sectors of the disc should now be equal, and therod needs to be broader than before, say 50° or 60°, since it is torevolve very rapidly. 

First, let the rod and disc rotate in the same direction, the disc atits former rate, while the rod begins slowly and moves faster andfaster. At first there is a confused appearance of vague, radialshadows shuffling to and fro. This is because the rod is broad andmoves slowly (cf. P. 196, paragraph II). 

As the velocity of the rod increases, a moment will come when theconfusing shadows will resolve themselves into four (sometimes five)radial bands of one color with four of the other color and theappropriate transition-bands between them. The bands of either colorare symmetrically disposed over the disc, that is, they lie at rightangles to one another (if there are five bands they lie at angles of72°, etc. ). But this entire system of bands, instead of lyingmotionless over the disc as did the systems hitherto described, itselfrotates rapidly in the opposite direction from disc to rod. As the rodrotates forward yet faster, no change is seen except that the systemof bands moves backward more and more slowly. Thus, if one rotate therod with one's own hand, one has the feeling that the backwardmovement of the bands is an inverse function of the increase invelocity of the rod. And, indeed, as this velocity still increases, the bands gradually come to rest, although both the disc and the rodare rotating rapidly. 

But the system of bands is at rest for only a particular rate of therod. As the latter rotates yet faster, the system of bands nowcommences to rotate slowly forward (with the disc and rod), then moreand more rapidly (the velocity of the rod still increasing), until itfinally disintegrates and the bands vanish into the confused flickerof shadows with which the phenomenon commenced. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VII. Fig. 11. Fig. 12. Fig. 13. ]

This cycle now plays itself off in the reverse order if the speed ofthe rod is allowed gradually to decrease. The bands appear firstmoving forward, then more slowly till they come to rest, then movingbackward until finally they relapse into confusion. 

But let the rate of the rod be not decreased but always steadilyincreased. The bands will reappear, this time three of each color withsix transition-bands. As before, the system at first rotates backward, then lies still, and then moves forward until it is dissolved. As therod moves still faster, another system appears, two bands of eachcolor forming a diameter and the two diameters lying at right angles. This system goes through the same cycle of movements. When theincreased velocity of the rod destroys this system, another appearshaving one band of each color, the two lying on opposite sides of thecenter. The system goes through the same phases and is likewisedissolved. Now, at this point the rod will be found to be rotating atthe same speed as the disc itself. 

The explanation of the phenomenon is simple. The bands are notproduced by a single interruption of the vision of a sector by a rod, but each band is made up of successive superpositions on the retina ofmany such single-interruption bands. The overlapping of bands has beenalready described (cf. Fig. 10 and pp. 196-198); superposition dependsof course on the same principle. 

At the moment when a system of four bands of either color is seen atrest, the rod is moving just one fifth as rapidly as the disc; sothat, while the rod goes once around, either sector, say the greenone, will have passed behind it exactly four times, and at pointswhich lie 90° apart. Thus, four red bands are produced which lie atright angles to one another. But the disc is revolving at least 24times in a second, the rod therefore at least 4. 8 times, so thatwithin the interval of time during which successive stimuli stillcontribute to the characteristic effect the rod will have revolvedseveral times, and with each revolution four red bands at right anglesto one another will have been formed. And if the rod is moving_exactly_ one fifth as fast as the disc, each new band will begenerated at exactly that position on the disc where was thecorresponding band of the preceding four. The system of bands thusappear motionless on the disc. 

The movement of the system arises when the rate of the rod is slightlyless or more than one fifth that of the disc. If slightly less, thebands formed at each rotation of the rod do not lie precisely overthose of the previous rotation, but a little to the rear of them. Thenew set still lies mostly superposed on the previous sets, and sofuses into a regular appearance of bands, but, since each newincrement lags a bit behind, the entire system appears to rotatebackward. The apparatus is actually a cinematograph, but one whichgives so many pictures in the second that they entirely fuse and thestrobic movement has no trace of discontinuity. 

If the rod moves a trifle more than one fifth as fast as the disc, itis clear that the system of bands will rotate forward, since each newset of bands will lie slightly ahead of the old ones with which itfuses. The farther the ratio between the rates of rod and disc departsfrom exactly 1:5, whether less or greater, the more rapid will thestrobic movement, backward or forward, be; until finally thedivergence is too great, the newly forming bands lie too far ahead orbehind those already formed to fuse with them and so be apperceived asone system, and so the bands are lost in confusion. Thus the cycle ofmovement as observed on the disc is explained. As the rate of the rodcomes up to and passes one fifth that of the disc, the system of fourbands of each color forms in rapid backward rotation. Its movementgrows slower and slower, it comes to rest, then begins to whirlforward, faster and faster, till it breaks up again. 

The same thing happens as the rate of the rod reaches and exceeds justone fourth that of the disc. The system contains three bands of eachcolor. The system of two bands of each color corresponds to the ratio1:3 between the rates, while one band of each color (the two lyingopposite) corresponds to the ratio 1:2. 

If the rod and the disc rotate in opposite directions, the phenomenaare changed only in so far as the changed geometrical relationsrequire. For the ratio 1:3 between the two rates, the strobic systemhas four bands of each color; for 1:2, three bands of each color;while when the two rates are equal, there are two bands of each color, forming a diameter. As would be expected from the geometricalconditions, a system of one band of each color cannot be generatedwhen rod and disc have opposite motions. For of course the rod cannotnow hide two or more times in succession a sector at any given point, without hiding the same sector just as often at the opposite point, 180° away. Here, too, the cycle of strobic movements is different. Itis reversed. Let the disc be said to rotate forward, then if the rateof the rod is slightly less than one fourth, etc. , that of the disc, the system will rotate forward; if greater, it will rotate backward. So that as the rate of the rod increases, any system on its appearancewill move forward, then stand still, and lastly rotate backward. Thereason for this will be seen from an instant's consideration of wherethe rod will hide a given sector. 

It is clear that if, instead of using as 'rod' a single radial sector, one were to rotate two or more such sectors disposed at equal angularintervals about the axis, one would have the same strobic phenomena, although they would be more complicated. Indeed, a large number ofrather narrow sectors can be used or, what is the same thing, a seconddisc with a row of holes at equal intervals about the circumference. The disc used by the writer had a radius of 11 inches, and aconcentric ring of 64 holes, each 3/8 of an inch in diameter, lying 10inches from the center. The observer looks through these holes at thecolor-disc behind. The two discs need not be placed concentrically. 

When produced in this way, the strobic illusion is exceedingly pretty. Instead of straight, radial bands, one sees a number of brightlycolored balls lying within a curving band of the other color andwhirling backward or forward, or sometimes standing still. Then thesebreak up and another set forms, perhaps with the two colors changedabout, and this then oscillates one way or the other. A rainbow discsubstituted for the disc of two sectors gives an indescribablycomplicated and brilliant effect; but the front disc must rotate moreslowly. This disc should in any case be geared for high speeds andshould be turned by hand for the sake of variations in rate, andconsequently in the strobic movement. 

It has been seen that this stroboscope is not different in principlefrom the illusion of the resolution-bands which this paper has aimedto explain. The resolution-bands depend wholly on the purelygeometrical relations between the rod and the disc, whereby as bothmove the rod hides one sector after the other. The only physiologicalprinciples involved are the familiar processes by which stimulationsproduce after-images, and by which the after-images of rapidlysucceeding stimulations are summed, a certain number at a time, into acharacteristic effect. 

 * * * * *

 STUDIES IN MEMORY. 

 * * * * *

RECALL OF WORDS, OBJECTS AND MOVEMENTS. 

BY HARVEY A. PETERSON. 

Kirkpatrick, [1] in experimenting with 379 school children and collegestudents, found that 3-1/3 times as many objects were recalled asvisual words after an interval of three days. The experiment consistedin showing successively 10 written names of common objects in the onecase and 10 objects in the other at the rate of one every two seconds. Three days later the persons were asked to recall as many of eachseries as possible, putting all of one series together. The averagesthus obtained were 1. 89 words, 6. 29 objects. The children were notmore dependent on the objects than the college students. 

 [1] Kirkpatrick, E. A. : PSYCHOLOGICAL, REVIEW, 1894, Vol. I. , p. 602. 

Since the experiment just described was performed without laboratoryfacilities, Calkins[2] repeated it with 50 college women, substitutinglantern pictures for objects. She obtained in recall, after two days, the averages 4. 82 words, 7. 45 pictures. The figures, however, are thenumber of objects or words remembered out of ten, not necessarilycorrectly placed. Kirkpatrick's corresponding figures for collegewomen were 3. 22 words, 5. 44 objects. The two experiments substantiallyagree, Calkins' higher averages being probably due to the shorteningof the interval to two days. 

 [2] Calkins, M. W. : PSYCHOLOGICAL, REVIEW, 1898, Vol. V. , p. 451. 

Assuming, thus, that objects are better remembered than names indeferred recall, the question arises whether this holds true when theobjects and names are coupled with strange and arbitrary symbols--aquestion which is clearly of great practical interest from theeducational point of view, as it is involved in the pedagogicalproblem whether a person seeking to acquire the vocabulary of aforeign language ought to connect the foreign words with the familiarwords or with the objects themselves. And the further question arises:what are the facts in the case of movements instead of objects, andcorrespondingly in that of verbs instead of nouns. Both questions arethe problems of the following investigation. 

As foreign symbols, either the two-figure numbers were used ornonsense-words of regularly varying length. As familiar material, nouns, objects, verbs and movements were used. The words were alwaysconcrete, not abstract, by which it is meant that their meaning wascapable of demonstration to the senses. With the exception of a fewlater specified series they were monosyllabic words. The nouns mightdenote objects of any size perceptible to the eye; the objects, however, were all of such a size that they could be shown through a14×12 cm. Aperture and still leave a margin. Their size was thereforelimited. 

Concerning the verbs and movements it is evident that, while stillbeing concrete, they might be simple or complicated activitiesconsuming little or much time, and further, might be movements ofparts of the body merely, or movements employing other objects aswell. In this experiment complicated activities were avoided even inthe verb series. Simple activities which could be easily and quicklyimaged or made were better for the purpose in view. 

THE _A_ SET. 

The _A_ set contained sixteen series, _A_^{1}, _A_^{2}, _A_^{3}, etc. , to _A_^{16}. They were divided as follows:

 Numbers and nouns: _A_^{1}, _A_^{5}, _A_^{9}, _A_^{13}. Numbers and objects: _A_^{2}, _A_^{6}, _A_^{10}, _A_^{14}. Numbers and verbs: _A_^{3}, _A_^{7}, _A_^{11}, _A_^{15}. Numbers and movements: _A_^{4}, _A_^{8}, _A_^{12}, _A_^{16}. 

The first week _A_^{1-4} were given, the second week _A_^{5-8}, etc. , so that each week one series of each of the four types was given thesubject. 

In place of foreign symbols the numbers from 1 to 99 were used, exceptin _A_^{13-15}, in which three-figure numbers were used. 

Each series contained seven couplets, except _A_^{13-16}, which, onaccount of the greater difficulty of three-figure numbers, containedfive. Each couplet was composed of a number and a noun, object, verb, or movement. 

Certain rules were observed in the composition of the series. Sincethe test was for permanence, to avoid confusion no number was used inmore than one couplet. No two numbers of a given series were chosenfrom the same decade or contained identical final figures. No word wasused in more than one couplet. Their vowels, and initial and finalconsonants were so varied within a single series as to eliminatephonetic aids, viz. , alliteration, rhyme, and assonance. The kind ofassonance avoided was identity of final sounded consonants insuccessive words, _e. G. _, lane, vine. 

The series were composed in the following manner: After thetwenty-eight numbers for four series had been chosen, the words whichentered a given series were selected one from each of a number oflists of words. These lists were words of like-sounded vowels. Afterone word had been chosen from each list, another was taken from thefirst list, etc. As a consequence of observing the rules by whichalliteration, rhyme, and assonance were eliminated, the words of aseries usually represented unlike categories of thought, but where twowords naturally tended to suggest each other one of them was rejectedand the next eligible word in the same column was chosen. Thefollowing is a typical series from the _A_ set. 

 _A_^{1}. Numbers and Nouns. 

 19 42 87 74 11 63 38 desk girl pond muff lane hoop vine

The apparatus used in the _A_ set and also in all the later sets maybe described as follows: Across the length of a table ran a large, black cardboard screen in the center of which was an oblong aperture14 cm. High and 12 cm. Wide. The center of the aperture was on a levelwith the eyes of the subject, who sat at the table. The aperture wasopened and closed by a pneumatic shutter fastened to the back of thescreen. This shutter consisted of two doors of black cardboard slidingto either side. By means of a large bulb the length of exposure couldbe regulated by the operator, who stood behind the table. 

The series--consisting of cards 4×2½ cm. , each containing a printedcouplet--was carried on a car which moved on a track behind andslightly below the aperture. The car was a horizontal board 150 cm. Long and 15 cm. Wide, fixed on two four-wheeled trucks. It was dividedby vertical partitions of black cardboard into ten compartments, eachslightly wider than the aperture to correspond with the visual angle. A curtain fastened to the back of the car afforded a black backgroundto the compartments. The couplets were supported by being insertedinto a groove running the length of the car, 3 cm. From the front. Ashutter 2 cm. High also running the length of the car in front of thegroove, fastened by hinges whose free arms were extensible, concealedeither the upper or the lower halves of the cards at the will of theoperator; _i. E. _, either the foreign symbols or the words, respectively. A screen 15 cm. High and the same length as the car, sliding in vertical grooves just behind the cards and in front of thevertical partitions, shut off the objects when desired, leaving onlythe cards in view. Thus the apparatus could be used for all four typesof series. 

The method of presentation and the time conditions of the _A_ set wereas follows:--A metronome beating seconds was used. It was kept in asound-proof box and its loudness was therefore under control. It wasjust clearly audible to both operator and subject. In learning, eachcouplet was exposed 3 secs. , during about 2 secs. Of which the shutterwas fully open and motionless. During this time the subject read thecouplet inaudibly as often as he wished, but usually in time with themetronome. His object was to associate the terms of the couplet. Therewas an interval of 2 secs. After the exposure of each couplet, andthis was required to be filled with repetition of only the_immediately preceding couplet_. After the series had been presentedonce there was an interval of 2 secs. Additional, then a secondpresentation of it commenced and after that a third. At the completionof the third presentation there was an interval of 6 secs. Additionalinstead of the 2, at the expiration of which the test commenced. 

_A_^{13-16} had five presentations instead of three. The testconsisted in showing the subject either the numbers or the words inaltered order and requiring him to write as many of the absent termsas he could. In the object and movement series the objects were alsoshown and the movements repeated by the subject if words were thegiven terms. The time conditions in the test were, Exposure of a term 3 secs. Post-term interval in A^{1-12} 4 secs. Post-term interval in A^{13-16} 6 secs. 

This allowed the subject 7 secs. For recalling and writing each termin A^{1-12} and 9 sec. In A^{13-16}. If a word was recalled after thattime it was inserted, but no further insertions were made after thetest of a series had been completed. An interval of 3 min. Elapsedbetween the end of the test of one series and the beginning of thenext series, during which the subject recorded the English word of anycouplet in which an indirect association had occurred, and also hissuccess in obtaining visual images if the series was a noun or a verbseries. 

As already indicated, four series--a noun, an object, a verb, and amovement series--given within a half hour, constituted a day's workthroughout the year. Thus variations due to changes in thephysiological condition of the subject had to affect all four types ofseries. 

Two days later these series were tested for permanence, and in thesame way as the tests for immediate recall, with this exception:

 Post-term interval in A^{13-16} 8 secs. 

Thus 11 secs. Were allowed for the deferred recall of each term inA^{13-16}. 

In the movement series of this set, to avoid hesitation and confusion, the operator demonstrated to the subject immediately before the seriesbegan, once for each word, how the movements were to be made. 

The _A_ set was given to three subjects. The results of each subjectare arranged separately in the following table. In the tests the wordswere required in A^{1-4}, in A^{5-16} the numbers. The figures showthe number of terms correctly recalled out of seven couplets inA^{1-12} and out of five couplets in A^{13-16}, _exclusive_ ofindirect association couplets. The figures in brackets indicate thenumber of correctly recalled couplets per series in which indirectassociations occurred. The total number correctly recalled in anyseries is their sum. The figures in the per cent. Row give thepercentage of correctly recalled couplets left after discarding bothfrom the number recalled and from the total number of couplets giventhose in which indirect associations occurred. This simply diminishedthe subject's number of chances. A discussion of the propriety of thiselimination will be found later. In _A_^{1-12} the absent terms had tobe recalled exactly in order, to be correct, but in _A_^{13-16}, onaccount of the greater difficulty of the three-place numbers, any wereconsidered correct when two of the three figures were recalled, orwhen all three figures were correct but two were reversed in position, _e. G. _, 532 instead of 523. _N_ means noun series, _O_ object, _V_verb, and _M_ movement series. Series _A_^{1}, _A_^{5}, _A_^{9}, _A_^{13} are to be found in the first and third columns, _A_^{2}, _A_^{6}, _A_^{10}, _A_^{14} in the second and fourth, _A_^{3}, _A_^{7}, _A_^{11}, _A_^{15}, in the fifth and seventh, and _A_^{4}, _A_^{8}, _A_^{12}, _A_^{16} in the sixth and eighth columns. 

TABLE I. 

SHOWING IMMEDIATE RECALL AND RECALL AFTER TWO DAYS. 

 _M_. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6 7 3 1 6 7 2 1 A^{5-8} 5(1) 6 3(1) 6 6(1) 7 5(1) 6 A^{9-12} 7 7 4 6 7 6(1) 7 6(1) A^{13-16} 4 5 2 2 5 3 2 2 Total. 22(1) 25 12(1) 15 24(1) 23(1) 16(1) 15(1) Per cent. 88 96 48 58 96 92 64 66

 _S_. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6(1) 6 0 0 7 7 0 0 A^{5-8} 6 7 1 3 6 7 0 3 A^{9-12} 7 6 2 2 5 7 0 0 A^{13-16} 5 5 0 0 5 5 3 0 Total. 24(1) 24 3 5 23 26 3 3 Per cent. 96 92 12 19 88 100 12 12

 _Hu_. Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. A^{1-4} 6 7 0 1 5 6(1) 0 2 A^{5-8} 5(2) 7 1(2) 1 7 7 1 0 A^{9-12} 6(1) 7 2 2 6 7 0 5 A^{13-16} 4(1) 4(1) 0 2 5 5 0 1 Total. 21(4) 25(1) 3(2) 6 23 25(1) 1 8 Per cent. 95 100 14 24 88 100 4 32

These results will be included in the discussion of the results of the_B_ set. 

THE _B_ SET. 

A new material was needed for foreign symbols. After considerableexperimentation nonsense words were found to be the best adapted forour purpose. The reasons for this are their regularly varying lengthand their comparative freedom from indirect associations. An objectionto using nonsense syllables in any work dealing with the permanence ofmemory is their sameness. On this account they are not rememberedlong. To secure a longer retention of the material, nonsense wordswere devised in substantially the same manner as that in which Müllerand Schumann made nonsense syllables, except that these variedregularly in length from four to six letters. Thus the number ofletters, not the number of syllables was the criterion of variation, though of course irregular variation in the number of syllables was anecessary consequence. 

When the nonsense words were used it was found that far fewer indirectassociations occurred than with nonsense syllables. By indirectassociation I mean the association of a foreign symbol and its word bymeans of a third term suggested to the subject by either of the othersand connected at least in _his_ experience with both. Usually thisthird term is a word phonetically similar to the foreign symbol andideationally suggestive of the word to be associated. It is a verycommon form of mnemonic in language material. The following areexamples:

 cax, stone (Caxton); teg, bib (get bib); laj, girl (large girl); xug, pond (noise heard from a pond); gan, mud (gander mud). 

For both of these reasons nonsense words were the material used asforeign symbols in the _B_ set. 

The nonsense words were composed in the following manner. From a boxcontaining four of each of the vowels and two of each of theconsonants the letters were chosen by chance for a four-letter, afive-letter, and a six-letter word in turn. The letters were thenreturned to the box, mixed, and three more words were composed. At thecompletion of a set of twelve any which were not readily pronounceableor were words or noticeably suggested words were rejected and otherscomposed in their places. 

The series of the _B_ set were four couplets long. Each seriescontained one three-letter, one four-letter, one five-letter, and onesix-letter nonsense word. The position in the series occupied by eachkind was constantly varied. In all other respects the same principleswere followed in constructing the _B_ set as were observed in the _A_set with the following substitutions:

No two foreign symbols of a series and no two terms of a coupletcontained the same sounded vowel in accented syllables. 

The rule for the avoidance of alliteration, rhyme, and assonance wasextended to the foreign symbols, and to the two terms of a couplet. 

The English pronounciation was used in the nonsense words. Thesubjects were not informed what the nonsense words were. They werecalled foreign words. 

Free body movements were used in the movement series as in the _A_set. Rarely an object was involved, _e. G. _, the table on which thesubject wrote. The movements were demonstrated to the subject inadvance of learning, as in the _A_ set. 

The following are typical _B_ series:

 B2. Nonsense words and objects. 

 quaro rudv xem lihkez lid cent starch thorn

 B3. Nonsense words and verbs. 

 dalbva fomso bloi kyvi poke limp hug eat

 B4. Nonsense words and movements. 

 ohv wecolu uxpa haymj gnash cross frown twist

The time conditions for presenting a series remained practically thesame. In learning, the series was shown three times as before. Theinterval between learning and testing was shortened to 4 seconds, andin the test the post-term interval of _A^{13-16}_ retained (6 secs. ). This allowed the subject 9 secs. For recalling and writing each term. The only important change was an extension of the number of tests fromtwo to four. The third test was one week after the second, and thefourth one week after the third. In these tests the familiar word wasalways the term required, as in _A^{1-4}_, on account of thedifficulty of dealing statistically with the nonsense words. Theintervals for testing permanence in the _B_ set may be most easilyunderstood by giving the time record of one subject. 

TIME RECORD OF _Hu_. 

 Series. Im. Rec. Two Days. Nine Days. Sixteen Days. B^{1-4} Feb. 12 Feb. 14 Feb. 21 Feb. 28 B^{5-8} Feb. 19 Feb. 21 Feb. 28 Mch. 7 B^{9-12} Feb. 26 Feb. 28 Mch. 7 Mch. 14 B^{13-16} Mch. 5 Mch. 7 Mch. 14 Mch. 21

The two half-hours in a week during which all the work of one subjectwas done fell on approximately the same part of the day. When a numberof groups of 4 series each were to be tested on a given day they weretaken in the order of their recency of learning. Thus on March 7 theorder for _Hu_ was B^{13-16}, B^{9-12}, B^{5-8}. 

Henceforth there was also rotation within a given four series. Asthere were always sixteen series in a set, the effects of practice andfatigue within a given half-hour were thus eliminated. 

In the following table the results of the _B_ set are given. Itsarrangement is the same as in Table 1. , except that the figuresindicate the number of absent terms correctly recalled out of fourcouplets instead of seven or five. Where blanks occur, the series wasdiscontinued on account of lack of recall. As in Table 1. , the tablesin the first, third and fifth columns show successive stages of thesame series. Immediate recall is omitted because with rare exceptionsit was perfect, the test being given merely as an aid in learning. 

TABLE II. 

 SHOWING RECALL AFTER TWO, NINE, AND SIXTEEN DAYS. 

 Days. Two. Nine. Sixteen. Two. Nine. Sixteen. N. O. N. O. N. O. V. M. V. M. V. M. Series. _M. _ B^{1-4} 2(1) 4 1(1) 2 1(1) 2 4 4 4 2 4 2 B^{5-8} 3 1 2 1 1 1 2 2 2 1 1 1 B^{9-12} 2 3 0 3 0 2 3 2 2 0 2 2 B^{13-16} 2(1) 3 2(1) 0 2(1) 0 1 2 1 0 1 0 Total 9(2) 11 5(2) 6 4(2) 5 10 10 9 3 8 5 Per cent. 64 69 36 38 29 31 63 63 56 19 50 31

 _S. _ B^{1-4}¹ 0 2 0 0 0 1 0 1 B^{5-8} 0 0 0 0 B^{9-12}¹ 0 1 0 0 0 1 0 0 B^{13-16}² 0(2) 1 0(2) 1 0(2) 1 0 0(1) 0 0(1) 0 0(1) Total 0(2) 4 0(2) 1 0(2) 1 0 2(1) 0 1(1) 0 0(1) Per cent. 0 25 0 6 0 6 0 13 0 7 0 0

 _Hu. _ B^{1-4} 1(1) 4 0(1) 1 0(1) 2 1 3 0 2 0 0 B^{5-8} 0 1(1) 0 0(1) 0 0(1) 0 1 0 1 0 1 B^{9-12} 0 1 0 0 0 1 0 0 0 1 0 0 B^{13-16} 0(1) 0 0(1) 0 0(1) 0 0 4 0 0 0 0 Total 1(2) 6(1) 0(2) 1(1) 0(2) 3(1) 1 8 0 4 0 1 Per cent. 7 40 0 7 0 20 6 50 0 25 0 6

 _B. _ B^{1-4} 1 1(1) 0 0 0 0(1) 0 0 B^{6-8} 1 2 1 2 1 1 1 0 1 0 1 0 B^{9-12} 0 2(1) 0 0(1) 0 0(1) 0(1) 2 0 2 0 1 B^{13-16} 1 3 1 1 1 1 1 2 0 1 0 1 Total 3 8(2) 2 3(1) 2 2(1) 2(1) 4(1) 1 3 1 2 Per cent. 19 57 13 21 13 13 13 27 7 20 7 13

 _Ho. _ B^{1-4}¹ 3 2(1) 2 2(1) 1 0(1) 1(2) 1(2) 1(2) 0(2) 0(2) 0(2) B^{6-8} 1 1(1) 1 0(1) 1 0 0 1(1) 1 1 0 1 B^{9-12} 0(1) 1 0(1) 1 0(1) 0 1 1 1 1 0 0 B^{13-16}³ 0 0 0 0 0 0 0(1) 4 0(1) 2 0(1) 0 Total 4(1) 4(2) 3(1) 3(2) 2(1) 0(1) 2(3) 7(3) 3(3) 4(2) 0(3) 1(2) Percent. 33 30 25 23 17 0 17 58 25 33 0 8

 _Mo. _ B^{1-4} 3 3 3 1 4 1 0 2 0 2 0 2 B^{5-8} 1 4 1 1 1 2 1 2(2) 1 1(2) 1 1(2) B^{9-12} 2 4 2 4 1 4 0(1) 3(1) 1(1) 3(1) 1(1) 2 B^{13-16} 2(2) 4 2(2) 4 2(2) 2 1 4 1 4 1 4 Total 8(2) 15 8(2) 10 8(2) 9 2(1) 11(3) 3(1) 10(3) 3(1) 9(2) Percent. 57 94 57 63 57 56 13 85 20 79 20 69

 ¹Four presentations in learning. ²Five presentations in learning. ³Five days' interval instead of two. 

In the following summary the recall after two days is combined fromTables I. And II. For the three subjects _M_, _S_ and _Hu_, therebeing no important difference in the conditions of experimentation. For the three other subjects this summary is merely a résumé of TableII. The recall after nine and sixteen days in Table II. Is omitted, and will be taken up later. The figures are in all cases based on theremainders left after those couplets in which indirect associationsoccurred were eliminated both from the total number of coupletslearned and from the total number correctly recalled. _E. G. _, in thecase of nouns, _M_ learned, in all, 42 couplets in the _A_ and _B_sets, but since in 3 of them indirect associations occurred, only 39couplets are left, of which 21 were correctly recalled. This gives 54per cent. 

SUMMARY OF RECALL AFTER TWO DAYS. --FROM TABLES I. AND II. 

 N. O. V. M. M. 54 per cent. 62 per cent. 63 per cent. 61 per cent. S. 8 " 21 " 7 " 12 " Hu. 11 " 30 " 5 " 59 " B. 19 " 57 " 13 " 27 " Ho. 33 " 30 " 17 " 58 " Mo. 57 " 94 " 13 " 85 " Av. 30 per cent. 49 per cent. 20 per cent. 50 per cent. 

 Av. Gain in object couplets, 19 per cent. " " " movement couplets, 30 per cent. 

The first question which occurs in examining the foregoing tables isconcerning the method of treating the indirect associations, _i. E. _, obtaining the per cents. The number of couplets correctly recalled maybe divided into two classes: those in which indirect associations didnot occur, and those in which they did occur. Those in which they didnot occur furnish us exactly what we want, for they are results whichare entirely free from indirect associations. In them, therefore, acomparison can be made between series using objects and activities andothers using images. On the other hand, those correctly recalledcouplets in which indirect associations _did_ occur are not for ourpurposes pure material, for they contain not only the object-imagefactor but the indirect association factor also. The solution is toeliminate these latter couplets, _i. E. _, subtract them both from thenumber correctly recalled and from the total number of couplets in theset for a given subject. By so doing and by dividing the firstremainder by the second the per cents, in the tables were obtained. There is one exception to this treatment. The few couplets in whichindirect associations occurred but which were nevertheless_incorrectly_ recalled are subtracted only from the total number ofcouplets in the set. 

The method by which the occurrence of indirect associations wasrecorded has been already described. It is considered entirelytrustworthy. There is usually little doubt in the mind of a subjectwho comprehends what is meant by an indirect association whether ornot such were present in the particular series which has just beenlearned. If none occurred in it the subjects always recorded the fact. That an indirect association should occasionally be present on one dayand absent on a subsequent one is not strange. That a second termshould effect a union between a first and third and thereafterdisappear from consciousness is not an uncommon phenomenon ofassociation. There were thirteen such cases out of sixty-eightindirect associations in the _A_, _B_ and _C_ sets. In the tables theyare given as present because their effects are present. When thereverse was the case, namely, when an indirect association occurred onthe second, ninth or sixteenth day for the first time, it aided inlater recall and was counted thereafter. There were eight such casesamong the sixty-eight indirect associations. 

Is it possible that the occurrence of indirect associations in, _e. G. _, two of the four couplets of a series renders the retention ofthe other two easier? This could only be so when the intervals betweentwo couplets in learning were used for review, but such was never thecase. The subjects were required to fill such intervals withrepetitions of the preceding couplet only. 

The elimination of the indirect association couplets and theacceptance of the remainders as fair portrayals of the influence ofobjects and movements on recall is therefore a much nearer approach totruth than would be the retention of the indirectly associatedcouplets. 

The following conclusions deal with recall after two days only. Therecall after longer intervals will be discussed after Table III. 

The summary from Tables I. And II. Shows that when objects and nounsare coupled each with a foreign symbol, four of the six subjectsrecall real objects better than images of objects, while two, _M_ and_Ho_, show little or no preference. The summary also shows that whenbody movements and verbs are coupled each with a foreign symbol, fiveof the six subjects recall actual movements better than images ofmovements, while one subject, _M_, shows no preference. The samesubject also showed no preference for objects. With the subjects _S_and _B_ the preference for actual movements is not marked, and hasimportance only in the light of later experiments to be reported. 

The great difference in the retentive power of different subjects is, as we should expect, very evident. Roughly, they may be divided intotwo groups. _M_ and _Mo_ recall much more than the other four. Thesmall percentage of recall in the case of these four suggested thenext change in the conditions of experimentation, namely, to shortenwith them the intervals between the tests for permanence. This wasaccordingly done in the _C_ set. But before giving an account of thenext set we may supplement these results by results obtained fromother subjects. 

It was impossible to repeat this set with the same subjects, andinconvenient, on account of the scarcity of suitable words, to deviseanother set just like it. Accordingly, the _B_ set was repeated withsix new subjects. We may interpolate the results here, and then resumeour experiments with the other subjects. The conditions remained thesame as for the other subjects in all respects except the following. The tests after nine and sixteen days were omitted, and the remainingtest for deferred recall was given after one day instead of after two. In learning the series, each series was shown four times instead ofthree. The results are summarized in the following table. The figuresin the left half show the number of words out of sixteen which werecorrectly recalled. The figures in parentheses separate, as before, the correctly recalled indirect-association couplets. In the righthalf of the table the same results, omitting indirect-associationcouplets, are given in per cents, to facilitate comparison with thesummary from Tables I. And II. 

TABLE III. 

 SHOWING RECALL AFTER ONE DAY. 

 N. O. V. M. N. O. V. M. Bur. 6 10(1) 7(1) 5(4) 38 67 44 31 W. 5(3) 12(1) 6 9 31 75 38 56 Du. 1 11(1) 8 9 6 69 50 56 H. 9(1) 14 8 12 56 88 50 75 Da. 1(3) 7(4) 3(1) 9(3) 7 44 20 56 R. 7(2) 3(3) 5 5(1) 44 19 31 31 Total, 29(9) 57(10) 37(2) 49(8) Av. , 30 60 39 51

 Av. Gain in object couplets, 30 per cent. " " " movement couplets, 12 per cent. 

The table shows that five subjects recall objects better than imagesof objects, while one subject recalls images of objects better. Similarly, three subjects recall actual movements of the body betterthan images of the same, while with three neither type has anyadvantage. 

THE _C_ SET. 

In the _C_ set certain conditions were different from the conditionsof the _A_ and _B_ sets. These changes will be described under threeheads: changes in the material; changes in the time conditions; andchanges in the method of presentation. 

For lack of monosyllabic English words the verbs and movements weredissyllabic words. The nouns and objects were monosyllabic, as before. All were still concrete, and the movements, whether made or imaged, were still simple. But the movements employed objects, instead ofbeing merely movements of the body. 

For two of the subjects, _M_ and _Mo_, the time intervals between thetests remained as in the _A_ and the _B_ sets, namely, two days, ninedays, and sixteen days. With the four other subjects, _S, Hu, B, _ and_Ho_, the number of tests was reduced to three and the intervals wereas follows:

The I. Test, which as before was a part of the learning process, wasnot counted. The II. Test followed from 4½ to 6½ hours, or an averageof 5-3/8 hours, after the I. Test. The III. Test was approximately 16hours after the II. Test for all four subjects. 

The series were learned between 10 a. M. And 1:30 p. M. , the II. Testwas the same day between 4:30 and 5:10 p. M. , and the III. Test was thefollowing morning between 8:30 and 9:10 a. M. Each subject of coursecame at the same hour each week. 

Each series was shown three times, as in the _B_ set. 

A change had to be made in the length of exposure of each couplet inthe movement series. For, as a rule, movements employing objectsrequired a longer time to execute than mere movements of the body. Five seconds was found to be a suitable length of exposure. To keepthe three other types of series comparable with the movement series, if possible, their exposure was also increased from 3 to 5 secs. Theinterval of 2 secs, at the end of a presentation was omitted, and theinterval between learning and testing reduced from 4 secs, in the _B_set to 2 secs. 

In the movement series of the _A_ and _B_ sets, movements of parts ofthe body were chosen. But the number of such movements which a personcan conveniently make while reading words shown through an aperture islimited, and as stated above no single word was ever used in twocouplets. These were now exhausted. In the _C_ set, therefore, movements employing objects were substituted. The objects lay on thetable in a row in front of the subject, occupying a space about 50 cm. From left to right, and were covered by a black cambric cloth. Theywere thus all exposed at the same moment by the subject who, at asignal, laid back the cloth immediately before the series began, andin the same manner covered them at the end of the third presentation. Thus the objects were or might be all in view at once, and as a resultthe subject usually formed a single mental image of the four objects. 

With this kind of material it was no longer necessary for the operatorto show the subject in advance of the series what the movements werein order to avoid hesitation and confusion, for the objects were ofsuch a nature as obviously to suggest in connection with the words theproper movements. 

TABLE IV. 

 SHOWING RECALL AFTER TWO, NINE AND SIXTEEN DAYS FOR TWO SUBJECTS, AND AFTER FIVE HOURS AND TWENTY-ONE HOURS FOR FOUR OTHER SUBJECTS. 

 Days. Two. Nine. Sixteen Two. Nine. Sixteen N. O. N. O. N. O. V. M. V. M. V. M. Series _M. _ C^{1-4} 4 4 4 4 3 2 3 2 2 2 1 1 C^{5-8} 2 2 2 2 2 1 1 1 1 2 1 0 C^{9-12} 3 2 3 1 3 0 2 4 3 2 2 1 C^{13-16} 4 3(1) 4 2(1) 4 2(1) 3 4 2 3 2 3 Total 13 1(1) 13 9(1) 12 5(1) 9 11 8 9 6 5 Per cent. 81 73 81 60 75 33 56 69 50 56 38 31

 _Mo_ C^{1-4} 2 4 1 1 1 1 1 4 1 2 1 2 C^{5-8} 3 2 4 1 3 1 4 3(1) 4 3(1) 2 2(1) C^{9-12} 0 1 0 1 0 1 0 3 0 1 0 2 C^{13-16} 0 0(1) 0 0(1) 0 0(1) 1(1) 4 1(1) 2 0(1) 0 Total 5 7(1) 5 3(1) 4 3(1) 6(1) 14(1) 6(1) 8(1) 3(1) 6(1) Per cent. 31 46 31 20 25 20 40 93 40 53 20 40

 Hours. Five. Twenty-one. Five. Twenty-one N. O. N. O. V. M. V. M. Series _S. _ C^{1-4} 1 3 1 1 0 1 0 1 C^{5-8} 0(1) 3 0 2 0 1 0 1 C^{9-12} 0(1) 3 0(1) 4 3 4 3 4 C^{13-16} 1 3 1 3 2 3(1) 3 3(1) Total 2(2) 12 2(1) 10 5 9(1) 6 9(1) Per cent. 14 75 14 63 33 60 40 60

 _Hn. _ C^{1-4} 1 4 1 4 0 4 1 4 C^{5-8} 0(2) 1 0(2) 1 0(1) 2 1(1) 2(2) C^{9-12} 3 4 3 4 2 4 2 4 C^{13-16} 1 3 3 3 0 3(1) 0 2(1) Total 5(2) 12 7(2) 12 2(1) 13(3) 4(1) 12(3) Per cent. 36 75 50 75 14 100 29 92

 _B. _ C^{1-4} 3 4 3 4 3 4 3 4 C^{5-8} 3 2 3 3 2 2 2 4 C^{9-12} 2 4 2 3 2 1 2 2 C^{13-16} 3 4 3 4 2 4 2 4 Total 11 14 11 14 9 11 9 14 Per cent. 69 88 69 88 56 69 56 88

 _Ho. _ C^{1-4} 3(1) 2(2) 3(1) 2(2) 0 3(1) 0 1(1) C^{5-8} 3(1) 4 3(1) 4 3 3(1) 3 3(1) C^{9-12} 1(2) 4 1(2) 4 2(1) 3(1) 2(1) 3(1) C^{13-16} 0 2 0 2 2 4 2 4 Total 7(4) 12(2) 7(4) 12(2) 7(1) 13(3) 7(1) 11(3) Per cent. 58 92 58 92 50 100 50 85

The object series were also changed to conform to the movement series. Formerly the objects had been shown successively through the apertureand synchronously with their corresponding words; now they were on thetable in front of the subject and all uncovered and covered at once asin the movement series. The subjects therefore had a single mentalimage of these four objects also. 

In both the object and the movement series the objects as before weresmall and fairly uniform in size and so selected as not to betray tothe subject their presence beneath the cloth in the I. Test. In theII. , III. And IV. Tests there were no objects on the table. 

The previous table shows the results of the _C_ set. The figures givethe number of couplets correct out of four; the figures in bracketsgive the number of indirect associations; the total number recalled inany series is their sum. 

In the following summary the recall of _M_ and _Mo_ after two days andof _S, Hu, B_ and _Ho_ after twenty-one hours are combined. 

SUMMARY FROM TABLE IV. 

 N. O. V. M. _M. _ 81 per cent. 73 per cent. 56 per cent. 69 per cent. _Mo. _ 31 " 46 " 40 " 93 " _S. _ 14 " 63 " 40 " 60 " _Hu. _ 50 " 75 " 29 " 92 " _B. _ 69 " 88 " 56 " 88 " _Ho. _ 58 " 92 " 50 " 85 " ----------- ----------- ----------- ----------- Av. 51 per cent. 73 per cent. 45 per cent. 81 per cent. 

 Av. Gain in object couplets, 22 per cent. " " " movement couplets, 36 per cent. 

Before asking whether the results of the _C_ set confirm theconclusions already reached, we must compare the conditions of thethree sets to see whether the changes in the conditions in the _C_ sethave rendered it incomparable with the other two. The first change wasthe substitution of dissyllabic words in the verb and the movementseries in the place of monosyllabic words. Since the change was madein both the verb and the movement series their comparability with eachother is not interfered with, and this is the point at issue. Preliminary tests, however, made it highly probable that simpleconcrete dissyllabic words are not more difficult than monosyllabic in5 secs. Exposure. This change is therefore disregarded. 

The first important change introduced in the _C_ set was the reductionof the intervals between the tests for four subjects. The second wasthe lengthening of the exposure from 3 to 5 secs. These changes alsodo not lessen the comparability of the noun, object, verb and movementseries with one another, since they affected all series of the _C_set. 

The third change in the conditions was the substitution in themovement series of movements employing objects for movements of thebody alone, and the consequent placing of objects on the table in themovement and in the object series of which the subject obtained asingle mental image. All of the subjects were of the opinion that thissingle mental image was an aid in recall. Each of the objectscontributing to form it was individualized by its spatial order amongthe objects on the table. The objects shown through the aperture wereconnected merely by temporal contiguity. On this account the objectand the movement series of the _C_ set are not altogether comparablewith those of the _A_ and the _B_ sets. We should expect _a priori_that the object and the movement series in the _C_ set would be muchbetter recalled than those of the _A_ and the _B_ sets. 

The fourth change was from imaged or made movements of the body aloneto imaged or made movements employing objects. If, as the _A_ and the_B_ sets have already demonstrated, the presence of objects at all isan aid to recall, the movement series of the _C_ set should show agreater gain over their corresponding verb series than the simplemovements of the body in the _A_ and the _B_ sets showed over theircorresponding verb series. For, employing objects in movements isadding the aid of objects to whatever aid there is in making themovements. 

Turning to the results, we consider the _C_ set by itself withreference to the effect of the use of objects vs. Images in general. The summary from Table IV. Shows that under the conditions given, after intervals of from slightly less than one day to two days, fiveof the six subjects recall object couplets better than noun couplets. One subject, _M_ recalls noun couplets better. It also shows thatunder the conditions and after the intervals mentioned all sixsubjects recall movement couplets better than verb couplets. In viewof the small difference here and of his whole record, however, _M_ isprobably to be classed as indifferent in both substantive and actionseries. 

RECALL AFTER NINE AND SIXTEEN DAYS. 

Thus far recall after these longer intervals has not been discussed. The experiment was originally devised to test recall after two daysonly, but it was found that with two of the subjects, _M_ and _Mo_, recall for greater intervals could be obtained with slight additionaltrouble. This was accordingly done in the _B_ and _C_ sets. Theresults of the four other subjects in the _B_ set are not sosatisfactory on this point, because not enough was recalled. 

The most interesting fact which developed was an apparently slowerrate of forgetting, in many cases, of the nouns and verbs than of theobjects and movements. In the noun-object group of the _B_ set it isnoticeable in three out of the four possible subjects, viz. , _B, Ho_, and _Mo_. _M_ alone does not show it. The two other subjects, _S_ and_B_, did not recall enough for a comparison. In the verb-movementgroup of the _B_ set it is also marked in three out of the fourpossible subjects, viz. , _M_, _Ho_, and _Mo. B_ alone does not showit. It is also seen in the _C_ set in the results of _M_ and _Mo_, inboth the noun-object and the verb-movement groups. With the four othersubjects in the _C_ set it could not be noticed, since the series rantheir course in a day. In _M_ (verb-movement group, _C_ set) and _Mo_(noun-object group, _C_ set) the originally higher object or movementcurves actually fall below their corresponding noun or verb curves. 

The results of the tests for recall after nine and sixteen days aresummarized in the following tables. They should be compared with therecall of these same series after two days given in Tables II. AndIV. , nor should it be forgotten that all four types started withperfect immediate recall. The figures give per cents, correct aftereliminating indirect-association couplets. 

TABLE V. 

 SHOWING RECALL AFTER NINE AND SIXTEEN DAYS. --SUMMARY FROM _B_ SET. 

 Days. Nine. Sixteen Nine. Sixteen. N. O. N. O. V. M. V. M. _M. _ 36 38 29 31 56 19 50 31 _S. _ 0 6 0 6 0 7 0 0 _Hu. _ 0 7 0 20 0 25 0 6 _B. _ 13 21 13 13 7 20 7 13 _Ho. _ 25 23 17 0 25 33 0 8 _Mo. _ 57 63 57 56 20 79 20 69 Av. 22 26 19 21 18 31 13 21

TABLE VI. 

 SAME FOR _M_ AND _Mo_. --SUMMARY FROM _C_ SET. 

 Days. Nine. Sixteen. Nine. Sixteen. N. O. N. O. V. M. V. M. _M_. 81 60 75 33 50 56 38 31 _Mo_. 31 20 25 20 40 53 20 40

THE _D_ SET. 

A few series of nouns, objects, verbs, and movements dissociated fromforeign symbols were obtained. The material was of the same kind asthe words used in the couplet series, being mostly monosyllabic andseldom dissyllabic words. They had not been previously used with thesesubjects. Each series contained ten words or ten objects. The samekind of precautions were taken as in the couplet sets to avoidphonetic aids and the juxtaposition of words which suggest each other. The apparatus employed in the couplet sets was used. The objects inthe object series were shown through the aperture. Visual images wererequired in the noun and in the verb series. The noun and the objectseries were exposed at the rate of one word every 2 secs. (or 20 secs. For the series) for _M_, _S_, and _Hu_, and one every 3 secs. (or 30secs. For the series) for _B_, _Ho_, and _Mo_. Only one exposure ofthe series was given. At its completion the subject at once wrote asmany of the words or objects as he could recall. Two days later at thesame hour he was asked to write without further stimulus as many wordsof each series as he could recall, classifying them according to theirtype of series. 

The verbs were similar to the verbs of the couplet series. There was atendency in the verb series among most of the subjects to make a moreor less connected story of the verbs and thus some subjects couldretain all ten words for two days. This was an element not present inthe couplet verb series, according to the subjects, nor in any otherseries, and the subjects were, therefore, directed to eliminate it byimaging each action in a different place and connected with differentpersons. The effort was nearly successful, some of the subjectsconnecting two or three verbs, and others none. The movements employedten objects which were uncovered and covered by the subject as in the_C_ set. The exposure for the verbs and movements was 5 secs. For eachword, or 50 secs. For the series. The tests were the same as in theseries of ten nouns and ten objects, but in a number of cases (to bespecified in the table) it seemed best to shorten the interval fordeferred recall to one day. 

The series were always given in pairs--a noun and an object series, ora verb and a movement series forming a pair. Only one pair was givenper day and no other series of any kind were given on that day. Usually several days intervened between the II. Test of one pair andthe learning of the next, but in a little less than half of the casesa new pair was learned on the same day shortly after the II. Test ofthe preceding pair. 

The noun-object pairs and the verb-movement pairs were not given inany definite order with reference to each other. 

The figures in the following table indicate the number of words out often which the subject correctly recalled and placed in their propercolumns. Immediate recall is also given. 

TABLE VII. 

 Series. Im. Rec. Two Days. Im. Rec. Two Days. N. O. N. O. V. M. V. M. 

 _M. _ D^{1-4} 8 9 7 7 7 10 4 5 D^{5-8} 9 7 6 6 8 8 6 6 D^{9-12} 7 7 5 6 8 10 7 7 Av. 24 23 18 19 23 28 17 17

 _Mo_. D^{1-4} 6 6 2 1 8 10 0¹ 7¹ D^{5-8} 6 5 0¹ 3¹ 8 9 2 4 D^{9-12} 5 7 1¹ 6¹ 10 10 2 7 Av. 17 18 3 10 26 29 4 18

 _S_. D^{1-4} 8 9 2 3 9 10 6¹ 9¹ D^{5-8} 8 10 2 4 9 10 4¹ 9¹ D^{9-12} 8 10 2 5 8 10 3¹ 7¹ Av. 24 29 6 12 26 30 13 25

 _Hu. _ D^{1-4} 6 8 3 7 9 10 4 9 D^{5-8} 7 9 0 2 9 10 2 7 D^{9-12} 7 9 4 6 8 10 1 8 Av. 20 26 7 15 26 30 7 24

 _Ho. _ D^{1-4} 9 9 3 3 10 9 5 7 D^{5-8} 9 8 1 6 9 9 6¹ 8¹ D^{9-12} 8 8 5 5 10 10 6¹ 7¹ Av. 26 25 9 14 29 28 17 22

 ¹ One day. 

The results of the _D_ set strongly confirm the results of the _A_, _B_, and _C_ sets. Table VII. Shows that after from one to two days'interval four subjects recall objects better than nouns and movementsbetter than verbs. One subject, _M. _, shows no preference. 

CONCLUSIONS. 

We are now in a position to answer specifically the problem of thisinvestigation. The results show: (1) that those five subjects whorecall objects better than nouns (involving images) _when each occursalone_, also recall objects better than nouns when each is recalled bymeans of an unfamiliar verbal symbol with which it has been coupled;(2) that the same is true of verbs and movements; (3) that these factsalso receive confirmation on the negative side, viz. : the one subjectwho does not recall objects and movements better than nouns and verbs(involving images) _when they are used alone_, also does not recallthem better _when they are recalled by means of foreign symbols_ withwhich they have been coupled. 

MINOR QUESTIONS. 

The problem proposed at the outset of the investigation having beenanswered, two minor questions remain: (1) as to images, (2) indirectassociations. 

1. All the subjects were good visualizers. The images became clearusually during the first of the three presentations, _i. E. _, in 1-3secs. , and persisted until the next couplet appeared. In the secondand third presentations the same images recurred, rarely a new oneappeared. 

An interesting side light is thrown on M. 's memory by his work inanother experiment in which he was a subject. This experiment requiredthat the subject look at an object for 10 secs. And then after thedisappearance of its after-image manipulate the memory image. M. Showed unusually persistent after-images. The memory images whichfollowed were unusually clear in details and also persistent. Theywere moreover retained for weeks, as was shown by his surprisingability to recall the details of an image long past, and separatedfrom the present one by many subsequent images. His memory wascapacious rather than selective. His eyesight was tested and found tobe normal for the range of the apparatus. Possibly his age (55 yrs. )is significant, although one of the two subjects who showed thegreatest preference for objects and movements, Mo. , was only six yrs. Younger. The ages of the other subjects were S. 36 yrs. , Hu. 23 yrs. , B. 25 yrs. , Ho. 27 yrs. 

That some if not all of the subjects did not have objective images inmany of the noun and verb couplets if they were left to their owninitiative to obtain them is evident from the image records in the _A_set, in which the presence of the objective images was optional butthe record obligatory. The same subject might have in one noun or verbseries no visual images and in another he might have one for everycouplet of the series. After the completion of the _A_ set, the effectof the presence of the objective images in series of 10 nouns alone, or 10 objects alone after two days' interval, was tested. This wasmerely a repetition of similar work by Kirkpatrick after three days'interval, and yielded similar results. As a matter of fact some of thesubjects were unable wholly to exclude the objective images, but werecompelled to admit and then suppress them as far as possible, so thatit is really a question of degree of prominence and duration of theimages. 

The presence of the objective images having been shown to be an aid inthe case of series of nouns, the subjects were henceforth requested toobtain them in the noun and verb series of the _B_ and _C_ sets, andthe image records show that they were entirely successful in doing so. 

2. The total number of couplets in any one or in several sets may bedivided into two classes: (1) Those in which indirect associations didnot occur in the learning, and (2) those in which they did occur. Forreasons already named we may call the first pure material and thesecond mixed. We can then ascertain in each the proportion ofcorrectly recalled couplets after one, two, nine and sixteen days'interval, and thus see the importance of indirect associations as afactor in recall. This is what has been done in the following table. 

The figures give the number of couplets correctly or incorrectlyrecalled out of 64. In the case of the interval of one day the figuresare a tabulation of the III. Test (twenty-one hours) of the _C_ set, which contained 16 series of 4 couplets each. The figures for theintervals of two, nine and sixteen days are a tabulation of the _B_set, which also contained 16 series of 4 couplets each. _C_ denotescorrect, _I_ incorrect. 

TABLE VIII. 

SHOWING GREATER PERMANENCE OF COUPLETS IN WHICH INDIRECT ASSOCIATIONSOCCURRED. 

 Pure Material. Mixed Material. Days. One. Two. Nine. Sixteen. One. Two. Nine. Sixteen. C I C I C I C I C I C I C I C I _M. _ 40 22 23 39 22 40 2 0 2 0 3 0 _Mo. _ 36 22 31 27 29 29 6 0 6 0 5 1 _S. _ 27 34 6 55 2 59 1 60 2 1 3 0 3 0 3 0 _Hu. _ 35 22 16 45 5 56 4 57 6 1 3 0 3 0 3 0 _B. _ 48 16 17 43 9 51 7 53 0 0 4 0 1 3 1 3 _Ho. _ 37 15 17 30 13 36 3 46 10 2 9 6 8 7 7 8

 Total: 147 87 132 217 83 268 66 285 18 4 27 6 23 10 21 12 P'c't. : 63 37 38 62 24 76 19 81 82 18 82 18 70 30 64 36

We see from the table that the likelihood of recalling couplets inwhich indirect associations did not occur in learning is 63 per cent. After one day, and that there is a diminution of 44 per cent. In thenext fifteen days. The fall is greatest during the second day. On theother hand, the likelihood of recalling couplets in which indirectassociations did occur is 82 per cent. After one day, and there is adiminution of only 18 per cent. During the next fifteen days. Thefading is also much more gradual. 

It is evident, then, that in all investigations dealing with languagematerial the factor of indirect associations--a largely accidentalfactor affecting varying amounts of the total material (in these sixsubjects from 3 per cent. To 23 per cent. ) is by far the mostinfluential of all the factors, and any investigations which haveheretofore failed to isolate it are not conclusive as to otherfactors. 

The practical value of the foregoing investigation will be found inits bearing upon the acquisition of language. While it is by no meansconfined to the acquisition of the vocabulary of a _foreign_ language, but is also applicable to the acquisition of the vocabulary of thenative language, it is the former bearing which is perhaps moreobvious. If it is important that one become able as speedily aspossible to grasp the meaning of foreign words, the results of theforegoing investigation indicate the method one should adopt. 

 * * * * *

MUTUAL INHIBITION OF MEMORY IMAGES. 

BY FREDERICK MEAKIN. 

The results here presented are the record of a preliminary inquiryrather than a definitive statement of principles. 

The effort to construct a satisfactory theory of inhibition has givenrise, in recent years, to a good deal of discussion. Ever since it wasdiscovered that the reflexes of the spinal cord are normally modifiedor restrained by the activity of the brain and Setschenow (1863)attempted to prove the existence of localized inhibition centers, theneed of such a theory has been felt. The discussion, however, has beenmainly physiological, and we cannot undertake to follow it here. Thepsychologist may not be indifferent, of course, to any comprehensivetheory of nervous action. He works, indeed, under a generalpresumption which takes for granted a constant and definite relationbetween psychical and cerebral processes. But pending the settlementof the physiological question he may still continue with the study offacts to which general expression may be given under some theory ofpsychical inhibition not inconsistent with the findings of thephysiologist. 

A question of definition, however, confronts us here. Can we, it maybe asked, speak of psychical inhibition at all? Does one consciousstate exercise pressure on another, either to induce it, or to expelit from the field? 'Force' and 'pressure, ' however pertinent tophysical inquiries, are surely out of place in an investigation of therelations between the phenomena of mind. Plainly a distinction has tobe made if we are to carry over the concept of inhibition from thedomain of nervous activity to the conscious domain. Inhibition cannot, it should seem, have the same sense in both. We find, accordingly, that Baldwin, who defines nervous inhibition as 'interference with thenormal result of a nervous excitement by an opposing force, ' says ofmental inhibition that it 'exists in so far as the occurrence of amental process prevents the simultaneous occurrence of other mentalprocesses which might otherwise take place. '[1]

 [1] Baldwin, J. M. : 'Dictionary of Philosophy and Psychology, ' New York and London, 1901, Vol. I. , article on 'Inhibition. '

Even here, it may be said, there is in the term 'prevents' animplication of the direct exercise of force. But if we abstract fromany such implication, and conceive of such force as the terminhibition seems to connote, as restricted to the associated neural orphysiological processes, no unwarranted assumptions need be importedby the term into the facts, and the definition may, perhaps, suffice. 

Some careful work has been done in the general field of psychicalinhibition. In fact, the question of inhibition could hardly beavoided in any inquiry concerning attention or volition. A. Binet[2]reports certain experiments in regard to the rivalry of consciousstates. But the states considered were more properly those ofattention and volition than of mere ideation. And the same authorreports later[3] examples of antagonism between images and sensations, showing how the latter may be affected, and in some respectsinhibited, by the former. But this is inhibition of sensations ratherthan of ideas. Again, Binet, in collaboration with Victor Henri, [4]reports certain inhibitory effects produced in the phenomena ofspeech. But here again the material studied was volitional. Morerecently, G. Heymans[5] has made elaborate investigation of a certainphase of 'psychische Hemmung, ' and showed how the threshold ofperception may be raised, for the various special senses, by theinteraction of rival sensations, justly contending that this shiftingof the threshold measures the degree in which the original sensationis inhibited by its rival. But the field of inquiry was in that casestrictly sensational. We find also a discussion by Robert Saxinger, [6]'Ueber den Einfluss der Gefühle auf die Vorstellungsbewegung. ' But thetreatment there, aside from the fact that it deals with the emotions, is theoretical rather than experimental. 

 [2] Binet, A. : _Revue Philosophique_, 1890, XXIX. , p. 138. 

 [3] Binet, A. : _Revue Philosophique_, 1890, XXX. , p. 136. 

 [4] Binet, A. , et Henri, V. : _Revue Philosophique_, 1894, XXXVII. , p. 608. 

 [5] Heymans, G. : _Zeitschrift f. Psych. U. Physiol. D. Sinnesorgane_, 1899, Bd. XXI. , S. 321; _Ibid. _, 1901, Bd. XXVI. , S. 305. 

 [6] Saxinger, R. : _Zeitschrift f. Psych. U. Physiol. D. Sinnesorgane_, 1901, Bd. XXVI. , S. 18. 

In short, it appears that though much has been said and done upon thegeneral subject of psychical inhibition, experimental inquiry into theinhibitory effect of one idea upon another--abstraction made, as faras possible, of all volitional influence--virtually introduces us to anew phase of the subject. 

The term 'idea, ' it should be noted, is here used in its broadestsense, and includes the memory image. In fact, the memory image andits behavior in relation to another memory image formed the materialof the first part of the research, which alone is reported here. Apparatus and method were both very simple. 

The ideas to be compared were suggested by geometrical figures cut outof pasteboard and hung, 25 cm. Apart, upon a small black stand placedon a table in front of the observer, who sat at a distance of fourfeet from the stand. The diagrams and descriptions which follow willshow the character of these figures. 

Before the figures were placed in position, the subject was asked toclose his eyes. The figures being placed, a few seconds' warning wasgiven, and at the word 'look' the subject opened his eyes and lookedat the objects, closing his eyes again at the word 'close. ' The timeof exposure was five seconds. This time was divided as equally aspossible between the two figures, which were simultaneously exposed, the observer glancing freely from one to the other as in the commonobservation on which our ideas of objects are founded. At the end ofthe exposure the subject sat with closed eyes and reported the severalappearances and disappearances of the ideas or mental images of theobjects just presented. The conditions required of him were that heshould await passively the entry of the rival claimants on hisattention, favoring neither and inhibiting neither; that is to say, hewas to remit all volitional activity, save so far as was necessary torestrict his attention to the general field upon which the ideatedobjects might appear, and to note what occurred on the field. Theperiod of introspection, which followed immediately the disappearanceof such retinal images as remained, after the closing of the eyes tothe external objects, lasted sixty seconds. The reports, like thesignals, were given in a just audible tone. They were in such terms as'right--left, ' 'small--large, ' 'circle--star, ' terms the simplest thatcould be found, or such as seemed, in any given case, most naturallyor automatically associated with the object, and therefore leastlikely to disturb the course of the observation. And each report wasnoted down by the experimenter at the instant it was given, with thetime of each phase, in seconds, as indicated by a stop-watch under theexperimenter's eye. 

It will be remarked that the attitude required of the observer was onewhich is not commonly taken. And it may be objected that the resultsof an attitude so unusual towards objects so ghostly and attenuatedmust be too delicate, or too complex, or influenced by too many aliensuggestions, to be plumply set down in arabic numerals. The subjects, in fact, did at first find the attitude not easy to assume. A visualobject may hold the attention by controlling the reflexes of the eye. But an ideational object has ordinarily no sure command of theconscious field save under the influence of a volitional idea or somestrongly toned affectional state. But with a little practice thedifficulty seemed to disappear. The subject became surer of hismaterial, and the mental object gradually acquired the same sort ofindividuality as the visual object, though the impression it mademight be less intense. 

After a few preliminary experiments, figures were devised for thepurpose of testing the effect of mere difference in the complexity ofoutline. That is to say, the members of every pair of objects were ofthe same uniform color-tone (Bradley's neutral gray No. 2), presentedthe same extent of surface (approximately 42 sq. Cm. ), were exposedsimultaneously for the same length of time (5 seconds), and were incontour usually of like general character save that the bounding linein the one was more interrupted and complex than in the other. 

In another series the variant was the extent of surface exposed, thecolor-tone (neutral gray), outline, and other conditions being thesame for both members of each pair. The smaller figures were of thesame area as those of the preceding series; in the larger figures thisarea was doubled. Only one member of each pair is represented in thediagrams of this and the next series. 

In a third series brightness was the variant, one member of each pairbeing white and the other gray (Bradley's cool gray No. 2). All otherconditions were for both figures the same. 

In still another series strips of granite-gray cardboard half acentimeter wide were cut out and pasted on black cards, some instraight and some in broken lines, but all of the same total length(10 cm. ). These were exposed under the same general conditions asthose which have already been described, and were intended to show therelative effects of the two sorts of lines. 

TABLE I. 

 1 2 3 4 5 Totals. Averages. L R L R L R L R L R L R L R I. 45 45 25 29 27 27 31 24 36 20 164 145 32. 8 29 II. 20 25 28 28 28 19 31 31 28 14 135 117 27 23. 5 III. 11 12 17 28 0 7 0 15 27 23 55 85 11 17 IV. 7 6 47 22 17 21 17 45 31 30 119 124 23. 8 24. 8 V. 27 33 46 36 40 31 44 31 26 35 183 165 36. 6 33. 2 VI. 11 14 32 29 34 21 14 35 0 46 91 145 18. 2 29 VII. 36 33 30 30 50 50 22 22 52 52 190 187 38 37. 4 VIII. 41 44 33 33 45 45 34 44 37 28 190 194 38 38. 8 IX. 45 45 39 46 42 47 47 47 44 44 217 229 43. 4 45. 8 X. 40 39 24 25 19 21 21 23 18 25 122 133 24. 4 26. 6 XI. 51 53 52 50 42 42 42 42 42 42 229 229 45. 8 45. 8

 334 349 373 356 344 331 303 359 341 359 1695 1754 30. 8 31. 9

 The Arabic numerals at the head of the columns refer, in every table, to the corresponding numerals designating the objects in the diagram accompanying the table. 

 _L_: left-hand object. _R_: right-hand object. 

 The Roman numerals (_I_ to _XI_) indicate the different subjects. The same subjects appear in all the experiments, and under the same designation. Two of the subjects, _IV_ and _VIII_, are women. 

 The numbers under _L_ and _R_ denote the number of seconds during which the left-hand image and the right-hand image, respectively, were present in the period of introspection (60 seconds). 

 General average: _L_, 30. 8 sec. ; _R_, 31. 9 sec. 

[Illustration: FIG. 1. ]

_Series No. 1. _--For the purpose of obtaining something that mightserve as a standard of comparison, a series of observations was madein which the members of every pair were exact duplicates of eachother, and were presented under exactly the same conditions, spatialposition of course excepted. The records of these observations are forconvenience placed first as Table I. 

In treating the facts recorded in the accompanying tables as phenomenaof inhibition no assumption is implied, it may be well to repeat, thatthe ideational images are forces struggling with each other formastery. Nor is it implied, on the other hand, that they are whollyunconditioned facts, unrelated to any phenomena in which we areaccustomed to see the expression of energy. Inhibition is meaninglesssave as an implication of power lodged somewhere. The implication isthat these changes are conditioned and systematic, and that among theconditions of our ideas, if not among the ideas themselves, power isexerted and an inferior yields to a superior force. Such force, inaccordance with our general presupposition, must be neural orcerebral. Even mental inhibition, therefore, must ultimately refer tothe physical conditions of the psychical fact. But the reference, tohave any scientific value, must be made as definite as the case willallow. We must at least show what are the conditions under which astate of consciousness which might otherwise occur does not occur. When such conditions are pointed out, and then only, we have a case ofwhat has been called psychical inhibition; and we are justified incalling it inhibition because these are precisely the conditions underwhich physiological inhibition may properly be inferred. And, we mayadd, in order that the conditions may be intelligibly stated andcompared they must be referable to some objective, cognizable fact. Here the accessible facts, the experiential data, to which thepsychical changes observed and the cerebral changes assumed may bothbe referred, are visual objects, namely, the figures alreadydescribed. 

What may occur when these objects are precisely alike, and are seenunder conditions in all respects alike except as to spatial position, is indicated in Table I. The general average shows that the imagereferred to the left-hand object was seen some 30 seconds per minute;that referred to the right-hand image, some 31 seconds. Sometimesneither image was present, sometimes both were reported presenttogether, and the time when both were reported present is included inthe account. In this series it appears, on the whole, that each imagehas about the same chance in the ideational rivalry, with a slightpreponderance in favor of the right. Individual variations, which maybe seen at a glance by inspection of the averages, show an occasionalpreponderance in favor of the left. But the tendency is, in mostcases, towards what we may call right-handed ideation. 

_Series No. II. _--In the second series (Table II. ) we find that, otherthings being equal, _an increase in the relative complexity of theoutline favors the return of the image to consciousness_. Includingthe time when both images were reported present at once, the simplerappears but 27 seconds per minute as against 34 seconds for the morecomplex. No attempt was made to arrange the figures on any regularlyincreasing scale of complexity so as to reach quantitative results. The experiment was tentative merely. 

TABLE II. 

 1 2 3 4 S C S C S C S C I. 21. 5 23. 5 14. 5 35 22. 5 21. 5 15 27 II. 35. 5 21. 5 32. 5 48 32 33. 5 32. 5 21. 5 III. 27. 5 39 20. 5 47. 5 24. 5 46. 5 8 22. 5 IV. 31. 5 26. 5 38 23. 5 34. 5 22 24 29. 5 V. 48 50 48 39. 5 41. 5 51. 5 51 47. 5 VI. 11. 5 35 26. 5 28. 5 21 33 29 17 VII. 29. 5 35 47 47 10. 5 52 29. 5 33. 5 VIII. 12. 5 41 32 28. 5 13 26. 5 17 41. 5 IX. 10. 5 25. 5 27. 5 34. 5 14. 5 44 33 44. 5 X. 24 25. 5 20 23 16. 5 28 23 21 XI. 46 46. 5 31. 5 53. 5 18 53. 5 27 50. 5

 298 369 338 408. 5 248. 5 412 289 356

 5 6 7 Averages. S C S C S C S C I. 20. 5 21 14. 5 27 7. 5 37. 5 16. 57 27. 50 II. 31. 5 32 50 45. 5 49. 5 39. 5 37. 64 34. 50 III. 19. 5 32. 5 13 31 29 18 20. 28 33. 85 IV. 40. 5 46. 5 27 30. 5 26 32 31. 64 30. 07 V. 47. 5 47. 5 50. 5 48. 5 38 38 46. 35 46. 07 VI. 14. 5 29 14 33 21 28. 5 19. 64 29. 14 VII. 25. 5 43 42. 5 30 28 41. 5 30. 35 40. 28 VIII. 8 34 24 27 33 14. 5 19. 92 30. 42 IX. 41. 5 27 29. 5 27. 5 29. 5 28 26. 57 33. 00 X. 10. 5 36. 5 17 27 18 25 18. 42 26. 57 XI. 21. 5 53. 5 40. 5 43. 5 30 45 30. 64 49. 42

 281 402. 5 322. 5 370. 5 309. 5 347. 5 27. 10 34. 62

 _S:_ Outline simple. 

 _C:_ Outline complex. 

 In this and the following tables the numbers in the body of the columns represent, in each case, the combined result of two observations, in one of which the simpler figure was to the left, in the other the more complex. The figures were transposed in order to eliminate any possible space error. 

 General average: _S_, 27. 10 sec. ; _C_, 34. 62 sec. 

Can anything be said, based on the reports, by way of explanation ofthe advantage which complexity gives? In the first place, the attitudeof the subject towards his image seems to have been much the same ashis attitude towards an external object: to his observation the imagebecame, in fact, an object. "When the image was gone, " says one, "myeyes seemed to be in search of something. " And occasionally the oneideated object was felt to exert an influence over the other. "Thecomplex seemed to affect the form of the simpler figure. " "It seemedthat the complex actually had the effect of diminishing the size ofthe simpler figure. " From time to time the images varied, too, indistinctness, just as the objects of perception vary, and the superiordistinctness of the more complex was frequently noted by the subjects. Now the importance of the boundary line in perception is wellunderstood. It seems to have a corresponding importance here. "What Inotice more in the simple figure, " says one observer, "is the mass; inthe complex, the outline. " "The simple seemed to lose its form, " saysanother, "the complex did not; the jagged edge was very distinct. " Andit is not improbable, in view of the reports, that irregularitiesinvolving change of direction and increase in extent of outlinecontributed mainly to the greater persistence of the more complicatedimage, the 'mass' being in both figures approximately the same. Nordid the advantage of the broken line escape the notice of the subject. "I found myself, " is the comment of one, "following the contour of thestar--exploring. The circle I could go around in a twinkle. " Again, "the points entered the field before the rest of the figure. " Andagain, "the angle is the last to fade away. "

[Illustration: FIG. 2. ]

Now this mental exploration involves, of course, changes in thedirection of the attention corresponding in some way to changes in thedirection of the lines. Does this shifting of the attention involveideated movements? There can be little doubt that it does. "I felt animpulse, " says one, "to turn in the direction of the image seen. " Andthe unconscious actual movements, particularly those of the eyes, which are associated with ideated movements, took place so often thatit is hard to believe they were ever wholly excluded. Such movements, being slight and automatically executed, were not at first noticed. The subjects were directed, in fact, to attend in all cases primarilyto the appearance and disappearance of the images, and it was onlyafter repeated observations and questions were put, that they becameaware of associated movements, and were able, at the close of anobservation, to describe them. After that, it became a common reportthat the eyes followed the attention. And as we must assume somecentral influence as the cause of this movement, which while the eyeswere closed could have no reflex relation to the stimulus of light, wemust impute it to the character of the ideas, or to their physicalsubstrates. 

The idea, or, as we may call it, in view of the attitude of thesubject, the internal sensory impression, thus seems to bear a doubleaspect. It is, in the cases noted, at once sensory and motor, or atany rate involves motor elements. And the effect of the activity ofsuch motor elements is both to increase the distinctness of the imageand to prolong the duration of the process by which it is apprehended. The sensory process thus stands in intimate dependence on the motor. Nor would failure to move the eyes or any other organ with themovement of attention, if established, be conclusive as against thepresence of motor elements. A motor impulse or idea does not alwaysresult in apparent peripheral movement. In the suppressed speech, which is the common language of thought, the possibility of incipientor incomplete motor innervations is well recognized. But where theperipheral movement actually occurs it must be accounted for. And asthe cause here must be central, it seems reasonable to impute it tocertain motor innervations which condition the shifting of the mentalattitude and may be incipient merely, but which, if completed, resultin the shifting of the eyes and the changes of bodily attitude whichaccompany the scrutiny of an external object. And the sensory processis, to some extent at least, conditioned by the motor, if, indeed, thetwo are anything more than different aspects of one and the sameprocess. [7]

 [7] Cf. Münsterberg, H. : 'Grundzüge d. Psychologie, ' Bd. I. , Leipzig, 1900, S. 532. 

But where, now, the subject is occupied in mentally tracing theboundaries of one of his two images he must inhibit all motorinnervations incompatible with the innervations which condition suchtracing: the rival process must cease, and the rival image will fade. He may, it is true, include both images in the same mental sweep. Theboundary line is not the only possible line of movement. In fact, wemay regard this more comprehensive glance as equivalent to anenlargement of the boundaries so as to include different mentalobjects, instead of different parts of but one. Or, since thedelimitation of our 'objects' varies with our attitude or aim, we maycall it an enlargement of the object. But in any case the mentaltracing of a particular boundary or particular spatial dimensionsseems to condition the sense of the corresponding content, and throughinhibition of inconsistent movements to inhibit the sense of adifferent content. No measure of the span of consciousness can, ofcourse, be found in these reports. The movements of the attention aresubtle and swift, and there was nothing in the form of the experimentsto determine at any precise instant its actual scope. All we needassume, therefore, when the images are said to be seen together, isthat neither has, for the time being, any advantage over the other indrawing attention to itself. If in the complete observation, however, any such advantage appears, we may treat it as a case of inhibition. By definition, an idea which assumes a place in consciousness whichbut for itself, as experiment indicates, another might occupy, inhibits the other. 

[Illustration: FIG. 3. ]

TABLE III. 

 1 2 3 4 5 6 S L S L S L S L S L S L I. 22 24 19. 5 23 20 26 21. 5 21 21 26 18 31 II. 31 39 31. 5 36 15 32. 5 11 22. 5 13. 5 24. 5 7. 5 23 III. 10. 5 43. 5 12 21. 5 13 14. 5 19 10. 5 18. 5 30. 5 7 18. 5 IV. 34. 5 29. 5 29. 5 24 40. 5 33 30. 5 32. 5 15 30 26 30 V. 31. 5 30 42 45 39 51 47 49. 5 41 37 46 45 VI. 22 20 20. 5 22 23. 5 22 25 16 24 20 22 25. 5 VII. 53. 5 53. 5 23. 5 23. 5 47. 5 47. 5 51 52 52. 5 53 51 52 VIII. 34 40. 5 23 29 21 22 22 37. 5 34. 5 35 27. 5 28 IX. 19. 5 45 19. 5 46 22 23. 5 23. 5 48 26 45. 5 19 44. 5 X. 16 30. 5 12 35 21 24. 5 8. 5 41 15. 5 33 19 28 XI. 38. 5 36. 5 21 48. 5 30 54. 5 31 55. 5 32 54 12 50

 313 392 254 353. 5 292. 5 381. 5 290 386 293. 5 388. 5 255 375. 5

 7 8 9 10 Averages S L S L S L S L S L I. 20. 5 31. 5 21. 5 28. 5 22. 5 28 22. 5 26 20. 90 26. 50 II. 14. 5 17. 5 19 20 11 4. 5 7 30. 5 16. 10 25. 00 III. 10 22 8. 5 26 17 16 8 16 12. 35 21. 90 IV. 27. 5 28. 5 35 30. 5 23. 5 46 27. 5 49. 5 28. 95 33. 35 V. 40. 5 35 24. 5 22. 5 21 31 21. 5 21. 5 35. 40 36. 75 VI. 22. 5 18. 5 11. 5 21 20 27 22. 5 24 21. 35 21. 60 VII. 44. 5 46. 5 52 51 33. 5 49 39. 5 50. 5 44. 85 47. 85 VIII. 19. 5 20 21 27 19. 5 27. 5 18. 5 22. 5 24. 05 29. 60 IX. 18. 5 46 13 42 20 42 18. 5 43 19. 95 44. 90 X. 18. 5 24 20. 5 21 20. 5 22 18. 5 28. 5 17. 00 28. 75 XI. 21 49 32 53. 5 38 53. 5 34. 5 46. 5 29. 00 50. 15

 257. 5 338. 5 258. 5 343 246. 5 346. 5 238. 5 358. 5 24. 54 33. 30

 _L_: large. _S_: small. 

 General average, _S_, 24. 54 sec. ; _L_, 33. 30 sec. 

_Series No. III. _--In the third series, where the variant is theextent of (gray) surface exposed, the preponderance is in favor of theimage corresponding to the larger object. This shows an appearance ofsome 33 seconds per minute as against 24 for the smaller (Table III. ). Here the most obvious thing in the reports, aside from the relativedurations, is the greater vividness of the favored image. Something, no doubt, is due to the greater length of boundary line and otherspatial dimensions involved in the greater size. And it is thissuperiority, and the ampler movements which it implies, which wereprobably felt by the subject who reports 'a feeling of expansion inthe eye which corresponds to the larger image and of contraction inthe other. ' But the more general comment is as to the greatervividness of the larger image. "The larger images seem brighterwhichever side they are on. " "The larger is a little more distinct, asif it were nearer to me. " "Large much more vivid than small. " Such arethe reports which run through the series. And they point, undoubtedly, to a cumulative effect, corresponding to a well-known effect insensation, in virtue of which greater extension may become theequivalent of greater intensity. In other words, the larger image madethe stronger impression. Now in external perception the strongerimpression tends to hold the attention more securely; that is, it ismore effective in producing those adjustments of the sensory organswhich perceptive attention implies. So here what was noticed as thesuperior brightness and distinctness of the larger image may besupposed to imply some advantage in the latter in securing thoseadjustments of the mental attitude which were favorable to theapprehension of that image. Advantage means here, again, in part atleast, if the considerations we have urged are sound, inhibition ofthose motor processes which would tend to turn attention to a rival. And here, again, the adjustment may reach no external organ. Anincipient innervation, which is all that we need assume as thecondition of a change of mental attitude, would suffice to block, orat least to hamper, inconsistent innervations no more complete thanitself. 

[Illustration: Fig. 4. ]

TABLE IV. 

 1 2 3 4 G W G W G W G W I. 15. 5 28. 5 21. 5 32. 5 20 33 21 28. 5 II. 39. 5 23 22. 5 22. 5 19 20. 5 35. 5 17. 5 III. 13. 5 12. 5 32 4. 5 8. 5 10 11. 5 11. 5 IV. 30 33. 5 38 36. 5 36 39. 5 37. 5 13. 5 V. 33. 5 32. 5 34. 5 32 33 35 45 36. 5 VI. 15 22 21 21 18. 5 22 12 22 VII. 53. 5 50 43 46 54. 5 55 56 56 VIII. 15. 5 24. 5 24 25 20 13 16. 5 21 IX. 17. 5 44 9. 5 46 18. 5 43. 5 16 42 X. 25. 5 19 29. 5 19 21 20. 5 23. 5 18 XI. 35 42. 5 13 29. 5 18. 5 46 16 38 294 332 288. 5 314. 5 267. 5 338 290. 5 304. 5

 5 6 7 8 G W G W G W G W I. 24 26. 5 23. 5 25 19. 5 30. 5 21 29 II. 21 29. 5 20 18. 5 29 16. 5 28. 5 14 III. 20. 5 8. 5 11 11. 5 10 14 23 16. 5 IV. 39. 5 28. 5 34. 5 22. 5 23 30. 5 33. 5 18 V. 45 53 48 51 45 29 32. 5 34. 5 VI. 21. 5 28 18 32 20. 5 19 21. 5 18 VII. 54. 5 56 54. 5 54. 5 45 46 49 49 VIII. 24 26. 5 23. 5 22. 5 24 17. 5 31 31. 5 IX. 16 44 14 43. 5 9 43. 5 13 44. 5 X. 24. 5 18 24 21. 5 25. 5 24 22 22. 5 XI. 20. 5 8. 5 15 36. 5 33 23 34 29 311 327 286 339 283. 5 293. 5 309 306. 5

 9 10 11 12 Averages. G W G W G W G W G W I. 25 25. 5 22. 5 21 25 26. 5 27 21. 5 22. 95 27. 33 II. 20 25 15 20 29 32 13. 5 20 24. 37 21. 58 III. 12 20 12. 5 17. 5 10. 5 21 3 23 14. 00 14. 25 IV. 33 19. 5 35. 5 28 21. 5 34. 5 25. 5 26. 5 32. 29 27. 58 V. 51 50 35 30. 5 40. 5 54. 5 45. 5 52. 5 40. 70 40. 91 VI. 13 29. 5 25 33. 5 28. 5 23 23. 5 27. 5 19. 83 24. 79 VII. 46. 5 39. 5 38. 5 44. 5 43. 5 47. 5 42. 5 34. 5 48. 41 48. 20 VIII. 17. 5 25. 5 22 15. 5 21 29 22. 5 21. 5 21. 79 22. 75 IX. 13 43. 5 12. 5 41. 5 15 42 11 40 13. 75 43. 16 X. 24 24 27 19 25 21. 5 23. 5 23. 5 24. 58 20. 87 XI. 13. 5 49 2. 5 43 14 34 23 22 19. 83 33. 41 268. 5 351 248 314 273. 5 365. 5 260. 5 312. 5 25. 61 29. 53

 _G:_ Gray. _W:_ White. 

 General average: _G_, 25. 61 sec. ; _W_, 29. 53 sec. 

_Series No. IV. _--This and the next following series do not suggestmuch that differs in principle from what has been stated already. Itshould be noted, however, that in the white-gray series (Table IV. )the persistence of the gray in ideation surprised the subjectsthemselves, who confessed to an expectation that the white wouldassert itself as affectively in ideation as in perception. But it isnot improbable that affective or ęsthetic elements contributed to theresult, which shows as high a figure as 25 seconds for the gray asagainst 29 for the white. One subject indeed (IV. ) found the grayrestful, and gives accordingly an individual average of 32 for thegray as against 27 for the white. More than one subject, in fact, records a slight advantage in favor of the gray. And if we must admitthe possibility of a subjective interest, it seems not unlikely that abald blank space, constituting one extreme of the white-black series, should be poorer in suggestion and perhaps more fatiguing thanintermediate members lying nearer to the general tone of the ordinaryvisual field. Probably the true function of the brightness quality infavoring ideation would be better shown by a comparison of differentgrays. The general average shows, it is true, a decided preponderancein favor of the white, but the individual variations prove it would beunsafe to conclude directly, without experimental test, from the lawsof perception to the laws of ideation. 

_Series No. V. _--The fifth series, which was suggested by the second, presents the problem of the lines in greater simplicity than thesecond; and, unlike the earlier series, it shows in all the individualaverages the same sort of preponderance as is shown in the generalaverage (straight line, 31; broken line, 38). The footings of thecolumns, moreover, show an aggregate in favor of the broken line inthe case of every pair of lines that were exposed together. Theresults in this case may therefore be regarded as cleaner and moresatisfactory than those reached before, and come nearer, one may say, to the expression of a general law. The theoretical interpretation, however, would be in both cases the same. 

[Illustration: FIG. 5. ]

TABLE V. 

 1 2 3 4 5 6 L A L A L A L A L A L A I. 28 26. 5 24. 5 29. 5 25 28 26 28. 5 26 29. 5 25. 5 29. 5 II. 35 41. 5 42 34. 5 31. 5 47. 5 53 50. 5 52 52 48 48 III. 16. 5 19. 5 24 29 41 29. 5 35. 5 29 21 40 39 40 IV. 40 41. 5 37 45 32. 5 45. 5 36. 5 43. 5 33. 5 38 36. 5 43. 5 V. 49 53 45 47 45. 5 36. 5 32. 5 51 37 46 40 51 VI. 18 31. 5 16 45 22. 5 30. 5 25 25 24. 5 37 25 22 VII. 43 39. 5 52 54. 5 52. 5 53. 5 51 54. 5 40. 5 55 48 48. 5 VIII. 23 23 27 29. 5 38 40 34. 5 32 23 37 42 38. 5 IX. 23 48 48 47. 5 35 46. 5 48 35 28. 5 48 46. 5 34. 5 X. 18 33 19. 5 31. 5 20. 5 30 22 29. 5 16. 5 35. 5 19. 5 33 XI. 22. 5 33. 5 18 41 26 23 19 35. 5 5 38 7 50. 5

 316 390. 5 353 434 370 410. 5 383 414 307. 5 456 377 439

 Averages. L A I. 25. 83 28. 58 II. 43. 58 45. 66 III. 29. 50 31. 16 IV. 36. 00 42. 83 V. 41. 50 47. 41 VI. 21. 83 31. 83 VII. 47. 83 50. 91 VIII. 31. 25 33. 33 IX. 38. 16 43. 25 X. 19. 33 32. 08 XI. 16. 25 36. 91

 31. 91 38. 54

 _L_: Line (straight line). _A_: Angle (broken line). 

 General average: _L_, 31. 91 sec. ; _A_, 38. 54 sec. 

TABLE VI. 

 1 2 3 4 5 6 P M P M P M P M P M P M I. 22 32. 5 23. 5 32 23. 5 32 22. 5 32. 5 23. 5 31. 5 21 39 II. 24. 5 32. 5 31. 5 49. 5 32 39 36 36 33. 5 42 28. 5 35 III. 8. 5 23. 5 0 36 0 31. 5 11. 5 5. 5 8. 5 14 3. 5 8. 5 IV. 30 49. 5 30. 5 42 24 48 27. 5 44 28 40. 5 43. 5 34. 5 V. 55. 5 55. 5 54. 5 54. 5 46. 5 53 34 36 41. 5 47 31 35. 5 VI. 19. 5 22. 5 19. 5 28 19. 5 28. 5 26. 5 27. 5 24. 5 29. 5 18. 5 36 VII. 45 56. 5 47. 5 55. 5 40. 5 40 48 54 33. 5 50 41 42. 5 VIII. 19. 5 24 0 40 27. 5 20. 5 13. 5 23 16 25 23 34. 5 IX. 28 49. 5 26. 5 48. 5 27. 5 45 18 45 21. 5 48. 5 42. 5 44. 5 X. 8 43. 5 22 29 8. 5 43. 5 9. 5 42. 5 16 35 12. 5 40. 5 XI. 5. 5 42. 5 7. 5 35. 5 16. 5 35. 5 7. 5 41 10 41. 5 8 32. 5

 24. 18 39. 27 23. 91 40. 95 24. 18 37. 86 23. 14 35. 18 23. 32 36. 77 24. 82 34. 82

 Indiv. Aver. P M I. 22. 666 33. 250 II. 31. 000 39. 000 III. 5. 333 19. 833 IV. 30. 583 43. 083 V. 43. 833 46. 916 VI. 21. 333 28. 666 VII. 42. 583 49. 750 VIII. 16. 583 27. 833 IX. 27. 333 46. 833 X. 12. 750 39. 000 XI. 9. 166 38. 083

 23. 92 37. 48

 _P_: Plain. _M_: Marked. 

 General average: Plain, 23. 92 sec. ; Marked, 37. 48 sec. 

Series No. VI. _--Both the figures in each pair of this series were ofthe same material (granite-gray cardboard) and of the same area andoutline, but the content of one of the two was varied with dark linesfor the most part concentric with the periphery. 

The advantage on the side of the figures with a varied content ismarked, the general averages showing a greater difference than isshown in any of the tables so far considered. And the advantageappears on the same side both in the individual averages and in theaverages for the different pairs as shown at the foot of the columns. There can be little doubt, accordingly, that we have here theexpression of a general law. 

For the meaning of this law we may consult the notes of the subjects:'The plain figure became a mere amorphous mass;' 'the inner linesreinforce the shape, for while previously the number of points in thisstar has increased (in ideation), here the number is fixed, and fixedcorrectly;' 'my attention traversed the lines of the content, andseemed to be held by them;' 'the variety of the marked objects wasfelt as more interesting;' 'the attention was more active whenconsidering the marked figures, passing from point to point of thefigure;' 'the surface of the plain figure was attended to as a wholeor mass, without conscious activity;' 'in the plain figure I thoughtof the gray, in the marked figure I thought of the lines;' 'part ofthe plain figure tended to have lines. '

The part played by the motor elements previously referred to insustaining attention and prolonging (internal) sensation is hereunmistakable. We have further evidence, too, of the value of the linein defining and strengthening the mental attitude. In a mass ofhomogeneous elements such as is presented by a uniform gray surface, the attention is equally engaged by all and definitely held by none. Monotony therefore means dullness. And the inhibition of incompatibleattitudes being as weak and uncertain as the attitudes actually butloosely assumed, the latter are readily displaced, and the sensationto which they correspond as readily disappears. Hence the greaterinterest excited by the lined figures. The lines give definiteness anddirection to the attention, and as definitely inhibit incompatibleattitudes. And the shutting out of the latter by the spontaneousactivity of the mind means that it is absorbed or interested in itspresent occupation. 

TABLE VII. 

 1 2 3 4 5 6 5 10 5 10 5 10 5 10 5 10 5 10 I. 29. 5 23 24. 5 21. 5 27 18. 5 28 26 27 20 25 29. 5 II. 25. 5 21 32. 5 42. 5 19. 5 33 27 33. 5 26 32 20 28. 5 III. 4. 5 18. 5 12. 5 5. 5 0 3. 5 7. 5 11 10. 5 18. 5 0 7 IV. 33 31. 5 28 32 42 44 25 45 38. 5 43 41 36. 5 V. 35 40. 5 35 52. 5 28 49. 5 43 31 42. 5 29 47. 5 50. 5 VI. 10. 5 34. 5 10. 5 34. 5 23 15 26 26. 5 22 27 19. 5 34. 5 VII. 27 42 28. 5 19 31. 5 49 39 45. 5 28. 5 50. 5 49. 5 51. 5 VIII. 13. 5 21. 5 19 15 21. 5 18 23 22. 5 19. 5 18 24. 5 21. 5 IX. 33 43. 5 36 37. 5 35 40 26 45 31. 5 44 21. 5 43. 5 X. 20. 5 23 22. 5 23 23 23. 5 22 27. 5 21. 5 29 21 34. 5 XI. 13. 5 29 32 16. 5 9. 5 36. 5 40. 5 8. 5 39. 5 8. 5 17. 5 30. 5

 22. 32 31. 50 25. 55 27. 23 23. 64 30. 05 27. 91 29. 27 27. 91 29. 05 26. 09 33. 45

 7 8 9 10 11 12 5 10 5 10 5 10 5 10 5 10 5 10 I. 22. 5 29 27. 5 25. 5 26 22 22. 5 27. 5 25. 5 25 22 28 II. 29 37. 5 32. 5 28 34 32 26 23 30. 5 28 25. 5 23 III. 20. 5 8. 5 12 16. 5 21 9 32 3 21. 5 15 8 22 IV. 31 26 39. 5 41. 5 37 29. 5 28. 5 37 36. 5 30. 5 33 31. 5 V. 38 34 39 46. 5 54 40 32. 5 46 43. 5 46 36. 5 50. 5 VI. 30 17 13 25 34. 5 26. 5 20. 5 27 27 35 27. 5 33 VII. 55. 5 50 42. 5 28 50. 5 15. 5 49 17. 5 43. 5 29. 5 44 26. 5 VIII. 16. 5 21. 5 18 17 17. 5 21. 5 21 22. 5 21. 5 23. 5 23 27. 5 IX. 41 46 45. 5 43. 5 46. 5 33 39 37. 5 32 35 33. 5 40 X. 24. 5 28. 5 26. 5 24 28. 5 25. 5 25. 5 25 22 30 24 23. 5 XI. 19. 5 26. 5 14 30 42. 5 2. 5 21. 5 30 22. 5 33 25. 5 24

 29. 82 29. 50 28. 18 29. 59 35. 64 23. 36 28. 91 26. 91 29. 64 30. 05 27. 50 29. 96

 Indiv. Aver. 5 10 I. 25. 58 24. 62 II. 27. 33 30. 16 III. 12. 50 11. 50 IV. 34. 41 35. 66 V. 39. 54 43. 00 VI. 22. 00 27. 95 VII. 40. 75 35. 37 VIII. 19. 87 20. 83 IX. 35. 04 40. 70 X. 23. 45 26. 41 XI. 24. 83 22. 95

 27. 75 29. 15

 5: refers to object exposed 5 seconds. 10: refers to object exposed 10 seconds. 

 General average: (5), 27. 75 sec. ; (10), 29. 15 sec. 

_Series No. VII. _--The object of this series was to determine theeffect in ideation of exposing for unequal lengths of time the twoobjects compared. The figures compared were of the same area andoutline, and were distinguished only by their color, one being red andthe other green. These colors were employed, after a preliminary test, as showing, on the whole, to nearly equal advantage in the individualchoice of colors. The shorter exposure was five seconds and the longerexposure ten seconds. The color that was to be seen the longer timewas exposed first alone; after five seconds the other was exposed; andthen both were seen for five seconds together, so that neither mighthave the advantage of the more recent impression. The two colors wereregularly alternated, and in one half of the series the longerexposure was to the right, in the other half to the left. The extrafive seconds were thus in each case at the beginning of theexperiment. 

The general averages show only a slight advantage in favor of thecolor which was exposed the longer time, namely, 29. 15 seconds, asagainst 27. 75 seconds. It is not easy to believe that the advantage ofsole occupancy of the visual field for five seconds, without anyoffsetting disadvantage in the next five seconds, should have soslight an effect on the course of ideation. And it is not improbablethat there was an offsetting disadvantage. In the presence of colorthe subject can scarcely remain in the attitude of quiet curiositywhich it is easy to maintain in the observation of colorless objects. A positive interest is excited. And the appearance of a new color inthe field when there is another color there already seems to becapable of exciting, by a sort of successive contrast different fromthat ordinarily described, an interest which is the stronger from thefact that the subject has already been interested in a differentcolor. That is to say, the transition from color to color (only redand green were employed) seems to be more impressive than thetransition from black to color. And, under the conditions of theexperiment, the advantage of this more impressive transition layalways with the color which was exposed the shorter time. 

Judging from the introspective notes, the outline seems to suffer, incompetition with a colored content, some loss of power to carry theattention and maintain its place in the ideation. "The colors tend todiffuse themselves, ignoring the boundary, " says one. "The images fadefrom the periphery toward the center, " says another. On the otherhand, one of the subjects finds that when both images are present thecolor tends to fade out. This may perhaps be explained by the remarkof another subject to the effect that there is an alternate shiftingof the attention when both images are present. An attitude ofcontinued and definite change, we may suppose, is one in which thecolor interest must yield to the interest in boundaries and definitespatial relations. 

Other interesting facts come out in the notes. One subject finds theideated plane farther away than the objective plane; another conceivesthe two as coinciding. The movement of the eyes is by this timedistinctly perceived by the subject. The reports run as follows:'Eye-movements seem to follow the changes in ideation;' 'I find myeyes already directed, when an image is ideated, to the correspondingside, and am sometimes conscious of the movement, but the movement isnot intended or willed;' 'in ideating any particular color I find myattention almost always directed to the side on which thecorresponding object was seen. ' This last observation seems to be truefor the experience of every subject, and, generally speaking, theimages occupy the same relative positions as the objects: the image ofthe right object is seen to the right, that of the left object to theleft, and the space between the two remains tolerably constant, especially for the full-faced figures. 

This fact suggested a means of eliminating the disturbing influence ofcolor, and its contrasts and surprises, by the substitution of grayfigures identical in form and size and distinguished only by theirspatial position. The result appears in the table which follows(VIII. ). 

_Series No. VIII. _--The object of this experiment was the same as thatof No. VII. Granite-gray figures, however, were substituted, for thereasons already assigned, in place of the red and green figures. Andhere the effect of additional time in the exposure is distinctlymarked, the general averages showing 32. 12 seconds for the image ofthe object which was exposed 10 seconds, as against 25. 42 seconds forthe other. 

TABLE VIII. 

 1 2 3 4 5 Indiv. Aver. 5 10 5 10 5 10 5 10 5 10 5 10 I. 26. 5 27 24. 5 30. 5 26. 5 28 27. 5 27. 5 26. 5 29 26. 3 28. 4 II. 32. 5 38. 5 27 36 29 28 17 14. 5 37. 5 27 28. 6 28. 8 III. 4. 5 13. 5 11 1. 5 10 11 7. 5 14. 5 12. 5 8. 5 9. 1 9. 8 IV. 23. 5 40. 5 27. 5 34 35. 5 38 35 28 17 39 27. 7 35. 9 V. 41 46 50 51. 5 43 42. 5 46 35. 5 31. 5 44 42. 3 43. 9 VI. 7. 5 27 18 25 21. 5 25. 5 7 44. 5 33. 5 19 17. 5 28. 2VIII. 24. 5 27 34. 5 32 36. 5 36 34. 5 38. 5 28 28. 5 31. 6 32. 4 IX. 17 46 25. 5 47. 5 44 47 40. 5 47. 5 48 48 35. 0 47. 2 X. 20 29 21 26. 5 25. 5 24. 5 27. 5 22 19. 5 23. 5 22. 7 25. 1 XI. 11 41. 5 9. 5 50 5. 5 43. 5 15. 5 40. 5 25. 5 32 13. 4 41. 5 20. 80 33. 60 24. 85 33. 45 27. 70 32. 40 25. 80 31. 30 27. 95 29. 85 25. 42 32. 12

 VII. --Absent. 

 5: refers to object exposed 5 seconds. 10: refers to object exposed 10 seconds. 

 General average: (5), 25. 42 sec. ; (10), 32. 12 sec. 

The interpretation of this difference may be made in accordance withthe principles already laid down. The ideated and actual movementswhich favor the recurrence and persistence of an idea are, on groundsgenerally recognized in psychology, much more likely to occur andrepeat themselves when the corresponding movements, or the samemovements in completer form, have frequently been repeated inobservation of the corresponding object. 

TABLE IX. 

 1 2 3 4 5 Indiv. Aver. 1st 2d 1st 2d 1st 2d 1st 2d 1st 2d 1st 2d I. 22. 5 32. 5 27 28 26. 5 28 26. 5 27. 5 26 29 25. 7 29. 0 II. 4. 5 43 9 29 3. 5 38 0 43 17 44. 5 6. 8 39. 5 III. 0 22 0 20. 5 9. 5 16. 5 0 23. 5 3. 5 9. 5 2. 6 18. 4 IV. 0 31 1 35. 5 4. 5 39 16. 5 32. 5 16 20. 5 7. 6 31. 7 V. 24 52. 5 41. 5 40 12 53. 5 22 55 22 50. 5 24. 3 50. 3 VII. 1. 5 52 0 48 0 54. 5 0 50. 5 0 46. 5 0. 3 50. 3VIII. 12 26 10 27. 5 11. 5 23. 5 13. 5 28. 5 15. 5 20 12. 5 25. 1 IX. 24 43. 5 20 42 25 42. 5 20. 5 44. 5 28 42. 5 23. 5 43. 0 X. 9 45. 5 19. 5 30 11 33 12 38 14. 5 30 13. 2 35. 3 XI. 12. 5 35 23. 5 29. 5 1 49 2 44 10. 5 52 9. 9 41. 9 11. 00 38. 30 15. 15 33. 00 10. 45 37. 75 11. 30 38. 70 15. 30 34. 50 12. 64 36. 45

 VI. --Absent. 

 From this point on the place of Miss H. (IV. ) is taken by Mr. R. The members in each pair of objects in this group were not exposed simultaneously. 

 1st: refers to object first exposed. 2d: refers to object last exposed. 

 General average: 1st, 12. 64 sec. : 2d, 36. 45 sec. 

What is here called ideated movement--by which is understood the ideaof a change in spatial relations which accompanies a shifting of theattention or a change in the mental attitude, as distinguished fromthe sense of movements actually executed--was recognized as such byone of the subjects, who says: "When the two objects are before me Iam conscious of what seem to be images of movement, or ideatedmovements, not actual movements. " The same subject also finds theimage of the object which had the longer exposure not only more vividin the quality of the content, but more distinct in outline. 

_Series No. IX. _--In this experiment the objects, which were ofgranite-gray cardboard, were exactly alike, but were exposed atdifferent times and places. After the first had been exposed fiveseconds alone, it was covered by means of a sliding screen, and thesecond was then exposed for the same length of time, the intervalbetween the two exposures being also five seconds. Two observationswere made with each pair, the first exposure being in one case to theleft and in the other case to the right. The object here was, ofcourse, to determine what, if any, advantage the more recent of thetwo locally different impressions would have in the course ofideation. The table shows that the image of the object last seen hadso far the advantage in the ideational rivalry that it remained inconsciousness, on the average, almost three times as long as theother, the average being, for the first, 12. 64 seconds; for thesecond, 36. 45 seconds. And both the individual averages and theaverages for the several pairs show, without exception, the samegeneral tendency. 

The notes show, further, that the image of the figure first seen wasnot only less persistent but relatively less vivid than the other, though the latter was not invariably the case. One subject had 'animpression that the images were farther apart' than in the serieswhere the exposure of the two objects was simultaneous, though thedistance between the objects was in all cases the same, the timedifference being, apparently, translated into spatial terms and addedto the spatial difference. The sort of antagonism which temporaldistinctions tend, under certain conditions, to set up between ideasis illustrated by the remark of another subject, who reports that 'theattention was fairly dragged by the respective images. ' And the factof such antagonism, or incompatibility, is confirmed by the extremelylow figure which represents the average time when both images werereported present at the same time. The two images, separated byprocesses which the time interval implies, seem to be more entirelyincompatible and mutually inhibitory than the images of objectssimultaneously perceived. For not only does the advantage of a fewseconds give the fresher image a considerable preponderance in itsclaim on the attention, but even the earlier image, after it has oncecaught the attention, usually succeeds in shutting out the other froma simultaneous view. 

TABLE X. 

 1 2 3 4 5 Indiv. Aver. V H V H V H V H V H V H I. 27. 5 27 26. 5 28 30. 5 24. 5 27. 5 28. 5 26 25 27. 60 26. 60 II. 45 43. 5 37 40 35. 5 28. 5 19 15. 5 30. 5 30. 5 33. 40 31. 60 III. 19 21 0 10. 5 19. 5 19 9 15 4. 5 16 10. 40 16. 30 IV. 47. 5 39 36 22. 5 44. 5 41. 5 47. 5 46 37 36 42. 50 37. 00 V. 56. 5 46. 5 42. 5 42. 5 48 45. 5 48. 5 48. 5 53 52 49. 70 47. 00 VI. 31. 5 28. 5 30. 5 30. 5 22 34. 5 34. 5 28. 5 25 26. 5 28. 70 29. 70 VII. 55 55 55 45. 5 38 20 55. 5 53. 5 56 56 51. 90 45. 80VIII. 39. 5 47 23. 5 23. 5 19 18. 5 26. 5 26. 5 26 20. 5 26. 90 27. 20 IX. 26. 5 46 38 42. 5 41 44 40. 5 46. 5 35. 5 39 36. 30 43. 60 X. 24. 5 25 26 25 25. 5 23 23. 5 28. 5 32. 5 20. 5 26. 40 24. 40 XI. 52 52 56. 5 54. 5 48 49. 5 45 47. 5 51. 5 47. 5 50. 60 50. 20

 38. 60 39. 14 33. 77 33. 09 33. 77 31. 68 34. 27 34. 95 34. 31 33. 60 34. 94 34. 49

 _V_: Vertical. _H_: Horizontal. 

 General average: Vertical, 34. 94 sec. ; Horizontal, 34. 49 sec. 

_Series No. X. _--The objects used in this experiment were straightlines, two strips of granite-gray cardboard, each ten centimeters longand half a centimeter wide, the one being vertical and the otherhorizontal. These were pasted on black cards and exposed in alternatepositions, each appearing once to the right and once to the left. Thefigures in the columns represent in each case the combined result oftwo such observations. 

The experiments with these lines were continued at intervals througha number of weeks, each individual average representing the result often observations, or of five pairs of exposures with alternatingobjects. 

The striking feature in the observations is the uniformity of theresults as they appear in the general averages and in the averages foreach pair as shown at the foot of the columns. There is some variationin the individual tendencies, as shown by the individual averages. Butthe general average for this group of subjects shows a difference ofless than half a second per minute, and that difference is in favor ofthe vertical line. 

This series will serve a double purpose. It shows, in the first place, that on the whole the vertical and the horizontal lines have a nearlyequal chance of recurrence in image or idea. It will serve, in thesecond place, as a standard of comparison when we come to consider theeffect of variations in the position and direction of lines. 

TABLE XI. 

 1 2 3 4 5 Indiv. Av. F O F O F O F O F O F O I. 24 31 26. 5 28. 5 27 29 22 33. 5 27. 5 28 25. 4 30. 0 II. 53. 5 50 52. 5 52. 5 56. 5 55. 5 43. 5 43. 5 56 51. 5 52. 4 50. 6 III. 3 21. 5 4 20 11 17 3. 5 27 0 20. 5 4. 3 21. 2 IV. 26. 5 30 11 48. 5 12. 5 53 12 51 23 51 17. 0 46. 7 V. 40. 5 56. 5 48 56 55. 5 55. 5 53 55. 5 53. 5 55. 5 50. 1 55. 58 VI. 27. 5 40. 5 23 31. 5 24. 5 32. 5 31 29 27 33. 5 26. 6 33. 4 VII. 50. 5 54 53. 5 56. 5 53. 5 53. 5 40. 5 52 55 55 50. 6 54. 2VIII. 1 33. 5 11 27 5 32 7. 5 39 4. 5 36. 5 5. 8 33. 6 IX. 35. 5 41. 5 45. 5 47 41. 5 41. 5 39 44. 5 41 41. 5 40. 5 43. 2 X. 19 30. 5 21. 5 30. 5 21 29. 5 16 37. 5 22. 5 30. 5 20. 0 31. 7 XI. 11. 5 52. 5 18 51. 5 14. 5 50. 5 23 50. 5 15 52. 5 16. 4 51. 5 26. 59 40. 14 28. 59 40. 86 29. 32 40. 86 26. 45 42. 09 29. 55 41. 45 28. 10 41. 08

 _F_: Full-faced. _O_: Outlined. 

 General average: full-faced, 28. 10 sec. ; outlined, 41. 08 sec. 

_Series No. XI. _--In this series full-faced figures were compared withoutline figures of the same dimensions and form. Material, granite-gray cardboard. The area of the full-faced figures was thesame as that of the figures of similar character employed in thevarious series, approximately 42 sq. Cm. ; the breadth of the lines inthe outline figures was half a centimeter. The objects in each pairwere exposed simultaneously, with the usual instructions to thesubject, namely, to regard each object directly, and to give to eachthe same share of attention as to the other. 

The form of the experiment was suggested by the results of earlierexperiments with lines. It will be remembered that the expresstestimony of the subjects, confirmed by fair inference from thetabulated record, was to the effect that lines show, in ideation as inperception, both greater energy and clearer definition than surfaces. By lines are meant, of course, not mathematical lines, but narrowsurfaces whose longer boundaries are closely parallel. To bring thesuperior suggestiveness of the line to a direct test was the object ofthis series. And the table fully substantiates the former conclusion. For the outline figure we have a general average of 41. 08 seconds perminute, as against 28. 10 seconds for the full-faced figure. 

The notes here may be quoted as corroborative of previous statements. "I notice, " says one, "a tendency of the color in the full-facedfigure to spread over the background"--a remark which bears out whathas been said of the relative vagueness of the subjective processesexcited by a broad homogeneous surface. To this may be added: "Thefull-faced figures became finally less distinct than the linear, andfaded from the outside in;" "the areal (full-faced) figure graduallyfaded away, while the linear remained. " Another comment runs: "I feelthe left (full-faced) striving to come into consciousness, but failingto arrive. Don't see it; feel it; and yet the feeling is connectedwith the eyes. " This comment, made, of course, after the close of anobservation, may serve as evidence of processes subsidiary toideation, and may be compared, in respect of the motor factors whichthe 'striving' implies, with the preparatory stage which Binet foundto be an inseparable and essential part of any given (vocal) motorreaction. [8]

 [8] Binet, A. Et Henri, V. : _op. Citat. _

_Series No. XII. _--Both the figures of each pair in this series werelinear, and presented the same extent of surface (granite-gray) withthe same length of line. In other words, both figures were constitutedof the same elements, and in both the corresponding lines ran in thesame direction; but the lines in the one were connected so as to forma figure with a continuous boundary, while the lines of the other weredisconnected, _i. E. _, did not inclose a space. The total length ofline in each object was twenty centimeters, the breadth of the linesfive millimeters. Both figures were arranged symmetrically withrespect to a perpendicular axis. 

[Illustration: FIG. 6. ]

TABLE XII. 

 1 2 3 4 5 Indiv. Av. L F L F L F L F L F L F I. 31. 5 24 30 24. 5 23. 5 32 25. 5 30. 5 27 29. 5 27. 5 28. 1 II. 55 55 56 56 56 56 56. 5 56. 5 54 54 55. 5 55. 5 III. 22 6 26. 5 9. 5 31. 5 1. 5 23 5. 5 28. 5 0 26. 3 4. 5 IV. 31 15 46. 5 20. 5 52 9. 5 49 6 55 18 46. 7 13. 8 V. 56 54 56 56 56 56 56. 5 56. 5 55. 5 55. 5 56. 0 55. 6 VI. 33 30 34 39. 5 31. 5 29. 5 26. 5 32 26 31. 5 30. 2 32. 5 VII. 55. 5 49. 5 56. 5 38 54. 5 35 57. 5 32. 5 38 27 52. 4 36. 4VIII. 26. 5 15. 5 21. 5 13. 5 25 17 25. 5 21 15 13. 5 22. 7 16. 1 IX. 45. 5 32. 5 44. 5 39 42. 5 35. 5 41. 5 37. 5 43 40. 5 43. 4 37. 0 X. 29. 5 23 36. 5 16 23 28. 5 35. 5 16. 5 29 23 30. 7 21. 4 XI. 52 8 49. 5 19 45. 5 25 43. 5 21. 5 15 31. 5 41. 1 21. 0 39. 77 28. 41 41. 77 30. 18 40. 10 29. 60 40. 05 28. 73 35. 10 29. 50 39. 32 29. 26

 L: Interrupted lines. F: Figure with continuous boundary. (Figure in outline. )

 General average: Lines, 39. 32 sec. ; figure, 29. 26 sec. 

The experiment was devised in further exploration of the effect of theline in ideation. The result fully bears out, when read in the lightof the introspective notes, what has been said of the importance ofthe motor element in ideation. It might have been supposed, in view ofthe importance usually attached to unity or wholeness of impression inarresting and holding the attention in external perception, that thecompleted figure would have the more persistent image. The generalaverages, however, stand as follows: Interrupted lines, 39. 32 secondsper minute; completed figure, 29. 26 seconds per minute. The individualaverages show slight variations from the tendency expressed in thesefigures, but the averages for the several pairs are all in harmonywith the general averages. 

The notes furnish the key to the situation: "I felt that I was doingmore, and had more to do, when thinking of the broken lines. " "Thebroken figure seemed more difficult to get, but to attract attention;continuous figure easy to grasp. " "Felt more active whencontemplating the image of the broken figure. " "In the broken figure Ihad a feeling of jumping from line to line, and each line seemed to bea separate figure; eye-movement very perceptible. " The dominance ofthe interrupted lines in ideation is evidently connected with the morevaried and energetic activity which they excited in the contemplatingmind. Apparently the attention cannot be held unless (paradoxical asit may sound) it is kept moving about its object. Hence, a certaindegree of complexity in an object is necessary to sustain our interestin it, if we exclude, as we must of course in these experiments, extraneous grounds of interest. Doubtless there are limits to thedegree of complexity which we find interesting and which compelsattention. A mere confused or disorderly complex, wanting altogetherin unity, could hardly be expected to secure attention, if there isany truth in the principle, already recognized, that the definite hasin ideation a distinct advantage over the vague. Here again the notessuggest the method of interpretation. "The broken lines, " says one, "tended to come together, and to take the form of the continuousfigure. " Another remarks: "The broken figure suggests a wholeconnected figure; the continuous is complete, the broken wants to be. "In virtue of their power to excite and direct the activity of theattention the interrupted lines seem to have been able to suggest theunity which is wanting in them as they stand. "The broken lines, " saysanother, "seemed to run out and unite, and then to separate again"--aremark which shows a state of brisk and highly suggestive activity inthe processes implied in attention to these lines. And a glance at thediagram will show how readily the union of the broken lines may bemade. These were arranged symmetrically because the lines of thecompleted figures were so arranged, in order to equalize as far aspossible whatever ęsthetic advantage a symmetrical arrangement mightbe supposed to secure. 

It thus appears that, whatever the effect in ideation of unity in theimpression, the effect is much greater when we have complexity inunity. The advantage of unity is undoubtedly the advantage which goeswith definiteness of impression, which implies definite excitationsand inhibitions, and that concentration of energy and intensity ofeffect in which undirected activity is wanting. But a bare unity, itappears, is less effective than a diversified unity. To what extentthis diversity may be carried we make no attempt to determine; but, within the limits of our experiment, its value in the ideationalrivalry seems to be indisputable. And the results of the experimentafford fresh proof of the importance of the motor element in internalperception. 

TABLE XIII. 

 1 2 3 4 5 Indiv. Av. F V F V F V F V F V F V I. 25 29 26 29 29. 5 26. 5 25. 5 30 24. 5 31 26. 1 29. 1 II. 56 56 55 55 54 54. 5 47. 5 47. 5 45 50 51. 5 52. 6 III. 2. 5 5. 5 2. 5 8. 5 6. 5 5 16. 5 9. 5 17 15 9. 0 8. 7 IV. 48 48 31. 5 31. 5 31 46 51. 5 51. 5 35 52 39. 4 45. 8 V. 54 54 56. 5 52 56 56 56 56 54 56 55. 3 54. 8 VI. 39 29 30 33. 5 35. 5 22. 5 32. 5 34 33. 5 24. 5 34. 1 28. 7 VII. 46 55 54. 5 46. 5 46. 5 50 49. 5 54 47 46 48. 7 50. 3VIII. 9 14. 5 23 20. 5 23. 5 22 18 14. 5 16 17 17. 9 17. 7 IX. 43 43 46. 5 46. 5 45. 5 45. 5 43. 5 43. 5 46 47. 5 44. 9 45. 2 X. 28 26. 5 21 29. 5 26. 5 26. 5 21. 5 31. 5 25 29 24. 4 28. 6 XI. 23. 5 46 19. 5 35. 5 20 46 24 47. 5 28. 5 19. 5 23. 1 38. 9 34. 00 36. 95 33. 27 35. 27 34. 05 36. 41 35. 09 38. 14 33. 77 35. 23 34. 03 36. 40

 F: Figure (in outline). V: Vertical lines. 

 General average: Figure, 34. 03 sec. ; vertical lines, 36. 40 sec. 

_Series No. XIII. _--In this series, also, both the figures of eachpair were constituted of the same elements; that is to say, both werelinear, and presented the same extent of surface (granite-gray), withthe same length of line, the total length of the lines in each figurebeing twenty centimeters and the breadth of the lines being threemillimeters. But while the lines of one figure were connected so as toform a continuous boundary, the lines of the other figure were allvertical, with equal interspaces. And, as in the last precedingseries, the two figures were formed by a different but symmetricalarrangement of the same lines. 

As before, the advantage is on the side of the disconnected lines. Inthis case, however, it is very slight, the general averages showing34. 03 seconds for the completed figure, as against 36. 40 seconds forthe lines. This reduction in the difference of the averages isprobably to be explained by the reduced complexity in the arrangementof the lines. So far as they are all parallel they would not be likelyto give rise to great diversity of movement, though one subject does, indeed, speak of traversing them in all directions. In fact, thecompleted figures show greater diversity of direction than the lines, and in this respect might be supposed to have the advantage of thelines. The notes suggest a reason why the lines should still prove themore persistent in ideation. "The lines appealed to me as a group; Itended always to throw a boundary around the lines, " is the comment ofone of the subjects. From this point of view the lines would form afigure with a content, and we have learned (see Series No. VI. ) that aspace with a varied content is more effective in ideation than ahomogeneous space of the same extent and general character. And thisunity of the lines as a group was felt even where no complete boundaryline was distinctly suggested. "I did not throw a boundary around thelines, " says another subject, "but they had a kind of unity. " It ispossible also that from the character of their arrangement the linesreinforced each other by a kind of visual rhythm, a view which issupported by the comments: 'The lines were a little plainer than thefigure;' 'figure shadowy, lives vivid;' 'the figure grew dimmertowards the end, the lines retained their vividness. '

On the whole, however, the chances are very nearly equal in the twocases for the recurrence of the image, and a comparison of this serieswith Series No. XII. Cannot leave much doubt that the greatereffectiveness of the lines in the latter is due to their greatercomplexity. In view, therefore, of the fact that in both series theobjects are all linear, and that the two series differ in no materialrespect but in the arrangement of the disconnected lines, thecircumstance that a reduction in the complexity of this arrangement isattended by a very considerable reduction in the power of the lines torecur in the image or idea is a striking confirmation of the soundnessof our previous interpretation. 

_Series No. XIV. _--In this series full-faced figures (granite-gray)similar in character to those made use of in former experiments, wereemployed. The objects were suspended by black silk threads, but whileone of them remained stationary during the exposure the other waslowered through a distance of six and one half centimeters and wasthen drawn up again. The object moved was first that on the righthand, then that on the left. As the two objects in each case wereexactly alike, the comparative effect of motion and rest in the objectupon the persistence in consciousness of the corresponding image wasobtained. The result shows a distinct preponderance in favor of themoved object, which has an average of 37. 39 seconds per minute asagainst 28. 88 seconds for the stationary object. The averages for thepairs, as seen at the foot of the columns, all run the same way, andonly one exception to the general tendency appears among theindividual averages. 

TABLE XIV. 

 1 2 3 4 5 Indiv. Av. S M S M S M S M S M S M I. 22. 5 28. 5 25 30. 5 24. 5 28 28 27. 5 25. 5 31 25. 1 29. 6 II. 47. 5 55 53 42 48. 5 53. 5 34. 5 39. 5 49 52 46. 5 48. 4 III. 3 18 7. 5 8. 5 0 7. 5 0 3. 5 0 4 2. 1 8. 3 IV. 45 45 33. 5 51. 5 11 50. 5 11 50 8 52. 5 21. 7 49. 9 V. 54. 5 51 53. 5 54. 5 49 51 30. 5 38. 5 56 55 48. 7 50. 0 VI. 21 32. 5 26 33 29. 5 37. 5 30 35 30 36 27. 3 34. 8 VII. 48 55 56. 5 49 41. 5 54. 5 44. 5 53 35. 5 54 45. 2 53. 1VIII. 10. 5 20. 5 20. 5 25 6 33 12. 5 29. 5 19 18 13. 7 25. 2 IX. 37. 5 43. 5 34. 5 45 36 47. 5 30 47. 5 29 48. 5 33. 4 46. 4 X. 13 39. 5 18 34 19 33. 5 19 33 10. 5 44 15. 9 36. 8 XI. 17. 5 43. 5 47. 5 32 27. 5 36 46 16. 5 52 16 38. 1 28. 8

 29. 09 39. 27 34. 14 36. 82 26. 59 39. 55 26. 00 33. 95 28. 59 37. 36 28. 88 37. 39

 S: Refers to figure left stationary. M: Refers to figure that was moved during exposure. 

 General average: S, 28. 88 sec. ; M, 37. 39 sec. 

The effectiveness of a bright light or of a moving object in arrestingattention in external perception is well understood. And the generaltestimony of the subjects in this experiment shows that it requiredsome effort, during the exposure, to give an equal share of attentionto the moving and the resting object. Table IV. , however, whichcontains the record of the observations in the white-gray series, shows that we cannot carry over, unmodified, into the field ofideation all the laws that obtain in the field of perception. Theresult of the experiment, accordingly, could not be predicted withcertainty. But the course of ideation, in this case, seems to followthe same general tendency as the course of perception: the restingobject labors under a great disadvantage. And if there is any force inthe claim that diversity and complexity in an object, with therelatively greater subjective activity which they imply, tend to holdthe attention to the ideated object about which this activity isemployed, the result could hardly be other than it is. There can be noquestion of the presence of a strong motor element where the objectattended to moves, and where the movement is imaged no less than thequalities of the object. In fact, the object and its movement weresometimes sharply distinguished. According to one subject, 'the imagewas rather the image of the motion than of the object moving. ' Again:'The introspection was disturbed by the idea of motion; I did not geta clear image of the moving object; imaged the motion rather than theobject. ' And a subject, who on one occasion vainly searched theideational field for sixty seconds to find an object, reports: 'I hada feeling of something going up and down, but no object. ' Clearly animportant addition was made to the active processes implied in theideation of a resting object, and it would be singular if this addedactivity carried with it no corresponding advantage in the ideationalrivalry. In one case the ideas of rest and of movement were curiouslyassociated in the same introspective act. "The figure which moved, "says the subject, "was imaged as stationary, and yet the idea ofmovement was distinctly present. "

The reports as to the vividness of the rival images are somewhatconflicting. Sometimes it is the moving object which was imaged withthe more vivid content, and sometimes the resting object. One reportruns: "The moving object had less color, but was more distinct inoutline than the stationary. " Sometimes one of the positions of themoving object was alone represented in the image, either the initialposition (on a level with the resting object) or a position lowerdown. On the other hand, we read: "The image of the moved objectseemed at times a general image that reached clear down, sometimeslike a series of figures, and not very distinct; but sometimes theseries had very distinct outlines. " In one case (the circle) theimage of the figure in its upper position remained, while the serialrepetitions referred to extended below. This, as might be supposed, isthe report of an exceptionally strong visualizer. In other cases theobject and its movements were not dissociated: "The moved object wasimaged as moving, and color and outline were retained. " And again:"Twice through the series I could see the image of the moving objectas it moved. " "Image of moved object moved all the time. "

TABLE XV. 

 1 2 3 4 5 Indiv. Av. Gray Red Gray Yellow Gray Green Gray Blue Gray Violet Gray Colored. 

 I. 26 29 27. 5 28. 5 26. 5 29 21. 5 27. 5 27. 5 26. 5 25. 8 28. 1 II. 35. 5 36. 5 45. 5 53. 5 53. 5 53. 5 53. 5 53. 5 55 55 48. 6 50. 4 III. 0 11 2. 5 19 10. 5 16 17. 5 8. 5 0 9 6. 1 12. 7 IV. 45 23. 5 8 53. 5 48 39 48 52 55. 5 35 40. 9 40. 6 V. 55. 5 55. 5 42 53 50 56 52. 5 50 44. 5 56. 5 49. 1 54. 2 VI. 22 33. 5 29 36. 5 28 43. 5 26 37. 5 39. 5 29 28. 9 36. 0 VII. 38. 5 39 56 56 49. 5 54. 5 47 47 45. 5 50 47. 3 49. 3VIII. 15 10. 5 15 19. 5 23 21 19. 5 24 20. 5 25 18. 6 20. 0 IX. 31. 5 49 19 42. 5 50 50 35. 5 46 48 39 36. 8 45. 3 X. 19 33 14. 5 37 29. 5 23 17 37. 5 23 31 20. 6 32. 3 XI. 11 49. 5 8 51. 5 9 43. 5 35 43. 5 24 47 17. 4 47. 0 27. 18 33. 64 24. 27 40. 95 34. 32 39. 00 33. 91 38. 82 34. 82 36. 64 30. 90 37. 81

 General average: Gray, 30. 90 sec. ; colored, 37. 81 sec. 

_Series No. XV. _--The figures in each pair of this series werefull-faced, and of the same shape and size, but one was gray and theother colored, the gray being seen first to the left, and then to theright. The colors used were of Prang's series (Gray, R. , Y. , G. , B. , V. ). In No. 1 the figures were in the form of a six-pointed star, andgray was compared with red. In No. 2 the figures were elliptical, andgray was compared with yellow. In No. 3 a broad circular band of graywas compared with the same figure in green. In No. 4 the figures werekite-shaped, and gray was compared with blue. In No. 5 a circularsurface of gray was compared with a circular surface of violet. Theobjects compared were exposed at the same time, under the usualconditions. 

As might perhaps be expected, the colored surfaces proved to be themore persistent in ideation, showing a general average of 37. 81seconds per minute as against 30. 90 seconds for the gray. 

The distinctness of the process of color apprehension is reflected inthe notes: "In the colored images I find the color rather than theform occupying my attention; the image seems like an area of color, asthough I were close to a wall and could not see the boundary;" andthen we have the significant addition, "yet I feel myself going aboutin the colored area. " Again: "In the gray the outline was moredistinct than in the colors; the color seems to come up as a shade, and the outline does not come with it. " Or again: "The gray has a moresharply defined outline than the color. " This superior definiteness inoutline of the gray figures is subject to exceptions, and one subjectreports 'the green outline more distinct than the gray. ' And even sobrilliant a color as yellow did not always obscure the boundary: "Theyellow seems to burn into my head, " says one of the subjects, "but theoutline was distinct. " The reports in regard to this color (yellow)are in fact rather striking, and are sometimes given in terms ofenergy, as though the subject were distinctly conscious of an activeprocess (objectified) set up in the apprehension of this color. Thereports run: "The yellow has an expansive power; there seemed to be nodefinite outline. " "The yellow seemed to exert a power over the grayto suppress it; its power was very strong; it seemed to beaggressive. "

TABLE XVI. 

 1 2 3 4 5 a b a b a b a b a b I. 0 0 0 0 0 0 0 0 0 0 II. 43 41 33 51 19 31 32 41 20 18 III. 0 6 0 0 3 11 13 16 0 0 IV. 56 28 23 35 0 11 48 56 35 25 V. 56 55 44 44 57 30 39 32 34 30 VI. 14 8 12 12 11 5 35 12 9 6 VII. 52 54 56 56 51 47 56 57 47 26 VIII. 15 0 18 21 24 39 26 10 23 21 IX. 28 25 39 31 23 28 26 36 25 17 X. 0 0 0 0 0 0 0 0 0 0 XI. 52 45 41 48 7 39 50 36 48 22 35. 11 29. 11 29. 55 33. 11 21. 66 26. 78 29. 55 26. 91 21. 91 15. 00

_Series No. XVI. _--The course of experimentation having shown thesuperior energy of lines, in comparison with surfaces, in stimulating, directing, and holding the attention, a series of figures was devisedto test the question whether the direction of the lines would have anyeffect upon the length of time during which _both_ images of a pair oflinear figures would be presented together. The materials used weregranite-gray strips half a centimeter wide. The letters (_a_) and(_b_) at the heads of the columns refer to the same letters in thediagram, and distinguish the different arrangements of the same pairof objects. The figures in the body of the columns show only thelength of time during which both images were reported present inconsciousness together. At the foot of the columns are shown theaverages for each pair. No general averages are shown, as the problempresented by each pair is peculiar to itself. 

[Illustration: FIG. 7. ]

The maximum is reached in No. 1_a_, where the angle has the arrowheadform and each angle points to the other. It should be remarked thatthe diagram is somewhat misleading in respect to the distance of thefigures, which in this as in the other experiments was 25 cm. Thefigures therefore were far enough away from each other to be perceivedand imaged in individual distinctness. But the 'energy' of the lines, especially where the lines united to form an acute angle, was oftensufficient to overcome the effect of this separation, and either tobring the figures nearer together or to unite them into a singleobject. The notes are very decisive in this regard. A few of them maybe cited: "The angles tended to join points. " "The figures showed atendency to move in the direction of the apex. " "The angles (2_a_)united to form a cross. " "When both figures (4_b_) were in mind I feltdisagreeable strains in the eyeballs; one figure led me to the rightand the other to the left. " The effect of the last-named figures(4_a_) seemed to be different from that of 1_a_ and 2_a_, though theapex of each angle was turned to that of the other in each of thethree cases. "The two angles, " says another subject, speaking of 4_a_, "appeared antagonistic to each other. " It will be observed that theyare less acute than the other angles referred to, and the confluentlines of each figure are far less distinctly directed towards thecorresponding lines of the opposing figure, so that the attention, sofar as it is determined in direction by the lines, would be lesslikely to be carried over from the one image to the other. 

On the other hand, when the angles were turned away from each otherthe legs of the angles in the two figures compared were brought intocloser relation, so that in 2_b_, for instance, the average is evenhigher than in 2_a_. Similarly the average in 3_b_, an obtuse angle, is higher than in 3_a_. The notes show that in such cases thecontrasted angles tended to close up and coalesce into a singlefigure with a continuous boundary. "The ends (2_b_) came together andformed a diamond. " "When the angles were turned away from each otherthe lines had an occasional tendency to close up. " "There was atendency to unite the two images (4_a_) into a triangle. " "The twofigures seemed to tug each other, and the images were in fact a littlecloser than the objects (4_a_). " "The images (4_a_) formed atriangle. " So with regard to the figures in 5_a_. "When both were inthe field there seemed to be a pulling of the left over to the right, though no apparent displacement. " "The two figures formed a square. "

The lowest average--and it is much lower than any other average in thetable--is that of 5_b_, in which the contrasted objects have neitherangles nor incomplete lines directed to any common point between theobjects. In view of the notes, the tabulated record of these twofigures (5_b_) is very significant, and strikingly confirms, by itsnegative testimony, what 1_a_ and 2_b_ have to teach us by theirpositive testimony. The averages are, in the three cases just cited:1_a_, 35. 11 seconds; 2_b_, 33. 11 seconds; 5_b_, 15 seconds per minute. 

On the whole, then, the power of the line to arrest, direct, and keepthe attention, through the greater energy and definiteness of theprocesses which it excites, and thereby to increase the chances of therecurrence and persistence of its idea in consciousness, is confirmedby the results of this series. The greatest directive force seems tolie in the sharply acute angle. Two such angles, pointing one towardsthe other, tend very strongly to carry the attention across the gapwhich separates them. (And it should be borne in mind that thedistance between the objects exposed was 25 cm. ) But the power of twoincomplete lines, similarly situated, is not greatly inferior. 

It thus appears that the attention process is in part, at least, amotor process, which in this case follows the direction of the lines, acquiring thereby a momentum which is not at once arrested by a breakin the line, but is readily diverted by a change in the direction ofthe line. If the lines are so situated that the attention processexcited by the one set is carried away from the other set, the one setinhibits the other. If, on the other hand, the lines in the one setare so situated that they can readily take up the overrunning orunarrested processes excited by the other set, the two figures supporteach other by becoming in fact one figure. The great importance of themotor elements of the attention process in ideation, and thus in thepersistence of the idea, is evident in either phase of the experiment. 

RECAPITULATION. 

 Seconds Seconds. 1 Figures alike: Left 30. 8 Right 31. 9 2 " unlike: Simple 27. 10 Complex 34. 62 3 " " Small 24. 54 Large 33. 30 4 " " Gray 25. 61 White 29. 53 5 " " Line 31. 91 Angle 38. 54 6 " " Plain 23. 92 Marked 37. 48 7 " " (colored) 5 seconds 27. 75 10 seconds 29. 15 8 " " (gray) 5 seconds 25. 42 10 " 32. 12 9 " " 1st exposure 12. 64 2d exposure 36. 45 10 " " Vertical line 34. 94 Hor. Line 34. 49 11 " " Full-faced 28. 10 Outline 41. 08 12 " " Figure 29. 26 Int. Lines 39. 32 13 " " Figure 34. 03 Vert. Lines 36. 40 14 " " Stationary 28. 88 Moved 37. 39 15 " " Gray 30. 90 Colored 37. 81 16 (See Table XVI. )

If we put these results into the form of propositions, we find:

1. That when the objects are similar surfaces, seen under similarconditions, the chances of the recurrence and persistence of theirimages are, on the whole, practically equal. 

2. That surfaces bounded by complicated outlines have an advantage inideation, other things equal, over surfaces bounded by simpleoutlines. 

3. That as between two objects of unequal area--color, form, and otherconditions being the same--the larger object has the advantage in theideational rivalry. 

4. That the image of a white object has a like advantage over theimage of a gray object. 

5. That broken or complex lines have in ideation an advantage overstraight or simple lines. 

6. That an object with varied content, other conditions remaining thesame, has an advantage over an object with homogeneous surface. 

7 and 8. That an increase of the time during which the attention isgiven to an object increases the chances for the recurrence of itsimage or idea. 

9. That of two objects to which attention is directed in succession, the object last seen has a distinct advantage in the course ofideation following close on the perception of the objects. 

10. That lines of similar appearance and equal length, one of which isvertical and the other horizontal, have, like surfaces of similarappearance and form and equal dimensions, practically equal chances ofrecurrence and survival in ideation, the slight difference in theirchances being in favor of the vertical line. 

11. That as between two figures of similar form and equal dimensions, one of which has a filled homogeneous content and the other is a mereoutline figure, the latter has a marked advantage in the course ofideation. 

12. That of two linear and symmetrical figures, of which one is anoutline figure with continuous boundary, and the other consists of thesame linear elements, similarly disposed, as the first, but has itslines disconnected so that it has no continuous boundary, the latterfigure has the advantage in ideation. 

13. That if, with material similar to that described in paragraph 12, the disconnected lines are arranged so as to be vertical andequidistant, the advantage in ideation still remains with thedisconnected lines, but is much reduced. 

14. That if one of two figures, of similar appearance and form and ofequal dimensions, is kept in motion while it is exposed to view, andthe other is left at rest, the image of the moving object is the morepersistent. 

15. That, under like conditions, colored objects are more persistentin ideation than gray objects. 

16. That lines and sharp angles, as compared with broad surfaces, havea strong directive force in the determination of the attention totheir images or ideas; that this directive force is strongest in thecase of very acute angles, the attention being carried forward in thedirection indicated by the apex of the angle; but that uncompletedlines, especially when two such lines are directed towards eachother, have a similar and not much inferior force in the control ofthe course of ideation. 

If we should seek now to generalize these experimental results, theywould take some such form as the following:

Abstraction made of all volitional aims and all ęsthetic or affectivebias, the tendency of an object to recur and persist in idea depends(within the limits imposed by the conditions of these experiments)upon the extent of its surface, the complexity of its form, thediversity of its contents, the length and recency of the time duringwhich it occupies the attention, the definiteness of the directionwhich it imparts to the attention (as in the case of angles andlines), its state of motion or of rest, and, finally, its brightnessand its color. 

These conditions, however, are for the most part but conditions whichdetermine the energy, diversity, complexity and definiteness of theactive processes involved in the bestowal of attention upon itsobject, and the experiments show that such active processes are asessential in ideation as in perception. The stability of an image, orinternal sensation, thus depends on the activity of its motoraccompaniments or conditions. And as the presence of an image to theexclusion of a rival, which but for the effect of these motoradvantages would have as strong a claim as itself to the occupation ofconsciousness (cf. Series I. , X. ), may be treated as a case ofinhibition, the greater the relative persistence of an image or ideathe greater we may say is the 'force' with which it inhibits itsrival. Exclusive possession of the field involves, to the extent towhich such possession is made good, actual exclusion of the rival; andexclusion is inhibition. Our generalization, accordingly, may take thefollowing form:--

The inhibitory effect of an idea, apart from volitional or emotionalbias, depends upon the energy, diversity, complexity and definitenessof the motor conditions of the idea. 

 * * * * *

CONTROL OF THE MEMORY IMAGE. 

BY CHARLES S. MOORE. 

Since Gallon's classic investigation in the field of mental imageryseveral similar investigations have been pursued in the samedirection, chiefly, however, for the purpose of discovering andclassifying types of imagination. 

Little has been done in the line of developing and studying theproblems of the memory image proper, and still less, in fact almostnothing, is to be found bearing on the control of the visual memoryimage. The general fact of this control has been presented, withgreater or less detail, based upon returns from questionaries. Gallonhimself, for example, having referred to instances in which thecontrol was lacking, goes on to say[1]: "Others have complete masteryover their mental images. They can call up the figure of a friend andmake it sit on a chair or stand up at will; they can make it turnround and attitudinize in any way, as by mounting it on a bicycle orcompelling it to perform gymnastic feats on a trapeze. They are ableto build up elaborate structures bit by bit in their mind's eye andadd, substract or alter at will and at leisure. "

 [1] Gallon, Francis: 'Inquiries into Human Faculty and its Development, ' London, 1883, p. 109. 

More recent writers classify the students, or other persons examined, according to these persons' own statements with regard to the natureand degree of control over the mental images which they considerthemselves to possess. An article by Bentley[2] is the only study of aspecific problem of the memory image. After a glance at the literaturewith reference to methods pursued in the investigation of problems ofmemory in general, Bentley outlines 'a static and genetic account' ofthe memory image in particular, and presents details of experiments'carried on for the special investigation of the visual memory imageand its fidelity to an original presentation. '

 [2] Bentley, I. M. : 'The Memory Image and its Qualitative Fidelity, ' _Am. Journ. Of Psychol. _, 1899, XI. , pp. 1-48. 

Of the many memory problems as yet unattacked, that of the control ofthe mental image is one of the most interesting. The visual imageobviously offers itself as the most accessible and the experimentsdescribed in this report were undertaken with the purpose of findingout something about the processes by which control of this image issecured and maintained. The report naturally has two aspects, onenumerical and the other subjective, presenting the statements of thesubjects as to their inner experiences. 

The term 'suppression' is used as a convenient one to cover theenforced disappearance of the designated image, whether it be directlyforced out of consciousness (a true suppression) or indirectly causedto disappear through neglect, or limitation of the attention to theother image which is to be retained. 

As this was an investigation of the control of memory images, thepresence of these images under conditions most favorable to theirvividness and distinctness was desirable. An immediate mental recallat the end of five seconds of visual stimulation, under favorablethough not unusual conditions of light, position and distance, seemedmost likely to secure this desideratum. Experimentation showed thatfive minutes was, on the whole, a suitable period in which to securethe information needed without developing a fatigue in the subjectwhich would vitiate the results. 

The experiments made in the visual field were restricted to visualmemory images which were called up by the subject during the fiveminutes succeeding a five seconds' presentation of one or two objects. The subject sat, with his eyes closed, about four feet from a wall orscreen, before which the object was placed. At a signal the eyes wereopened, and at a second signal five seconds later they were closed. Ifan after-image appeared the subject reported its disappearance, andthen called up the image of the object just presented, and reported asto its clearness, vividness, persistency and whatever phenomena arose;and when directed he sought to modify the image in various ways to bedescribed later. 

There were six subjects in experiments conducted during the winter of1900-1901, and six (five being new ones) in experiments of the fallof 1901. They were all good visualizers, though they differed in thereadiness with which they visualized respectively form or color. 

The experiments of the first few weeks were designed to establish thefact of control by the subjects over a single visual memory image asto its position, size, outline, color, movement and presence. Ingeneral it was established that a considerable degree of control inthese particulars existed in these subjects. 

Later, two objects were presented at a time, and were such smallarticles as a glass ball, a book, a silk purse, an eye-glass case, aniron hook, and so forth. Still later, colored squares, triangles, ordiscs were used exclusively. 

The investigation followed these lines: I. Movements of a singleimage; II. Changes of color of a single image; III. Movements of twoimages in the same and in different directions; IV. Suppression of oneof two images; V. Movements of a single image, the object having beenmoved during the exposure. 

I. MOVEMENTS OF A SINGLE IMAGE. 

The first table gives the time in seconds taken to move voluntarily asingle image (of a colored square or disc) to the right, left, up ordown, and in each case to restore it to its original position. Therewere thirty movements of each kind for each of the six subjects, making one hundred and eighty for each direction and also for eachreturn, the total of all movements being fourteen hundred and forty. The distance to which the subjects moved the images was not fixed, butwas in most cases about twelve inches. The time was taken with astop-watch, and includes the time between the word of command, 'right, ' etc. , of the director and the verbal report 'now' of thesubject. It includes, therefore, for each movement two reaction times. The subject reported 'now' the instant the color reached, or appearedat, the designated place, not waiting for the completion of the shapewhich usually followed. Two of the subjects (H. And K. ) took muchlonger than the other four, their combined average time being almostexactly four times the combined average time of the other four. 

TABLE I. 

 MOVEMENTS OF A SINGLE IMAGE. 

 30 Movements of Each Kind for Each Subject Average Time in Seconds. 

 To To Subjects Right Return Left Return Up Return Down Return Averages B. 1. 30 1. 07 1. 06 1. 11 1. 13 0. 58 0. 73 0. 46 0. 45 0. 55

 G. 1. 44 1. 15 0. 99 0. 82 1. 10 0. 92 0. 89 0. 76 0. 57 0. 78

 H. 7. 12 6. 42 5. 96 5. 85 6. 34 4. 51 4. 41 4. 36 4. 40 4. 42

 I. 1. 28 1. 34 1. 62 1. 47 1. 43 0. 67 0. 62 0. 86 0. 72 0. 72

 J. 1. 71 1. 42 1. 40 1. 14 1. 50 1. 34 1. 53 0. 77 0. 74 1. 09

 K. 4. 81 4. 64 3. 29 3. 28 4. 01 2. 40 2. 71 1. 91 1. 56 2. 14

 Averages 2. 95 2. 67 2. 39 2. 23 2. 59 1. 72 1. 82 1. 52 1. 41 1. 62

NUMERICAL. 

The general averages for the different movements show that movement tothe right was hardest, to the left next; while movement downward wasthe easiest. A marked exception is seen in I. , for whom the upwardmovement was the hardest and movement to the right was the easiest. J. Found movement to the left hardest. For the return movements, thegeneral averages show that the return from the left is the hardest, from the right next; while from below is the easiest. Here again I. Found the return from above the hardest and from below the nexthardest; while from the left was the easiest. 

Arranging the subjects in the order of the average time, taken for allthe movements, including the returns to the original position, we have

 H. 5. 35 average time out and back. K. 3. 07 " " " " " J. 1. 29 " " " " " I. 1. 07 " " " " " G. . 94 " " " " " B. . 84 " " " " "

SUBJECTIVE. 

All the six subjects whose time records appear in Table I. And alsofour others whose time was not recorded reported eye movements, or atendency to eye movement. A. And K. Reported that when the image wasdim there was accommodation as for long vision and when the image wasvivid there was accommodation as for near vision. B. Ideated the newposition and the eye movement occurred automatically. G. Reported acontraction of the scalp muscles and a tendency to cast the eyes upand locate the image at the back of the head inside; this was aninveterate habit. He reported also accommodation for the differentdistances of the image and an after-feeling of strain in the head. H. Reported a strong tendency in the eyes to return to the center, _i. E. _, the original position, and to carry the image back there. Allthe subjects frequently reported a sense of relief in the eye muscleswhen the command to return the image to the center was given--also, atension in the forehead in the upward movement which was accentuated(with H. ) when there was headache. J. Reported, 'always eye strain, 'and noticed that the eyes usually turned as far as the new position, but sometimes stopped short of it. K. Reported first an eye movement, then an ideation of the image in the new position. E. And H. Turnedthe head to right and left for movements of the image in thosedirections. A. , B. , E. And F. Believed that they could inhibit the eyemovement. Subjects were at times unconscious of eye movements. H. Articulated the names of the colors of the image and found that itaided the movement of the image to say to himself, for example: "Don'tyou see that blue square there?"

All but J. Reported a loss in vividness and also, though to a lessdegree, in distinctness whenever the image was moved away from thecenter. J. Found no difference. H. Reported that details of the objectwhich were reproduced in the image when at the center were notdiscernible in the image in other positions, also that at the left theimage was more vivid than at the right. B. 's memory image of a watch, three minutes after it was called up, was still so clear that he readfrom it the time. E. , who was an experienced photographer, had nodifficulty in recalling outline, light and shade, but had difficultyin reproducing color. I. Frequently lost the form in making therequired improvements. 

Under manipulation the memory image usually retained its distinctnessand vividness with no loss or with but slight loss when in itsoriginal position, to the end of the five minutes of the experiment. The image, also, seldom disappeared except for the momentarydisappearances in passing from one position to another, which arereferred to later. Under passive observation of the memory imagedisappearances, though of short duration, were frequent and there wasa noticeable fading away of color and loss of outline. 

The memory image almost without exception, when first recalled, waslocated in the direction and at the distance of the object presented. 

In moving from the center to right and left the image remained in thesame plane with a few exceptions; in moving up and down it moved on anarc whose center was at the eye. This was especially true of thedownward motion, which was almost always to a greater distance thanany of the other motions. 

C. , D. , F. And H. Felt the need of a support for the image in anyexcept the central position. This was true especially of the positionabove the center, but was entirely overcome by practice by C. , F. AndH. , and partially by D. In movements where time was to be recorded, the distance was from six to eighteen inches, but the image could becarried by all the eleven subjects to any part of the room or beyondthe room. Usually the method followed was to fix the attention on thesuggested position and then the image appeared there, sometimescomplete at the outset, but usually in part at first, then developinginstantly to completion. When the subject was requested to trace theimage _in transitu_, this could usually be accomplished, but the timewas much longer. Frequently, in such a case, the image was lost duringthe last third or fifth of its journey. J. "felt conscious of asomething that went in the suggested direction but did not developdetails out of this material; had to await development of the image atthe new locality. " "At times _forced_ this development out of thevague something that seemed to go over. " G. Had 'no feeling oftransition in space. ' K. Did not perceive the image _in transitu_. I. Perceived the image _in transitu_ when the movement was away from thecenter but when the image was to return to the center its passage wastoo quick to be followed; 'it came out at the center. '

J. Noticed that in moving from the center the image took a curved pathtowards himself, and that the position _to_ which the image movedalways seemed further away than the position _from_ which it came, butthe new position seemed to be readjusted when the next movementoccurred. 

The return to the center seemed easier to all the subjects except G. , who was conscious of no difference between the movements with respectto ease. Several described the return to the center as like the returnof a small ball snapped back by a stretched elastic cord. 

With D. A suggestion of weight in the perception of the object was ahindrance to moving its memory image. Also the image of a short pieceof brass tubing persisted in rolling off the table and along the floorand could not be held stationary. Other objects rotated rapidly, andmuch effort was needed to 'slow down' the rotation and to bring theobjects to rest and keep them at rest. 

II. CHANGES OF COLOR OF A SINGLE IMAGE. 

Tables II. And III. Show the results of experiments in changing thecolor of a single image. This was usually a square, sometimes a disc. The time of optical perception was five seconds. After thedisappearance of after-images, if there were any, eighteen totwenty-four changes were made in the color of the memory image, occupying from four and a half to six minutes. 

The colors were saturated blue, green, yellow and red, and each onewas changed into each of the other colors and then restored. The orderof change was varied to avoid uniformity of succession. The fourcolors were shown to the subjects each day before the experimentsbegan, to establish a standard. The time was taken with a stop-watch, and includes the time between the director's word of command, 'green, 'etc. , and the subject's report, 'now, ' or 'green, ' etc. It includes, therefore, two reaction times. The subject reported 'now' the instanthe secured the desired color, not waiting for the completion of theshape that usually followed. 

TABLE II. 

 CHANGES OF COLOR. SINGLE IMAGE. 72 CHANGES OF EACH COLOR. 

 [Label 1: Subject. ] [Label 2: To Green. ] [Label 3: Return to Blue. ] [Label 4: To Yellow. ] [Label 5: Return to Blue. ] [Label 6: To Red. ] [Label 7: Return to Blue. ] [Label 8: To Blue. ] [Label 9: Return to Green. ] [Label 10: To Yellow. ] [Label 11: Return to Green. ] [Label 12: To Red] [Label 13: Return to Green. ]

 From Blue. From Green. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

 B. 1. 72 0. 50 1. 66 0. 38 1. 81 0. 50 1. 23 0. 56 1. 10 0. 65 1. 33 0. 56 G. 1. 15 0. 60 1. 10 0. 79 0. 89 0. 65 1. 75 0. 87 1. 04 0. 75 1. 35 0. 71 H. 4. 67 4. 25 4. 87 4. 06 4. 81 3. 83 5. 27 4. 50 5. 81 4. 89 5. 37 4. 94 I. 2. 27 1. 25 1. 77 1. 19 1. 83 1. 25 2. 15 0. 93 1. 71 1. 04 1. 92 1. 15 J. 1. 38 0. 81 1. 29 0. 94 1. 29 0. 95 1. 65 1. 08 1. 15 0. 77 1. 60 0. 81 K. 2. 35 1. 71 1. 96 1. 66 2. 10 1. 19 2. 25 1. 25 2. 17 1. 73 2. 44 1. 27

 Av. 2. 26 1. 52 2. 11 1. 50 2. 15 1. 39 2. 41 1. 53 2. 15 1. 65 2. 34 1. 57

 [Label 1: Subject. ] [Label 2: To Blue. ] [Label 3: Return to Yellow. ] [Label 4: To Green. ] [Label 5: Return to Yellow. ] [Label 6: To Red. ] [Label 7: Return to Yellow. ] [Label 8: To Blue. ] [Label 9: Return to Red. ] [Label 10: To Green. ] [Label 11: Return to Red. ] [Label 12: To Yellow. ] [Label 13: Return to Red. ]

 From Yellow. From Red. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

 B. 1. 79 1. 06 1. 35 0. 87 1. 89 1. 10 1. 54 0. 58 1. 71 0. 62 1. 31 0. 71 G. 1. 50 1. 10 1. 48 0. 87 1. 31 0. 88 1. 33 0. 92 1. 35 0. 91 0. 77 0. 58 H. 5. 02 4. 54 5. 73 3. 91 6. 15 4. 17 6. 35 3. 91 5. 89 4. 69 5. 54 4. 37 I. 2. 29 1. 31 2. 54 1. 19 2. 29 1. 27 2. 85 1. 10 2. 50 1. 21 1. 65 1. 31 J. 1. 35 0. 98 1. 35 0. 65 1. 27 0. 88 1. 42 1. 04 1. 31 1. 02 1. 25 0. 85 K. 3. 02 1. 52 3. 21 2. 04 2. 23 1. 79 2. 54 1. 56 2. 66 1. 60 2. 88 1. 81

 Av. 2. 49 1. 76 2. 61 1. 59 2. 52 1. 68 2. 67 1. 51 2. 57 1. 68 2. 23 1. 62

TABLE III. 

 CHANGES TO THE FOUR COLORS. 

 Average time in seconds. 72 changes from and 72 changes to each color. 

 [Label 1: To Blue. ] [Label 2: Return from Blue. ] [Label 3: To Green. ] [Label 4: Return from Green. ] [Label 5: To Yellow. ] [Label 6: Return from Yellow. ] [Label 7: To Red. ] [Label 8: Return from Red. ]

 [1] [2] [3] [4] [5] [6] [7] [8] From blue, 2. 26 1. 52 2. 11 1. 50 2. 12 1. 39 " green, 2. 38 1. 53 2. 16 1. 64 2. 33 1. 57 " yellow, 2. 49 1. 75 2. 61 1. 59 2. 52 1. 68 " red, 2. 67 1. 52 2. 58 1. 68 2. 27 1. 62

 Average, 2. 52 1. 60 2. 48 1. 59 2. 17 1. 58 2. 33 1. 55

 _Changes from_ a presented color. _Returns to_ a presented color. 216 movements. 216 movements. 

 _From_ presented yellow, 2. 52 _To_ presented yellow, 1. 67 " " red, 2. 49 " " red, 1. 61 " " green, 2. 29 " " green, 1. 58 " " blue, 2. 16 " " blue, 1. 47

 Average, 2. 37 Average, 1. 58

 _Changes to_ a color _from_ _Returns from_ a color _to_ a presented color. A presented color. 216 movements. 216 movements. 

 _To_ blue, 2. 52 _From_ blue, 1. 60 " green, 2. 48 " green, 1. 59 " red, 2. 33 " yellow, 1. 58 " yellow, 2. 17 " red, 1. 55

 Average, 2. 37 Average, 1. 58

The six subjects fall into two groups--three, H. , I. , and K. , takinglonger than the other three. As in the previous experiment H. Wasmarkedly longer than any of the others. 

There were seventeen hundred and twenty-eight changes in all, including returns to the original color. There were two hundred andsixteen changes from each of the four colors as presented, to each ofthe other three and, of course, the same number of returns to thepresented color. 

The change to blue from the other presented colors was the mostdifficult and the change to yellow was the easiest. 

The averages (216 exp. Each) are, Sec. To blue, 2. 55 " green, 2. 48 " red, 2. 33 " yellow, 2. 17

The returns to the presented colors did not differ greatly from eachother, the averages (216 exp. Each) being:

 Sec. From blue, 1. 603 " green, 1. 597 " yellow, 1. 589 " red, 1. 549

From red appears to be the easiest change, and from blue the hardest. 

The getting away from a presented blue was the easiest and from apresented yellow the most difficult, as seen by these averages (216exp. Each):

 Sec. From yellow, 2. 54 " red, 2. 49 " green, 2. 29 " blue, 2. 16

The returns to the presented colors show that it was hardest to getback to the presented yellow, easiest to get back to the presentedblue, the averages (216 exp. Each), being:

 Sec. To yellow, 1. 67 " red, 1. 61 " green, 1. 58 " blue, 1. 47

The facts as to blue and yellow shown by these four tables of averagesmay be expressed also in this way:

If a blue square was shown, it was easier to change the blue memoryimage into the other colors, and also easier to get back the bluememory image after such changes, than if any other of the three colorswas presented. 

If another color than blue was shown it was harder to change thememory image of that color to blue than to any of the other colors, and also harder to get back to the memory image of that color fromblue than from any of the other three colors. 

If a yellow square was shown, it was harder to change the yellowmemory image into the other colors, and also harder to get back theyellow memory image after such changes than if any other of the threecolors was presented. 

If another color than yellow was shown, it was easier to change thememory image of that color to yellow than to any of the three othercolors, and also easier to get back to the memory image of that colorfrom the yellow than from any of the other three colors except red. 

If we combine _all_ the changes into a color (both changes fromanother presented color and returns to this color previouslypresented) we find that changes to green are hardest, to yelloweasiest. The averages (for 432 exp. Each) are, Sec. To green, 2. 03 " blue, 1. 99 " red, 1. 97 " yellow, 1. 92

The changes away from a color (both from this color previouslypresented and from this color to the other previously presentedcolors) show that it was hardest to get away from yellow, easiest toget away from blue, the averages (for 432 exp. Each) being:

 Sec. From yellow, 2. 06 " red, 2. 02 " green, 1. 94 " blue, 1. 88

As for the subjects, all six found yellow the easiest to change into, one finding red equally easy. 

SUBJECTIVE. 

For seven of the subjects, mental repetition of the name of the color(usually accompanied by articulatory movements) tended to bring up thecolor, and one other subject occasionally used this method of bringingabout a change that was difficult. With D. The color did not come atrepetition of the name. G. Was assisted by auditory recall of thename. Nine subjects reported a feeling of strain, usually in the eyesas of focusing, occurring especially when there seemed a difficulty inproducing the desired change. The tension attended almost exclusivelychanges of the presented color, not restorations of that color. For D. This strain was considerable, for G. There was also an after-feelingof strain in the head. For G. The image was clearest when the feelingof strain was least, and J. Secured the promptest and clearest resultswhen he could most nearly rid himself of anxiety as to the result. K. In one instance (a change from green to yellow) became conscious ofthe setting of his jaws and motions of feet and body in aid of hisattempt. H. Frequently had the feeling of physical fatigue. 

In most cases the restoration of the presented color was as a completesquare, triangle, etc. In changes from the presented color the newcolor appeared at a corner, or edge, or as a patch at the center. WithE. The "color flashed over the whole field and then had to berestricted to the figure. " B. "held the outline, emptied of the oldcolor, while it was filled in with the new. " D. "had a clear outline, and the new color came in small blotches inside, and effort spreadthem out to cover the whole figure. " For I. The "new color camesliding in from the right side over the old, which, however, disappeared as if it were moving out of focus. " With A. The new colorusually came from either the lower left-hand or the upper right-handcorner. F. Kept a clear outline and the new color came in from theright. 

When E. Found it difficult to create at the center the desired color, he thought of some object (garment, grass, sky, etc. ) of that colorand then transferred it to fill in the outline preserved at thecenter. B. Moved the colored figure aside and in its place put one ofthe desired color, moved the new figure up to the old and theresuperposed it. With G. The new colors seemed of new material and therewas felt to be an accumulation about the center, of oldcolor-material. Then he located the square outside of this imaginarydebris and began again. H. Found that the colors of his ownexperiments, in which he used color squares framed in black, came tohis mind at the names of the desired colors, and the association soongave him the figure also. I. Located the new colors around thepresented one, first all at the right; then green at the left, red atthe right, yellow above, when presented blue was at the center; thenyellow and green were at the upper left-hand corner, while red camefrom behind. The new color 'slid in over the old. ' It was found easierto secure the desired color when its position was known beforehand. J. Also used a similar device. He 'turned towards the places and broughtout the required color and filled the central outline with it. ' Hetried to break up this scheme and got red without going after it butfound himself 'at a loss to find the colors. ' Later he succeeded sothat the required color simply appeared in the outline of the oldcolor at the center. K. Turned his eyes to corners of the centraloutline, then to the center, and found that this aided in developingthe desired color from the corners inward. When difficulty arose, heexperienced muscular tension in body and legs and jaws. 

Five of the subjects considered the change from a presented color toblue the hardest and one found the change to red hardest. Green wasplaced second in difficulty by one, and blue second by the one whofound red the hardest. Three reported the change to yellow the easiestand two the change to red. 

The change from red to yellow caused 'an unpleasant sensation' in C. And the new figure 'had a maroon halo. '

A. In returning from green or blue to yellow passed through a gray;so, once, in changing from yellow to green, and once, green to red. With A. Blue retinal clouds, which often came, aided changes to blueand hindered at times changes to other colors. B. Had a fusion ofyellow and red in changing from yellow to red. G. Had a tendency toleave uncolored the lower left-hand corner and it 'was wood-colored';G. Had a gray image as the result of fusion of retinal clouds with redmemory image. With H. Blue always came in as robin's-egg blue, whichthen had to be changed to the standard blue. In one instant the greenmemory image seemed to shift into a purple and change to a positiveretinal image which interfered with changes to other colors. J. Foundwhistling and humming an aid in relaxing an unnatural state of tensionwhich would hinder the best results. To increase the vividness of theimage he would recall the black background on which the coloredsquares had hung. In one experiment K. Became 'desperately tired ofyellow, ' which was the presented color, so that his 'mind was ready tojump to any color rather than yellow. ' The returns to yellow were, inthis experiment, slower than the changes from yellow. 

The images sometimes changed sizes, being at times smaller, butusually larger than the object. In one experiment of C. The image wasfour times the size of the object, which was a green square with sidesof one inch. 

III. MOVEMENTS OF TWO IMAGES IN THE SAME AND IN DIFFERENT DIRECTIONS. 

Table IV. Gives the results of experiments in the movements of twoimages, the objects presented being colored squares or discs. Time ofperception was five seconds. After the disappearance of after-images, if there were any, eighteen to twenty-four movements with returns tooriginal positions were made, occupying five or six minutes. Thecolors were saturated blue, green, yellow and red. Four of themovements were such as separated the two images, and in four the twomoved uniformly. The first four movements were right and left, leftand right, up and down, down and up; the left-hand object followed thefirst direction indicated. The right-and-left movements involved thecrossing of the images. The last four were _both_ to right, to left, up, down. The time was taken with a stop-watch and includes the timebetween the director's word of command and the subject's report, 'now. ' It includes, therefore, two reaction times. The subjectreported the instant the colors reached, or appeared at, the suggestedpositions. 

It is to be noticed that H. Was very much slower than any of theothers in making the movements, both out and back; and that K. , whilealso slower (though much less so than H. ) in making the movementsoutward, was no slower in making the return movements. 

TABLE IV. 

 MOVEMENTS OF TWO IMAGES. 

 Twenty movements of each kind for each subject. Averages in seconds. 

 In Opposite Directions. 

 Subj. L. -R. Ret. R. -L. Ret. U. -D. Ret. D. -U. Ret. 

 B. 1. 82 2. 90 2. 10 2. 27 0. 86 0. 87 0. 73 0. 86

 G. 3. 02 2. 86 2. 68 2. 63 1. 98 2. 25 1. 63 2. 01

 H. 9. 18 10. 30 7. 50 7. 15 5. 16 6. 90 5. 36 5. 21

 I. 4. 17 3. 52 3. 40 3. 37 1. 26 1. 47 1. 23 1. 31

 J. 2. 17 2. 90 2. 87 2. 27 1. 05 1. 63 1. 02 1. 13

 K. 5. 51 6. 43 5. 16 4. 81 1. 43 1. 48 1. 20 1. 23

 Ave. 4. 32 4. 82 3. 82 3. 75 1. 96 2. 43 1. 87 1. 96

 Average of all movements involving separation (480), 4. 18. Returns, 2. 06. 

 In Same Direction. 

 Subj. R. Ret. L. Ret. U. Ret. D. Ret. 

 B. 1. 31 1. 22 1. 30 1. 11 0. 72 0. 67 0. 72 0. 85

 G. 2. 66 2. 35 3. 01 2. 53 2. 00 1. 86 2. 22 1. 86

 H. 8. 45 7. 91 5. 66 7. 66 6. 53 5. 95 5. 96 6. 11

 I. 2. 57 2. 27 2. 13 2. 05 0. 97 1. 26 1. 00 1. 13

 J. 1. 11 1. 16 1. 08 11. 5 0. 68 0. 90 0. 73 0. 71

 K. 3. 97 3. 91 3. 60 4. 07 1. 35 1. 50 1. 75 1. 71

 Ave. 3. 33 3. 14 2. 79 3. 10 2. 04 2. 02 2. 04 2. 06

 Average of all movements together (480), 3. 09. Returns, 2. 04. 

NUMERICAL. 

There were nineteen hundred and twenty movements in all, including thereturns to the original positions. 

In the order of difficulty as shown by the time taken, the movementsstand as follows, the numbers being the averages in seconds for onehundred and twenty movements of each kind:

 1. Right and left (_i. E. _, crossing), 4. 82 sec. 2. Left and right, 4. 32 " 3. Up and down, 3. 82 " 4. Down and up, 3. 75 " 5. Both right, 3. 33 " 6. Both left, 3. 14 " 7. Both down, 3. 10 " 8. Both up, 3. 04 "

SUBJECTIVE. 

In the experiments in which the time was recorded, there was nodisappearance of either image except where movements were madesuccessively. In these cases frequently the image which was awaitingits turn vanished until the first image was placed, a time varyingfrom a quarter of a second to three or four seconds. Occasionally theimage already placed would vanish, while the other was _en route_; thesubject's attention in both these cases being centered exclusively onthe image he desired to move. This was especially the case when thedistances to which the images were moved were great, as to the ends ofthe room or to ceiling and floor. In other experiments, where, afterthe movements took place, the images were held for a short time, therewere disappearances of one image or the other ranging from one quarterof a second to fifteen seconds, most of the absences, however, beingunder five seconds. The absences were more numerous in the latter halfof the five minutes covered by the experiment. Occasionally a noise inthe adjoining room or in the street made the images disappear. 

The greater ease of vertical as compared with horizontal movementsrecalls an observation of Ladd, [3] in which the idioretinal light waswilled into the shape of a cross. Ladd says: "The vertical bar of thecross seems much easier to produce and to hold steadily in the field. "This present observation is also in accord with that described abovein the case of movements of a single image. 

 [3] Ladd, G. T. : 'Direct Control of the Retinal Field, ' PSYCH. REV. , 1894, L, pp. 351-355. 

On several occasions G. Reported that the crossing movement was theeasiest, and that the return to the original places was not easierthan the other movements. In one experiment he reported the field atthe center cloudy, so that it was a relief to get away from it. G. 'stime records on these occasions did not support his feeling withregard to the return to the original places, but they show that thecrossing movements were, in two or three instances, quicker than the'left-and-right' movement, and the impression of promptness thus madepersisted to the end of the experiment. The four movements in whichboth images moved uniformly were easier than the four in whichmovements in different directions were involved. 

All the subjects were frequently conscious of eye movements, and morefrequently conscious of a tendency to eye movement, which was, however, inhibited. That the strain in the eyes was practicallyconstant during all the movements away from the original places, seemsevident from the unanimous reports of a sense of relaxing and reliefin the eyes, attending the movement of returning to the originalplaces. The distance to which the images were moved was a powerfulfactor in producing this sense of strain. When the two images weremoved and held but a few inches apart there was no sense of strain andno conscious alternation of attention. Practice increased greatly thedistance at which the images could be held apart without consciousalternation of attention, but the strain of holding them apart and ofinhibiting eye movement increased with the distance. 

In the movements for which the time was recorded the distances varied, according to the subject, from six to eighteen inches, and varied attimes with each subject. In the experiments without time record, A. , B. , C. , E. , F. And H. Reported that they were able to move the imagesapart to ceiling and to floor, or to the opposite ends of the room, and to hold them there both in consciousness at the same time withouteither alternation of attention or eye movement, a tendency to whichwas felt but was inhibited. I. Held them two feet apart withoutfluctuation of attention. A. Reported: "I tend to turn my body to leftor to right when I move the images in either of these directions. " C. , H. And I. Said: "The eyes diverge when one image moves slowly to theright and one to the left. " D. Found a slight movement of the eyeswhich could be detected by the fingers placed lightly on the lids, when the attention was alternating between the images. K. Hadconvergence and divergence of the eyes for crossing and separationrespectively and he was accustomed to run his eye over the outline ofthe image. Strain in the scalp muscles was reported by A. , B. , E. , F. And G. The up-and-down movements were universally characterized by afeeling as if one eye tended to move up and the other down. C. Unconsciously inclined his head to the left in such movements as if tomake the line of the two eyes parallel with the direction of themovement. 

E. , when holding the images two feet apart, had a strong feeling ofdifference of accommodation when alternating in observation and sojudged the two to be in different planes. 

When the movement seemed difficult the strain was greater, and when animage became dim the effort to restore its brightness or itsdistinctness of outline was accompanied by a feeling of bringing itnearer by accommodation and near focusing. J. Found that the twoimages approached each other when he attempted to secure greatervividness. An analogous instance is that of A. G. C. , a subject quotedin 'Mental Imagery of Students, ' by French. [4] In calling up the imageof a die this subject held up his hand as if it held the die. Whenthere was no sense of strain the hand was fourteen inches from hisface, but when effort was made to image all the sides of the die atonce he unconsciously moved his hand to within four inches of hiseyes. French says in this connection: "Situation depends on theattention involved and the inference is near that this phenomenon maybe connected with feelings of convergence and accommodation which sooften accompany concentrated visual attention. "

 [4] French, F. C. : PSYCH. REVIEW, 1902, IX. , p. 40. 

The movements were assisted by mentally saying, 'this image is here, that image is there, ' in the case of D. , G. , H. , I. And K. ; or, attimes, by articulating the names of the image, or of the color whenthe image was of a colored object. I. Found it easy to hold outlines, but in order to retain colors in the movements of separation, he hadto speak the names continually. H. Also repeated the namescontinually, as, for example, 'violet here, orange there. '

A. Represented the line of vision as going to each of the two images, which seemed connected by a line, thus making a triangle, and thenpictured himself as standing off and seeing himself looking at theimages. When the two objects were solid and the images were to becrossed, B. Carried one image above or below the other, but when theobjects were colored surfaces he conceived them as pure colors so thatthere was no sense of impenetrability to interfere with their crossingand they glided by each other. In the up-and-down movements he movedone at a time. C. And D. Had to construct some support for the images. In most of the experiments H. First moved the images to a greaterdistance away, somewhat higher up and a little farther apart. In thisnew position the images appeared smaller and the suggested movementswere made more easily. Sometimes in crossing two colored images heobserved a partial mixture of the colors. J. Found that a sharpmovement of the head in the required direction aided materially inmoving the images, and when the objects were colored surfaces fastenedto the same card he found it necessary either to conceive the card asof rubber or to picture it as cut in two before he could make themovements of the images. 

With A. , B. , C. And D. There were instances of unwilled movements ofthe images, in the experiments where the movements were not timed. These were much more frequent with D. Than with the others, and tocheck them required prolonged effort. The more common movements ofthis sort were rotation of the image, change of its position, separation of its parts (if detachable in the object) and change ofshape. E. Had a return of the two images of a preceding experimentwhich persisted in staying a few seconds and which were as vivid asthe two legitimate occupants of the mental field. 

The images were duplicated five times on different days with A. , andonce each with C. , F. And K. 

A. 's cases were these. The 'wraith' of a small box whose image was outat the right, appeared above the other image off at the left and itwas turned with a corner to the front. Again, at the central positioneach image was duplicated, the true pair being of full size, brightand distinct, the false pair small, dim and on a more distant plane, _i. E. _, behind the others. One of the extra images persisted againstall effort to banish it, for fifty-five seconds. Again, when twelveinches apart each image was similarly duplicated. In the fourthinstance the images were at the center of the field. In the fifth, theright image, eight inches from the center, was duplicated, the extraimage being still farther away and above. This second image was verydark, dim and vague in outline, and came and went slowly. The rightimage of C. , when seven feet from the center, had a dim double aboveit. F. Had moved the right-hand image (a violet disc) close to theleft when a blue disc also appeared above it. Though repeating theword 'violet' he had imaged the violet disc as blue. K. Was holdingthe two images a foot and a half apart when an extra pair appeared atthe center. Both pairs persisted for sixty seconds and then the outerpair vanished, and the inner, the false pair, grew brighter. 

As was said in the case of a single image, so with double images, themotion could be traced and often was traced when the movements wereaway from the original positions, but on the return to the originalpositions the images were not usually seen _in transitu_. For ten ofthe subjects, the image moved downward uniformly on an arc whosecenter was at the eye; and often the right and left movements werelikewise on an arc. With E. The ends of the arc for motion right andleft were higher also. H. , I. And J. Reported that all the movementswere in the same plane. The upward movement was always to a lessdistance and the downward movement to a greater distance than thehorizontal movements. 

In most cases the images were the size of the percepts, in a number ofcases smaller, and in a few cases larger. This was determined bycomparison between the image and the percept immediately on openingthe eyes and seeing the object at the end of the five minutes occupiedby the experiment. A similar mode of comparison showed that, in abouthalf of the experiments, the images were at the end of five minutesapproximately equal to the percept in clearness and distinctness ofoutline. A comparison of these results with those obtained in a seriesof experiments involving passive observation of the image seems toindicate that active manipulation of the image tends to maintain thequalitative fidelity of the image when at its original position. During the progress of the experiments the reports were almostunanimous and constant that at its original position the image wasvivid and distinct, but lost in both respects when away from thatposition, the loss being greater the greater the distance to which itwas moved. Frequently there was fluctuation, --a loss of vividness andthen a restoration, --which A. Frequently found to be rhythmical, whilein general it was evident that an increase of effort or of attentionwas successful in restoring lost vividness and distinctness. 

D. , after three minutes, read the time in the image of a watch. Insuperposing green on yellow, in two instances, the yellow shonethrough, making a mixed color, and again, in moving a green disc and ayellow disc, the green became suffused with yellow, so that the twodiscs were one yellow and the other greenish-yellow. For C. , similarity in the two objects presented tended to make both imagesless vivid and distinct and to render more difficult their retentionand manipulation. When one of the two objects partially overlapped theother it was difficult to separate the two images, and the area ofcontact was very vague in the image of the under one, and when thescrutiny reached that portion the other image returned to its originaloverlapping position. 

IV. SUPPRESSION OF ONE OF TWO IMAGES. 

The next tables (V. And VI. ) give the results of experiments insuppressing one of two images, the objects presented being saturatedcolor squares, discs, triangles, etc. , placed side by side, one abovethe other, or a smaller one superposed on a larger. The time ofperception was five seconds. After the disappearance of after-images, if there were any, the subject was directed to suppress one of the twomemory images, the one to be suppressed being indicated by thedirector. The subject reported as soon as the indicated imagedisappeared, and reported any return of the suppressed image and itslater disappearance in consequence of his efforts. Also he reportedany disappearance and reappearance of the retained image. Five minuteswas the limit of the time for the experiments with a few exceptions. The times were recorded, and those given for the first suppressioninclude the time between the director's command and the subject'sreport 'now' or 'gone, ' and include, therefore, two reaction times. The later suppressions include but one reaction time. 

TABLE V. 

 SUMMARY OF ALL SUPPRESSIONS. AVERAGE TIME IN SECONDS. 

 [Label 1: Image Suppressed] [Label 2: No of Exper. ] [Label 3: Time of First Supp. ] [Label 4: Time of Ab. Of Supp. Im. ] [Label 5: No. Of Later Supp. ] [Label 6: Time of Later Supp. ] [Label 7: No. Of Ab. Of Supp. Im. ] [Label 8: Time of Ab. Of Supp. Im. ] [Label 9: Time of All Supp. ] [Label 10: Time of All Absence of Supp. Im. ]

 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] Right. 46 11. 59 82. 39 221 8. 43 216 35. 74 8. 94 43. 93 Left. 43 11. 89 79. 34 175 7. 79 173 44. 86 8. 60 51. 26 Upper. 22 11. 67 49. 77 150 6. 26 147 29. 75 6. 95 32. 35 Lower. 17 14. 23 64 71 7. 88 70 46. 68 9. 11 50. 04 Central. 42 18. 24 96. 93 357 3. 90 352 18. 13 5. 41 26. 54 Marginal. 20 14. 25 181. 57 24 8. 93 24 78. 08 11. 35 125. 12 Sundry. 7 8. 71 127. 21 19 13. 34 19 47. 27 12. 09 68. 78 Averages. 13. 48 91. 25 6. 46 32. 14 7. 60 41. 86

TABLE VI

 SUPPRESSIONS GROUPED BY SUBJECTS. AVERAGE TIME IN SECONDS. 

 [Label 1: Subject] [Label 2: No. Of Exp. ] [Label 3: Time of First Supp. ] [Label 4: Time of Ab. Of Supp. Im. ] [Label 5: No. Of Later Supp. ] [Label 6: Time of Later Supp. ] [Label 7: No. Of Ab. Of Supp. Im. ] [Label 8: Time of Ab. Of Supp. Im. ] [Label 9: Time of All Supp. ] [Label 10: Time of All Ab. Of Supp. Im. ]

 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] A. 11 28. 32 11. 29 117 14. 90 114 10. 35 16. 05 10. 44 B. 29 5. 79 270. 44 5 0. 25 5 138. 80 4. 98 251. 08 C. 18 7. 88 43. 08 64 3. 94 63 67. 49 4. 81 62. 07 D. 14 23. 28 190. 07 6 31. 66 5 204. 60 25. 80 193. 89 F. 10 12. 67 86. 07 230 1. 95 230 67. 92 2. 40 10. 09 G. 21 21. 88 20. 39 190 9. 97 184 19. 37 11. 15 19. 47 H. 21 15. 27 73. 27 47 10. 30 47 84. 48 11. 84 81. 02 I. 26 9. 77 53. 83 96 5. 06 94 61. 34 6. 06 59. 72 J. 26 3. 59 32. 18 209 1. 40 208 31. 69 1. 64 31. 75 K. 21 21. 63 71. 90 53 14. 75 51 70. 04 16. 70 31. 83 Averages. 13. 48 91. 25 6. 46 32. 14 7. 60 41. 86

There were ten subjects in most of the experiments, and the markeddifferences in the individual records which were evident in theprevious experiments did not exist here except in the case of A. , forwhom alone the time required to obtain the suppression exceeded thetime of absence of the suppressed image. 

In several experiments the subjects were unable to suppress theindicated image, which in five cases was the image at the center of adisc and in two cases the outer portion of the disc. Further, fivefailures were by one subject, D. , and one each by A. And F. Thestatistical report here given includes only the results of thesuccessful experiments. Forty-four of the one hundred and ninety-sevenwere completely successful, as the suppressed image did not returnthroughout the entire period. The following table shows the groupingof the experiments according to the recurrence of the suppressedimage:

 Returned 0 times, 44 " 1 " 26 " 2 " 18 " 3 " 25 " 4 " 16 " 5 " 16 " 6 to 10 " 28 " more than 10 times, 24 Total, 197

Seventy-three and three fifths per cent. Of all the experiments havefive or fewer returns of the suppressed images. 

The subjects suppressed the image as soon as possible after eachreturn, the average time taken to accomplish these later suppressionsbeing 6. 46 sec. , while the average time of absence of the suppressedimage was 32. 14 sec. 

Including the first efforts and the first absences of the suppressedimage, the average time required to suppress the image was 7. 60 sec. , and the average time of absence of the suppressed image was 41. 86 sec. 

Arranging the subjects according to the average time they required toaccomplish a suppression, we have the following order. J. And F. Hadmore recurrences of the suppressed image than any of the othersubjects. 

 J. 1. 64 sec. F. 2. 40 " C. 4. 80 " B. 4. 98 " I. 6. 06 " G. 11. 15 " H. 11. 84 " A. 16. 05 " K. 16. 70 " D. 25. 80 "

Arranging them by the average absence of the suppressed image we havethis order:

 B. 251. 08 sec D. 193. 89 " H. 81. 02 " C. 62. 07 " I. 59. 72 " K. 31. 83 " J. 31. 75 " G. 19. 47 " A. 10. 44 " F. 10. 09 "

It is to be remarked, however, that the ability to keep the suppressedimage out of the field increased with practice and that A. And F. Hadless than half the number of experiments that the rest had. D. , whohad but two thirds as many as most of the other subjects and thereforehad less practice in suppressing the image, stands yet second inrespect to this ability. 

If we compare the subjects with regard to _first_ efforts and _first_absences only, we obtain the following orders:

 According to Ave. Time req. According to Ave. Absence for first Suppression. Of Image after first Suppression. J. 3. 59 sec. B. 270. 44 sec. B. 5. 79 " D. 190. 07 " C. 7. 88 " F. 86. 07 " I. 9. 77 " H. 73. 27 " F. 12. 67 " K. 71. 90 " H. 15. 27 " I. 53. 83 " K. 21. 63 " C. 43. 08 " G. 21. 88 " J. 32. 18 " D. 23. 28 " G. 20. 39 " A. 28. 32 " A. 11. 29 "

Arranging the groups of images suppressed according to the averagetimes of all suppressions and absences we have these orders:

 Suppression. Absences. Central Images, 5. 41 Marginal Images, 125. 12 Upper " 6. 95 Sundry " 68. 78 Left " 8. 60 Left " 51. 26 Right " 8. 94 Lower " 50. 04 Lower " 9. 11 Right " 43. 93 Marginal " 11. 35 Upper " 32. 35 Sundry " 12. 09 Central " 26. 54

SUBJECTIVE. 

Most of the subjects imaginatively placed the image to be suppressedbehind the screen, in a drawer, in their closed hands, pushed itforward into the remote distance, sliced up, burned up, or pulverizedand so destroyed it. B. And D. 'thought it away' directly, withoutmechanism or device, or got rid of it 'by a pure act of will. 'Superposition was tried, frequently with success, but at times theunder image shone through. When the objects were colored discs onesuperposed on the other, the subject spread over the whole surface thecolor of the image to be retained, but at times this resulted in therebeing two shades of the upper color, and a yellow above a red changedto an orange. When red was above yellow, the red appeared more highlyilluminated. Associations with objects of the color of the retainedimage were found helpful but tended to modify the original color. Suchassociations also, at times, by secondary associations brought backthe suppressed image. For example, when thinking of buttercups toenforce a yellow image, the picture of grass surrounding the flowersbrought back the suppressed green image. Concentration of theattention on the image to be retained and an ignoring of the otherwas, on the whole, the method usually and successfully followed. Thisconcentration was helped by imagining the image marked off into minutesquares which were carefully counted. Numerous other devices of asimilar character were used. Objects having many details and thoselending themselves readily to suggestions of action (as a chinaanimal) were the most helpful in enabling the subject to concentratehis attention on their image to the exclusion of another. Somesubjects conceived themselves as tracing with a pencil the outline anddetails of the retained image. Frequently, when the two images wereoriginally near each other and one alone was being held by closescrutiny of its parts, when this scrutiny reached the part of theimage which was nearest the position of the suppressed image, thesuppressed image returned. The original association between the twoimages was often broken up by change of the position or shape of theone to be suppressed. But devices soon became 'worn out' and new oneshad to be resorted to. 

Motor impulses played a large part in the process of suppression, suchas head and eye movement away from the image to be suppressed, contraction of the muscles of the forehead and scalp, occasional'setting' of the teeth, pressure together of the hands when they weresupposed to be holding the image and of the knees under likecircumstances. The eye traced outline and details and the moreactively it could be so employed the more successful was thesuppression. The sensations of accommodation and of focusingpreviously referred to were repeated in this series. Enunciation alsowas very common. 

Frequent comparison of the image with the percept was made at theclose of experiments and showed the utmost diversity in size, vividness and distinctness. During an experiment when the suppressedimage came back, it was rarely more than a mere blur of color; in twoor three instances the form came without color. Green was found to bea difficult color to hold. C. Had an orange after-image from aretained yellow image, a red image having been suppressed. Between theimages of a gray disc and an orange disc, three inches apart, he hada blue disc. J. , while suppressing an orange disc and retaining agreen disc, noticed that 'when off the fovea the whole green discbecame bright orange. ' There was always a sense of readiness on thepart of the suppressed image to slip back. As C. Expressed this, "Thething suppressed exists in the fringe of consciousness. " The recurringimage usually came back at its original position even when theretained image was being held in a different part of the field. Insuch cases the retained image at once resumed its original place. 

G. And J. Were successful in proportion as they freed themselves fromthe nervous strain of anxiety as to the result. 

V. MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURINGTHE EXPOSURE. 

In an additional series of experiments with five of the same subjects(B. , G. , H. , I. And K. ), the object was moved during the five secondsof exposure either right, left, up or down, a distance of about six toeight inches, and back again. In this way the subject was suppliedwith further material of a pure memory type and it was believed thatsome addition to our knowledge of the nature of the control of theimage might thus be made by securing data contrasting the constructionand the more purely reminiscent work of the imagination. 

The question proposed is as follows: Does the fact that a certainmovement of an object was presented to the optical perception give anadvantage in time, or ease, to the mental recall of that object as somoving, over its recall as moving in other directions? The subjectiveexperiences during such recalls may be expected to throw light uponthe matter. 

The subject, with closed eyes, was requested to move the mental imageof the object in the four directions indicated above, returning itafter each movement to its original position, and the time of eachmovement was recorded and, as well, the report of the subject withregard to his subjective experiences. There were sixteen hundredmovements in all, eight hundred away from the original position of theimage (two hundred in each of the four directions mentioned above) andeight hundred in returning to the original position. 

Besides these experiments, other movements of the object duringexposure were made, such as inversion, rotation, change from thevertical to the horizontal position and vice versa, rolling, obliquemovements and the subjective phenomena were recorded when the subjecthad repeated with the image the designated movements. In all theexperiments the objects were moved by the hand of the conductor of theexperiment. 

Table VII. Gives the time record in seconds of these experiments foreach subject under each of the four variations: Movement of the objectto right, left, up, down. 

TABLE VII. 

 MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE TIME OF OPTICAL STIMULATION. AVERAGE TIME IN SECONDS. TEN MOVEMENTS IN EACH DIRECTION FOR EACH SUBJECT. 

 _a_. Object moved to right. 

 Subject R. Return L. Return Up Return Down Return Aver. B. 0. 57 0. 75 0. 62 0. 60 0. 64 0. 35 0. 42 0. 37 0. 62 0. 44 G. 0. 55 0. 60 0. 55 0. 57 0. 57 0. 27 0. 25 0. 27 0. 25 0. 26 H. 6. 95 6. 90 6. 47 6. 40 6. 65 5. 40 5. 55 4. 50 5. 00 5. 11 I. 2. 05 2. 10 2. 05 2. 22 2. 10 1. 15 1. 35 1. 32 1. 57 1. 35 K. 2. 35 2. 97 2. 42 2. 62 2. 59 1. 17 1. 20 1. 17 1. 55 1. 28 Ave. 2. 49 2. 66 2. 02 2. 48 2. 52 1. 67 1. 75 1. 53 1. 80 1. 69

 Ave. To right, 2. 49 Ave. Of other movements, 2. 52 Grand average, 2. 10

 _b_. Object moved to left. B. 0. 72 0. 60 0. 62 0. 60 0. 64 0. 52 0. 40 0. 52 0. 42 0. 47 G. 0. 67 0. 45 0. 55 0. 67 0. 59 0. 42 0. 35 0. 35 0. 37 0. 37 H. 8. 22 5. 95 6. 52 6. 42 6. 78 5. 82 4. 10 4. 37 5. 55 4. 96 I. 2. 40 1. 30 2. 25 2. 72 2. 17 1. 97 1. 22 0. 95 1. 47 1. 40 K. 2. 45 2. 57 2. 25 2. 00 2. 30 1. 70 1. 60 1. 32 1. 35 1. 49 Ave. 2. 89 2. 17 2. 44 2. 48 2. 50 2. 09 1. 53 1. 50 1. 83 1. 74

 Ave. To left, 2. 17 Ave. Of other movements, 2. 60 Grand average, 2. 12

 _c_. Object moved up. B. 0. 75 0. 62 0. 42 0. 57 0. 59 0. 32 0. 50 0. 42 0. 37 0. 40 G. 0. 65 0. 57 0. 45 0. 47 0. 54 0. 35 0. 27 0. 25 0. 27 0. 29 H. 6. 77 6. 25 6. 85 6. 15 6. 57 5. 27 5. 55 5. 30 5. 30 5. 35 I. 2. 47 2. 27 1. 85 2. 65 2. 31 1. 25 1. 00 0. 87 1. 10 1. 05 K. 3. 40 2. 72 1. 42 2. 20 2. 44 1. 50 1. 37 1. 27 1. 17 1. 33 Ave. 2. 81 2. 49 2. 20 2. 41 2. 48 1. 74 1. 74 1. 62 1. 70 1. 69

 Ave. Up, 2. 20 Ave. Of other movements, 2. 57 Grand average, 2. 08

 _d_. Object moved down. B. 0. 80 0. 72 0. 70 0. 57 0. 70 0. 42 0. 42 0. 50 0. 42 0. 44 G. 0. 60 0. 60 0. 55 0. 47 0. 55 0. 25 0. 25 0. 27 0. 27 0. 26 H. 6. 77 6. 80 6. 80 8. 77 7. 29 5. 90 6. 35 4. 55 5. 55 5. 59 I. 2. 30 2. 20 2. 22 1. 80 2. 13 1. 30 1. 20 1. 15 1. 42 1. 27 K. 3. 15 2. 75 2. 95 2. 30 2. 79 1. 62 1. 57 1. 12 1. 25 1. 39 Ave. 2. 72 2. 61 2. 64 2. 78 2. 69 1. 90 1. 92 1. 52 1. 78 1. 79

 Ave. Down, 2. 78 Ave. Of other movements, 2. 66 Grand average, 2. 24

NUMERICAL. 

As each movement may be compared with three other movements, and asthere were five subjects and four variations in the conditions, thereare sixty opportunities of comparing the time required to move theimage in the direction in which the object was moved with the timetaken to move it in the other directions. In 45 instances the time wasless, in 3 the same, and in 12 greater. 

These twelve instances occurred with two subjects, three (to left)occurring with K. And nine (three each right, up, down) occurring withH. The cause was the same in all twelve instances, both H. And K. Reporting that (in these cases) they had great difficulty in obtaininga reasonably vivid and distinct image when directed to move the imagein the direction in which the object had been moved. The attempt tomove the image resulted in a vague image spread continuously over theentire area that had been covered by the moving object, and the effortto obtain the image at the desired position only was serious and tookan appreciably longer time than usual. It is to be noted, also, thatthe time usually taken by H. Is uniformly very much greater than thetime taken by the other subjects. Yet, even with these instancesincluded, the average time of all movements of the image in thedirection in which the object had been moved is less than the averagetime of the other movements, the former being 2. 41 seconds, thelatter, 2. 59 seconds. 

TABLE VIII. 

 MOVEMENTS OF A SINGLE IMAGE. 

 I. , OBJECT PREVIOUSLY MOVED; II. , OBJECT NOT MOVED. 

 Average Time Given in Seconds. 

 Subjects: B. G. H. I II I II I II To right, 0. 57 1. 30 0. 55 1. 46 6. 95 7. 15 Return, 0. 35 0. 58 0. 27 0. 92 5. 40 4. 51 To left, 0. 60 1. 06 0. 45 1. 15 5. 95 6. 42 Return, 0. 40 0. 73 0. 35 0. 89 4. 10 4. 41 Up, 0. 42 1. 05 0. 45 0. 99 6. 85 5. 96 Return, 0. 42 0. 46 0. 25 0. 76 5. 30 4. 36 Down, 0. 57 1. 10 0. 47 0. 82 8. 77 5. 85 Return, 0. 42 0. 45 0. 27 0. 06 5. 55 4. 40 General 0. 54 1. 13 0. 48 1. 10 7. 13 6. 34 Averages, 0. 40 0. 55 0. 28 0. 66 5. 09 4. 42

 Subjects: I. K. I II I II To right, 2. 05 1. 28 2. 35 4. 80 Return, 1. 15 0. 67 1. 17 2. 40 To left, 1. 30 1. 34 2. 57 4. 63 Retur, 1. 22 0. 62 1. 60 2. 73 Up, 1. 85 1. 62 1. 42 3. 29 Return, 0. 87 0. 86 1. 27 1. 90 Down, 1. 80 1. 36 2. 30 3. 27 Return, 1. 42 0. 72 1. 25 1. 56 General 1. 75 1. 40 2. 16 4. 00 Averages, 1. 16 0. 72 1. 32 2. 15

If the record of H. Is omitted from Table VII. , _a, c, _and _d_, andthat of K. From VII. , _b_ (as these are the records of the twelveexceptions), the former average becomes 1. 44 seconds, the latter 1. 86seconds. 

The following table affords the means of comparing the time taken inmoving the image in the direction in which the object had been movedwith the time taken in moving the image in the same direction whenthere had been no movement of the object. The averages are obtainedfrom the records of Tables VII. And I. 

We have here twenty comparisons each of movements away from theoriginal positions and movements back to the original positions:

 In the first case, 15 took less time under I. , 5 took more time under I. 

 The 5 cases of more time occurred with two subjects (H. , 3 and I. , 2). 

 In the second case, 12 took less time under I. , 8 took more time under I. 

 The 8 cases of more time occurred with three subjects (G. , 1; H. , 3; I. , 4). 

If we omit H. 's record and take the general averages for each subject, we find the following advantages in time in form of movements wherethe object had been moved;

 B. , 0. 59 seconds. G. , 0. 52 " K. , 1. 84 "

But I. , 0. 35 seconds in favor of movements when the object had notbeen moved. 

Combining these results, we have 0. 74 sec. As the average gain in timefor these four subjects. 

SUBJECTIVE. 

With one exception (G. ), the subjects found Movements I. , movements inthe direction in which the object had been moved, easier thanMovements II. In Movements II. The eye seemed to construct and compelthe motion, which was not the case with Movements I. , in which the eyefollowed the motion. The distance to which the image went in MovementsI. Seemed predetermined, and these movements seemed exact copies ofthe original movement of the object, being purely reminiscent andreproducing its irregularities when there were any. Also, the imagewas usually seen _in transitu_ both out and back, which was never thecase with Movements II. Eye movement and enunciation were much lessfrequent and the image was more vivid and distinct in Movements I. 

 * * * * *

 STUDIES IN ĘSTHETIC PROCESSES. 

 * * * * *

Transcriber's Note:

 Rhythmic measures in the first 2 articles of this section are transcribed as follows:

 | delineates measure q quarter note q. Dotted quarter note e eighth note % quarter rest

 Major accent of the measure is indicated by a >, either above or in front of the beat. Minor accent of the measure is indicated by . , used in the same way. 

 > . | q q q q | or | >q q . Q q | represent the same rhythmic pattern. 

 * * * * *

THE STRUCTURE OF SIMPLE RHYTHM FORMS. 

BY ROBERT MACDOUGALL. 

I. PROBLEMS AND METHODS OF EXPERIMENTATION. 

The investigation of the problems presented by the psychologicalphenomena of rhythm has of late years occupied much attention and beenpushed in a variety of different directions. Some researches have beenconcerned with an analysis of rhythm as an immediate subjectiveexperience, involving factors of perception, reaction, memory, feeling, and the like; others have had to do with the specificobjective conditions under which this experience arises, and theeffect of changes in the relations of these factors; still others havesought to coördinate the rhythm experience with more general laws ofactivity in the organism, as the condition of most effective action, and to affiliate its complex phenomena upon simpler laws ofphysiological activity and repose; while a fourth group has undertakena description of that historical process which has resulted in theestablishment of artistic rhythm-types, and has sought to formulatethe laws of their construction. [1]

 [1] Description: (1) Of the psychological factors of the rhythm experience: Angell and Pierce, Ettlinger, Hauptmann, Mentz, Meumann, Stumpf, Wundt, et al. (2) Of its objective conditions and products: Binet et Courtier, Bolton, Ebhardt, Hurst and McKay, Meumann, Schumann, Sievers, et al. (3) Of its physiological accompaniments: Bolton, Brücke, Dogiel, Hausegger, Mach, Mentz, Ribot, Sherrington, Scripture, Smith, et al. (4) Of its historical evolution: Bücher, Moritz, Scherer, et al. 

This differentiation has already made such progress as to constitutethe general topic a field within which specialization is called for, instead of an attempt to treat the phenomenon as a whole. It is thepurpose of this paper to describe a set of experiments having to dowith the second of these problems, the constitution of objectiverhythm forms. In the determination of such forms it is, of course, impossible to avoid the employment of terms descriptive of theimmediate experience of rhythm as a psychological process, or tooverlook the constant connection which exists between the two groupsof facts. The rhythm form is not objectively definable as a stabletype of stimulation existing in and for itself; the discrimination oftrue and false relations among its elements depends on the immediatereport of the consciousness in which it appears. The artistic form issuch only in virtue of its arousing in the observer that peculiarquality of feeling expressed in calling the series of sensory stimulirhythmically pleasing, or equivalent, or perfect. In no other way thanas thus dependent on the appeal which their impression makes to theęsthetic consciousness can we conceive of the development andestablishment of fixed forms of combination and sequence among thosetypes of sensory stimulation which arouse in us the pleasurableexperience of rhythm. The artistic rhythm form cannot be defined asconstituted of periods which are 'chronometrically proportionate, ' ormathematically simple. It is not such in virtue of any physicalrelations which may obtain among its constituents, though it may bedependent on such conditions in consequence of the subordination tophysical laws of the organic activities of the human individual. Theview must be subjectively objective throughout. 

The need for simplicity and exactness has led to the very generalemployment of material as barely sensorial as could be devised for thecarrying on of experiments upon rhythm. Rich tones and complexcombinations of them are to be avoided, for these qualities arethemselves immediate sources of pleasure, and the introduction of theminto the material of experimentation inevitably confuses the analysiswhich the observer is called upon to make of his experience and of thesources of his pleasure in it. Still more objectionable than thepresence of such complex musical tones in an investigation of rhythmis the introduction of the symbols of rational speech in concretepoetical forms. This element can be only a hindrance to the perceptionof pure rhythmical relations, in virtue of the immediate interestwhich the images called up by the verbal signs possess, and further, in view of the fact that the connections of significant thought imposeupon the purely rhythmical formulation of the series of stimulationsan unrelated and antagonistic principle of grouping, namely, thelogical relations which the various members of the series bear to oneanother. 

The demand for a simplification of the material which supports therhythm experience, for the purpose of obtaining a more exact controlover the conditions of experimentation, has been met by the inventionof a variety of devices whereby the sequences of music, song andpoetical speech have been replaced by elementary conventional symbolsas the vehicle of the rhythmical impression or expression. On the oneside there has commonly been substituted for musical tones andrhythmical speech the most simple, sharply limited and controllablesounds possible, namely, those due to the action of a telephonereceiver, to the vibrations of a tuning-fork placed before theaperture of a resonator, or to the strokes of metallic hammers fallingon their anvils. On the other side, the form of the reproduced rhythmhas been clarified by the substitution of the finger for the voice ina series of simple motor reactions beaten out on a more or lessresonant medium; by the use--when the voice is employed--ofconventional verbal symbols instead of the elements of significantspeech; and--where actual verse has been spoken--by a treatment of thewords in formal staccato scansion, or by the beating of timethroughout the utterance. The last of these methods is a haltingbetween two courses which casts doubt on the results as characteristicof either type of activity. There is no question that the rhythmicforms of recitative poetry differ vastly from those of instrumentalmusic and chanted speech. The measures of spoken verse are elastic andfull of changefulness, while those of music and the chant maintain avery decided constancy of relations. The latter present determinabletypes of grouping and succession, while it is questionable whether theforms of relationship in spoken verse can ever be considered apartfrom the emotion of the moment. In so far as the rhythmic form whichthese differing modes of expression embody are to be made the subjectof experimental investigation their characteristic structures shouldbe kept intact as objects of analysis in independent experiments, instead of being combined (and modified) in a single process. 

The apparatus employed in the course of the present investigationconsisted of four different pieces of mechanism, one affording thevehicle of expression throughout the series of reproduced rhythms, theothers providing the auditory material of the various rhythmsapperceived but not designedly reproduced. The first of theseconsisted of a shallow Marey tambour, placed horizontally upon a tablewith its rubber film upwards, and connected by means of rubber-tubingwith a pneumographic pen in contact with the revolving drum of akymograph. A Deprez electric marker, aligned with the pneumographicstylus, afforded a time record in quarter seconds. Upon this tambour, placed within comfortable reach of the reactor's hand, the variousrhythm types were beaten out. The impact of the finger-tip on thetense surface of the drum gave forth a faint and pleasing but at thesame time clearly discernible and distinctly limited sound, whichresponded with audible variations of intensity to the differingstresses involved in the process of tapping, and which I haveconsidered preferable to the short, sharp stroke of the Kraepelinmouth-key employed by Ebhardt. The rate of revolution in the drum wasso adjusted to the normal range of excursion in the pneumographic penas to give sharp definition to every change of direction in the curve, which hence allowed of exact measurements of temporal and intensivephases in the successive rhythm groups. These measurements were madeto limits of 1. 0 mm. In the latter direction and of 0. 5 mm. In theformer. [2]

 [2] Professor Binet's doubt (_L'Année Psychologique_ 1895, p. 204) that the propulsion of air from the elastic chamber and the rebound of the pen might interfere with the significance of the graphic record is more serious in connection with the application of this method to piano playing than here; since its imperfection, as that writer says, was due to the force and extreme rapidity of the reactions in the former case. The present series involved only light tapping and was carried on at a much slower average rate. 

The second piece of apparatus consisted of an ordinary metronomeadjusted to beat at rates of 60, 90, and 120 strokes per minute. Thisinstrument was used in a set of preliminary experiments designed totest the capacity of the various subjects for keeping time by fingerreaction with a regular series of auditory stimulations. 

The third piece of apparatus consisted of an arrangement for producinga series of sounds and silences, variable at will in absolute rate, induration, and, within restricted limits, in intensity, by theinterruptions of an electrical current, into the circuit of which hadbeen introduced a telephone receiver and a rheostat. Portions of theperiphery of a thin metallic disc were cut away so as to leave ataccurately spaced intervals, larger or smaller extents of the originalboundary. This toothed wheel was then mounted on the driving-shaft ofan Elbs gravity motor and set in motion. Electrical connections andinterruptions were made by contact with the edge of a platinum slipplaced at an inclination to the disc's tangent, and so as to bearlightly on the passing teeth or surfaces. The changes in form of amercury globule, consequent on the adhesion of the liquid to thepassing teeth, made it impossible to use the latter medium. Theabsolute rate of succession in the series of sounds was controlled byvarying the magnitudes of the driving weights and the resistance ofthe governing fans of the motor. As the relation of sounds andintervals for any disc was unalterable, a number of such wheels wereprepared corresponding to the various numerical groups and temporalsequences examined--one, for example, having the relations expressedin the musical symbol 3/4 | >q e |*; another having that represented inthe symbol 4/4 | >q e e |;* and so on. Variations in intensity wereobtained by mounting a second series of contacts on the same shaft andin alignment with those already described. The number of thesesecondary contacts was less than that of the primary connections, their teeth corresponding to every second or third of those. Theconnections made by these contacts were with a second loop, which alsocontained within its circuit the telephone receiver by which thesounds were produced. The rheostatic resistances introduced into thissecond circuit were made to depart more or less from that of thefirst, according as it was desired to introduce a greater or slighterperiodic accent into the series. This mechanism was designed for thepurpose of determining the characteristic sequences of long and shortelements in the rhythm group. 

 *Transcriber's Note:

 The original article showed "3/4 | q q q |" and "4/4 | q q q q |". Applying the erratum after the article (below) resulted in fewer beats per measure than indicated by the time signature. Other possibilities are "3/4 | >q e q. |" and "4/4 | >q e e q q |". 

 "ERRATUM:

 On page 313, line 23, the musical symbols should be a quarter note, accented, followed by an eighth note; in the following line the symbols should be a quarter note, accented, followed by two eighth notes. "

The fourth piece of apparatus consisted essentially of a horizontalsteel shaft having rigidly attached to it a series of metallicanvils, fifteen in number, on which, as the shaft revolved, themembers of a group of steel hammers could be made to fall insuccession from the same or different heights. The various parts ofthe mechanism and their connections may be readily understood byreference to the illustration in Plate VIII. On the right, supportedupon two metal standards and resting in doubly pivoted bearings, appears the anvil-bearing shaft. On a series of shallow grooves cutinto this shaft are mounted loose brass collars, two of which arevisible on the hither end of the shaft. The anvils, the parts andattachments of which are shown in the smaller objects lying on thetable at the base of the apparatus, consist of a cylinder of steelpartly immersed in a shallow brass cup and made fast to it by means ofa thumb-screw. This cup carries a threaded bolt, by which it may beattached to the main shaft at any position on its circumference byscrewing through a hole drilled in the collar. The adjustment of theanvils about the shaft may be changed in a moment by the simplemovement of loosening and tightening the thumb-screw constituted bythe anvil and its bolt. The device by which the extent of thehammer-fall is controlled consists of cam-shaped sheets of thin woodmounted within parallel grooves on opposite sides of the loose collarsand clamped to the anvils by the resistance of two wedge-shapedflanges of metal carried on the anvil bolt and acting against thesides of slots cut into the sheets of wood at opposite sides. Theperiphery of these sheets of wood--as exhibited by that one lyingbeside the loose anvils on the table--is in the form of a spiral whichunfolds in every case from a point on the uniform level of the anvils, and which, by variations in the grade of ascent, rises in the courseof a revolution about its center to the different altitudes requiredfor the fall of the hammers. These heights were scaled in inches andfractions, and the series employed in these experiments was asfollows: 1/8, 2/8, 3/8, 5/8, 7/8, 15/8, 24/8 inch. Upon acorresponding pair of standards, seen at the left of the illustration, is mounted a slender steel shaft bearing a series of sections of brasstubing, on which, in rigid sockets, are carried the shafts of a set ofhammers corresponding in number and position to the anvils of themain axis. By means of a second shaft borne upon two connected armsand pivoted at the summit of the standards the whole group of hammersmay at any moment be raised from contact with the cams of the mainshaft and the series of sounds be brought to a close withoutinterrupting the action of the motor or of the remainder of theapparatus. By this means phases of acceleration and retardation in theseries, due to initial increase in velocity and its final decrease asthe movement ceases, are avoided. The pairs of vertical guides whichappear on this gearing-shaft and enclose the handles of the severalhammers are designed to prevent injury to the insertions of the hammershafts in their sockets in case of accidental dislocations of theheads in arranging the apparatus. This mechanism was driven by anelectrical motor with an interposed reducing gear. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VIII. Opposite p. 314. ]

The intervals between the successive hammer-strokes are controlled inthe following way: on the inner face of the group of pulleys mountedon the main shaft of the mechanism (this gang of pulleys appears atthe extreme right in the illustration) is made fast a protractorscaled in half degrees. Upon the frame of the standard supportingthese pulleys is rigidly screwed an index of metal which passescontinuously over the face of the scale as the shaft revolves. Thepoints of attachment (about the shaft) of the cams are determined bybringing the point of fall of each cam in succession into alignmentwith this fixed index, after the shaft has been turned through thedesired arc of its revolution and made fast by means of thethumb-screw seen in the illustration at the near end of the shaft. Thus, if three strokes of uniform intensity are to be given at equalintervals apart and in continuous succession, the points of fall ofthe hammers will be adjusted at equal angular distances from oneanother, for example, at 360°, 240°, and 120°; if the temporalrelations desired be in the ratios 2:1:1, the arrangement will be360°, 180°, 90°; if in the ratios 5:4:3, it will be 360°, 210°, 90°;and so on. If double this number of hammers be used in a continuousseries the angular distances between the points of fall of thesuccessive hammers will of course be one half of those given above, and if nine, twelve, or fifteen hammers be used they will beproportionately less. 

An interruption of any desired relative length may be introducedbetween repetitions of the series by restricting the distribution ofangular distances among the cams to the requisite fraction of thewhole revolution. Thus, if an interruption equal to the durationincluded between the first and last hammer-falls of the series bedesired, the indices of position in the three cases described abovewill become: 360°, 270°, 180°; 360°, 240°, 180°, and 360°, 260°, 180°. In the case of series in which the heights of fall of the varioushammers are not uniform, a special adjustment must be superimposedupon the method of distribution just described. The fall of the hammeroccupies an appreciable time, the duration of which varies with thedistance through which the hammer passes. The result, therefore, of anadjustment of the cams on the basis adopted when the height of fall isuniform for all would appear in a reduction of the interval followingthe sound produced by a hammer falling from a greater height than therest, and the amount of this shortening would increase with everyaddition to the distance through which the hammer must pass in itsfall. In these experiments such lags were corrected by determiningempirically the angular magnitude of the variation from its calculatedposition necessary, in the case of each higher member of the series ofdistances, to make the stroke of the hammer on its anvil simultaneouswith that of the shortest fall. These fixed amounts were then added tothe indices of position of the several cams in each arrangement ofintervals employed in the experiments. 

This apparatus answers a variety of needs in practical manipulationvery satisfactorily. Changes in adjustment are easily and quicklymade, in regard to intensity, interval and absolute rate. If desired, the gradation of intensities here employed may be refined to thethreshold of perceptibility, or beyond it. 

The possible variations of absolute rate and of relative intervalswithin the series were vastly more numerous than the practicalconditions of experimentation called for. In two directions theadaptability of the mechanism was found to be restricted. Thedurations of the sounds could not be varied as were the intervalsbetween them, and all questions concerning the results of suchchanges were therefore put aside; and, secondly, the hammers andanvils, though fashioned from the same stuff and turned to identicalshapes and weights, could not be made to ring qualitatively alike; andthese differences, though slight, were sufficiently great to becomethe basis of discrimination between successive sounds and of therecognition upon their recurrence of particular hammer-strokes, thereby constituting new points of unification for the series ofsounds. When the objective differences of intensity were marked, theseminor qualitative variations were unregarded; but when the stressesintroduced were weak, as in a series composed of 3/8-, 2/8-, 2/8-inchhammer-falls, they became sufficiently great to confuse or transformthe apparent grouping of the rhythmical series; for a qualitativedifference between two sounds, though imperceptible when comparison ismade after a single occurrence of each, may readily become thesubconscious basis for a unification of the pair into a rhythmicalgroup when several repetitions of them take place. 

In such an investigation as this the qualification of thesubject-observer should be an important consideration. Thesusceptibility to pleasurable and painful affection by rhythmical andarrhythmical relations among successive sensory stimuli varies withinwide limits from individual to individual. It is of equal importanceto know how far consonance exists between the experiences of a varietyof individuals. If the objective conditions of the rhythm experiencediffer significantly from person to person it is useless to seek forrhythm forms, or to speak of the laws of rhythmical sequence. Consensus of opinion among a variety of participators is the onlyfoundation upon which one can base the determination of objectiveforms of any practical value. It is as necessary to have many subjectsas to have good ones. In the investigation here reported on, workextended over the two academic years of 1898-1900. Fourteen persons inall took part, whose ages ranged from twenty-three to thirty-nineyears. Of these, five were musically trained, four of whom were alsopossessed of good rhythmic perception; of the remaining nine, sevenwere good or fair subjects, two rather poor. All of these had hadprevious training in experimental science and nine were experiencedsubjects in psychological work. 

II. THE ELEMENTARY CONDITIONS OF THE APPEARANCE OF THE RHYTHMIMPRESSION. 

The objective conditions necessary to the arousal of an impression ofrhythm are three in number: (_a_) Recurrence; (_b_) Accentuation;(_c_) Rate. 

(_a_) _Recurrence. _--The element of repetition is essential; theimpression of rhythm never arises from the presentation of a singlerhythmical unit, however proportioned or perfect. It does appearadequately and at once with the first recurrence of that unit. If therhythm be a complex one, involving the coördination of primary groupsin larger unities, the full apprehension of its form will, of course, arise only when the largest synthetic group which it contains has beencompleted; but an impression of rhythm, though not of the form finallyinvolved, will have appeared with the first repetition of the simplestrhythmical unit which enters into the composition. It is conceivablethat the presentation of a single, unrepeated rhythmical unit, especially if well-defined and familiar, should originate a rhythmicalimpression; but in such a case the sensory material which supports theimpression of rhythm is not contained in the objective series but onlysuggested by it. The familiar group of sounds initiates a rhythmicprocess which depends for its existence on the continued repetition, in the form of some subjective accentuation, of the unit originallypresented. 

The rhythmical form, in all such cases, is adequately and perfectlyapprehended through a single expression of the sequence. [3] It lacksnothing for its completion; repetition can add no more to it, and is, indeed, in strict terms, inconceivable; for by its very recurrence itis differentiated from the initial presentation, and combinesorganically with the latter to produce a more highly synthetic form. And however often this process be repeated, each repetition of theoriginal sequence will have become an element functionally unique andlocally unalterable in the last and highest synthesis which the wholeseries presents. 

 [3] When the formal key-note is distinctly given, the rhythmical movement arises at once; when it is obscure, the emergence of the movement is gradual. This is a salient difference, as Bolton, Ettlinger and others have pointed out, between subjective rhythms and those objectively supported. 

Rhythmical forms are not in themselves rhythms; they must initiate thefactor of movement in order that the impression of rhythm shall arise. Rhythmical forms are constantly occurring in our perceptionalexperience. Wherever a group of homogeneous elements, so related as toexhibit intensive subordination, is presented under certain temporalconditions, potential rhythm forms appear. It is a mere accidentwhether they are or are not apprehended as actual rhythm forms. If thesequence be repeated--though but once--during the continuance of asingle attention attitude, its rhythmical quality will ordinarily beperceived, the rhythmic movement will be started. If the sequence benot thus repeated, the presentation is unlikely to arouse the processand initiate the experience of rhythm, but it is quite capable of sodoing. The form of the rhythm is thus wholly independent of themovement, on which the actual impression of rhythm in every casedepends; and it may be presented apart from any experience of rhythm. 

There is properly no repetition of identical sequences in rhythm. Practically no rhythm to which the ęsthetic subject gives expression, or which he apprehends in a series of stimulations, is constituted ofthe unvaried repetition of a single elementary form, the measures, | >q. Q |, or | >q. Q q |, for example. Variation, subordination, synthesis, are present in every rhythmical sequence. The regularsuccession is interrupted by variant groups; points of initiation inthe form of redundant syllables, points of finality in the form ofsyncopated measures, are introduced periodically, making the rhythmform a complex one, the full set of relations involved beingrepresented only by the complete succession of elements containedbetween any one such point of initiation and its return. 

(_b_) _Accentuation. _--The second condition for the appearance of therhythm impression is the periodic accentuation of certain elements inthe series of sensory impressions or motor reactions of which thatrhythm is composed. The mechanism of such accentuation is indifferent;any type of variation in the accented elements from the rest of theseries which induces the characteristic process of rhythmicaccentuation--by subjective emphasis, recurrent waves of attention, orwhat not--suffices to produce an impression of rhythm. It is commonlysaid that only intensive variations are necessary; but such types ofdifferentiation are not invariably depended on for the production ofthe rhythmic impression. Indeed, though most frequently the basis ofsuch effects, for sufficient reasons, this type of variation isneither more nor less constant and essential than other forms ofdeparture from the line of indifference, which forms are ordinarilysaid to be variable and inessential. For the existence of rhythmdepends, not on any particular type of periodical variation in thesensory series, but on the recurrent accentuation, under specialtemporal conditions, of periodic elements within such a series; andany recurrent change in quality--using this term to describe the totalgroup of attributes which constitutes the sensorial character of theelements involved--which suffices to make the element in which itoccurs the recipient of such accentuation, will serve as a basis forthe production of a rhythmical impression. It is the fact ofperiodical differentiation, not its particular direction, which isimportant. Further, as we know, when such types of variation arewholly absent from the series, certain elements may receive periodicalaccentuation in dependence on phases of the attention process itself, and a subjective but perfectly real and adequate rhythm arise. 

In this sense those who interpret rhythm as fundamentally dependent onthe maintenance of certain temporal relations are correct. Theaccentuation must be rhythmically renewed, but the sensory incentivesto such renewals are absolutely indifferent, and any given one of theseveral varieties of change ordinarily incorporated into rhythm may beabsent from the series without affecting its perfection as arhythmical sequence. In piano playing the accentual points of apassage may be given by notes struck in the bass register whileunaccented elements are supplied from the upper octaves; in orchestralcompositions a like opposition of heavy to light brasses, of cello toviolin, of cymbals to triangle, is employed to produce rhythmicaleffects, the change being one in _timbre_, combined or uncombinedwith pitch variations; and in all percussive instruments, such as thedrum and cymbals, the rhythmic impression depends solely on intensivevariations. The peculiar rhythmic function does not lie in theseelements, but in a process to which any one of them indifferently maygive rise. When that process is aroused, or that effect produced, therhythmic impression has been made, no matter what the mechanism mayhave been. 

The single objective condition, then, which is necessary to theappearance of an impression of rhythm is the maintenance of specifictemporal relations among the elements of the series of sensationswhich supports it. It is true that the subjective experience of rhythminvolves always two factors, periodicity and accentuation; the latter, however, is very readily, and under certain conditions inevitably, supplied by the apperceptive subject if the former be given, while ifthe temporal conditions be not fulfilled (and the subject cannotcreate them) no impression of rhythm is possible. The contributedaccent is always a temporally rhythmical one, and if the recurrence ofthe elements of the objective series opposes the phases of subjectiveaccentuation the rhythm absolutely falls to the ground. Of the twopoints of view, then, that is the more faithful to the facts whichasserts that rhythm is dependent upon the maintenance of fixedtemporal intervals. These two elements cannot be discriminated asforming the objective and subjective conditions of rhythmrespectively. Both are involved in the subjective experience and bothfind their realization in objective expressions, definable andmeasurable. 

(_c_) _Rate. _--The appearance of the impression of rhythm isintimately dependent on special conditions of duration in theintervals separating the successive elements of the series. Thereappears in this connection a definite superior limit to the absoluterate at which the elements may succeed one another, beyond which therapidity cannot be increased without either (_a_) destroyingaltogether the perception of rhythm in the series or (_b_)transforming the structure of the rhythmical sequence by thesubstitution of composite groups for the single elements of theoriginal series as units of rhythmic construction; and a less clearlymarked inferior limit, below which the series of stimulations failswholly to arouse the impression of rhythm. But the limits imposed bythese conditions, again, are coördinated with certain other variables. The values of the thresholds are dependent, in the first place, on thepresence or absence of objective accentuation. If such accents bepresent in the series, the position of the limits is still a functionof the intensive preponderance of the accented over the unaccentedelements of the group. Further, it is related to the active or passiveattitude of the ęsthetic subject on whom the rhythmical impression ismade, and there appear also important individual variations in thevalues of the limits. 

When the succession falls below a certain rate no impression of rhythmarises. The successive elements appear isolated; each is apprehendedas a single impression, and the perception of intensive and temporalrelations is gotten by the ordinary process of discrimination involvedwhen any past experience is compared with a present one. In theapprehension of rhythm the case is altogether different. There is nosuch comparison of a present with a past experience; the whole groupof elements constituting the rhythmic unit is present to consciousnessas a single experience; the first of its elements has never fallen outof consciousness before the final member appears, and the awareness ofintensive differences and temporal segregation is as immediate a factof sensory apprehension as is the perception of the musical qualitiesof the sounds themselves. 

The absolute value of this lower limit varies from individual toindividual. In the experience of some persons the successive membersof the series may be separated by intervals as great as one and onehalf (possibly two) seconds, while yet the impression is distinctlyone of rhythm; in that of others the rhythm dies out before half ofthat interval has been reached. With these subjects the apprehensionat this stage is a secondary one, the elements of the successivegroups being held together by means of some conventional symbolism, asthe imagery of beating bells or swinging pendulums. A certainvoluminousness is indispensable to the support of such slow measures. The limit is reached sooner when the series of sounds is given by thefall of hammers on their anvils than when a resonant body like a bellis struck, or a continuous sound is produced upon a pipe or a reed. 

In these cases, also, the limit is not sharply defined. The rhythmicalimpression gradually dies out, and the point at which it disappearsmay be shifted up or down the line, according as the ęsthetic subjectis more or less attentive, more or less in the mood to enjoy or createrhythm, more passive or more active in his attitude toward the seriesof stimulations which supports the rhythmical impression. Theattention of the subject counts for much, and this distinction--ofinvoluntary from voluntary rhythmization--which has been made chieflyin connection with the phenomenon of subjective rhythm, runs alsothrough all appreciation of rhythms which depend on actual objectivefactors. A series of sounds given with such slowness that at one time, when passively heard, it fails to produce any impression of rhythm, may very well support the experience on another occasion, if thesubject try to hold a specific rhythm form in mind and to find it inthe series of sounds. In such cases attention creates the rhythm whichwithout it would fail to appear. But we must not confuse the nature ofthis fact and imagine that the perception that the relations of acertain succession fulfil the the form of a rhythmical sequence hascreated the rhythmical impression for the apperceiving mind. It hasdone nothing of the kind. In the case referred to the rhythm appearsbecause the rhythmical impression is produced, not because the fact ofrhythmical form in the succession is perceived. The capacity of thewill is strictly limited in this regard and the observer is as reallysubject to time conditions in his effortful construction as in hiseffortless apprehension. The rhythmically constructive attitude doesnot destroy the existence of limits to the rate at which the seriesmust take place, but only displaces their positions. 

A similar displacement occurs if the periodic accentuations within theseries be increased or decreased in intensity. The impression ofrhythm from a strongly accented series persists longer, as retardationof its rate proceeds, than does that of a weakly accented series; therhythm of a weakly accented series, longer than that of a uniformsuccession. The sensation, in the case of a greater intensive accent, is not only stronger but also more persistent than in that of aweaker, so that the members of a series of loud sounds succeeding oneanother at any given rate appear to follow in more rapid successionthan when the sounds are faint. But the threshold at which theintervals between successive sounds become too great to arouse anyimpression of rhythm does not depend solely on the absolute loudnessof the sounds involved; it is a function also of the degree ofaccentuation which the successive measures possess. The greater theaccentuation the more extended is the temporal series which will holdtogether as a single rhythmic group. 

This relation appears also in the changes presented in beaten rhythms, the unit-groups of which undergo a progressive increase in the numberof their components. The temporal values of these groups do not remainconstant, but manifest a slight increase in total duration as thenumber of component beats is increased, though this increase is but afraction of the proportional time-value of the added beats. Parallelwith this increase in the time-value of the unit-group goes anincrease in the preponderance of the accented element over theintensity of the other members of the group. Just as, therefore, inrhythms that are heard, the greatest temporal values of the simplegroup are mediated by accents of the highest intensity, so inexpressed rhythms those groups having the greatest time-values aremarked by the strongest accentuation. 

Above the superior limit a rhythm impression may persist, but neitherby an increase in the number of elements which the unit groupcontains, nor by an increase in the rate at which these units followone another in consciousness. The nature of the unit itself istransformed, and a totally new adjustment is made to the material ofapprehension. When the number of impressions exceeds eight or ten asecond--subject to individual variations--the rhythmical consciousnessis unable longer to follow the individual beats, a period of confusionensues, until, as the rate continues to increase, the situation issuddenly clarified by the appearance of a new rhythm superimposed onthe old, having as its elements the structural units of the precedingrhythm. The rate at which the elements of this new rhythm succeed oneanother, instead of being more rapid than the old, has becomerelatively slow, and simple groups replace the previous large andcomplex ones. Thus, at twelve beats per second the rhythms heard bythe subjects in these experiments were of either two, three or fourbeats, the elements entering into each of these constituent beatsbeing severally three and four in number, as follows:

TABLE I. 

 > > Simple Trochaic, four beats per second: 1 2 3, 4 5 6; 7 8 9, 10 11 12. \___/ \___/ \___/ \______/ > ________ ___________ / \ / \ Dipodic Trochaic, " " " " 1 2 3, 4 5 6; 7 8 9, 10 11 12. \__/ \__/ \___/ \________/ >>> Simple Dactylic, three " " " 1 2 3 4, 5 6 7 8, 9 10 11 12. \____/ \____/ \_______/

The only impression of rhythm here received was of a trochaic ordactylic measure, depending upon an accent which characterized a groupand not a single beat, and which recurred only twice or thrice asecond. Sometimes the subjects were wholly unaware that the elementsof the rhythm were not simple, a most significant fact, and frequentlythe number reported present was one half of the actual number given. During the continuance of such a series the rhythm form changesfrequently in the apprehension of the individual subject from one toanother of the types described above. 

It cannot be too strongly insisted on that the perception of rhythm isan _impression_, an immediate affection of consciousness depending ona particular kind of sensory experience; it is never a construction, areflective perception that certain relations of intensity, duration, or what not, do obtain. If the perception of rhythm in a series ofimpressions were dependent on intellectual analysis anddiscrimination, the existence of such temporal limits as are actuallyfound would be inconceivable and absurd. So long as the perception ofthe uniformity or proportion of time-relations were possible, togetherwith the discrimination of the regular recurrence in the series ofpoints of accentuation, the perception of rhythm should persist, however great or small might be the absolute intervals which separatedthe successive members of the series. If it were the conception of acertain form of relation, instead of the reception of a particularimpression, which was involved, we should realize a rhythm whichextended over hours or days, or which was comprehended in the fractionof a second, as readily as those which actually affect us. 

The rate at which the elements of a series succeed one another affectsthe constitution of the unit groups of which the rhythmical sequenceis composed. The faster the rate, the larger is the number ofimpressions which enter into each group. The first to appear insubjective rhythm, as the rate is increased from a speed too slow forany impression of rhythm to arise, are invariably groups of two beats;then come three-beat groups, or a synthesis of the two-beat groupsinto four, with major and minor accents; and finally six-andeight-beat groups appear. When objective accentuation is present asimilar series of changes is manifested, the process here depending ona composition of the unit-groups into higher orders, and not involvingthe serial addition of new elements to the group. 

The time relations of such smaller and larger units are dependent onthe relative inertia of the mechanism involved. A definite subjectiverhythm period undoubtedly appears; but its constancy is not maintainedabsolutely, either in the process of subjective rhythmization or inthe reproduction of ideal forms. Its manifestation is subject to thespecial conditions imposed on it by such apprehension or expression. The failure to make this distinction is certain to confuse one'sconception of the temporal rhythmic unit and its period. Thevariations of this period present different curves in the two cases ofsubjective rhythmization and motor expression of definite rhythmforms. In the former the absolute duration of the unit-group suffersprogressive decrease as the rate of succession among the stimuli isaccelerated; in the latter a series of extensions of its totalduration takes place as the number of elements composing the unit isincreased. The series of relative values for units of from two toeight constituents which the finger reactions presented in thisinvestigation is given in the following table:

TABLE II. 

 No. Of Elements. Proportional Duration. Two, 1. 000 Three, 1. 109 Four, 1. 817 Five, 1. 761 Six, 2. 196 Seven, 2. 583 Eight, 2. 590

This progressive extension of the rhythm period is to be explained bythe mechanical conditions imposed on the expression of rhythm byprocesses of muscular contraction and release. Were it possible freelyto increase the rate of such successive innervations, we should expectto find a much greater constancy in the whole period occupied by theseries of reactions which composes the unit. The comparativelyunsatisfactory quality of these larger series, and the resolution ofthem into subgroups described elsewhere in this paper, are due to thisinability to accommodate the series of motor reactions to thesubjective rhythm period. 

On the other hand, the temporal value of the unit which appears as theresult of subjective rhythmization undergoes a progressive decrease inabsolute magnitude as the rate of succession among the undifferentiatedstimuli is accelerated. The series of values for units containing fromtwo to eleven constituents is given in the following table:

TABLE III. 

 No. Of Elements. Duration in Seconds. Two, 2. 00 Three, 1. 75 Four, 1. 66 Seven, 1. 75 Nine, 1. 50 Eleven, 0. 97

If the time-value of the simple rhythm group here depended solely onthe relation of the successive stimuli to the subjective rhythmperiod, no progressive diminution should be presented, for inproportion as the absolute value of the separating intervals decreasesthe true nature of this period should be more clearly manifested. Itis scarcely to be doubted that the complexity of its content islikewise a determinant of the temporal value of this period, and thatto this factor is to be attributed the changes which are herepresented. [4]

 [4] Bolton reports a similar decrease in the temporal value of the unit, and gives the following quantitative relations:

 Average length of 2-group, 1. 590 secs. " " " 3-group, 1. 380 " " " " 4-group, 1. 228 " " " " 6-group, 1. 014 " " " " 8-group, 1. 160 "

In subjective rhythmization the number of elements which compose theunit is dependent solely on the relation of the subjective rhythmperiod to the rate of succession among such elements. In objectiverhythm, as has been pointed out, a free treatment of the material isrendered impossible by the determination of specific points ofincreased stress, in virtue of which a new unit of change appears, namely, the whole period elapsing from any one occurrence ofaccentuation to its return. 

But this is not the sole determinant of the numerical limits of thesimple group in such objective rhythms. The structural unit mustindeed adhere to the scheme given by the period of the recurrentaccentuation; but the point at which simple successions of this figuregive place to complex structures (at which | >q. Q q_| is replaced by| >q. Q q;_q. Q q_|, for example) may conceivably be hastened orretarded by other factors than that of the simple rate of succession. The degrees of segregation and accentuation which characterize therhythmic unit are elements which may thus affect the higher synthesis. Increase in either of these directions gives greater definition to therhythmic figure and should tend to preserve the simple group inconsciousness. The latter relation was not made the subject of specialinvestigation in this research. The former was taken up at a singlepoint. The sounds were two in number, alternately accented andunaccented, produced by hammer-falls of 7/8 and 1/8 inch respectively. These were given at three rates of succession, and three differentdegrees of segregation were compared together. In the following tableis given, for six subjects, the average number of elements enteringinto the group-form, simple or complex, under which the rhythm wasapprehended:

TABLE IV. 

 Ratio of Beat-interval Value in Seconds of Average Interval, to Group-interval. 5/12 3/12 2/12 1. 000: 1. 400 3. 5 5. 3 9. 0 1. 000: 1. 000 4. 0 5. 4 9. 6 1. 000: 0. 714 5. 2 8. 4 10. 8

The quantitative relations presented by these figures are consistentthroughout. For every rate of speed the average rhythmic group issmallest when the interval separating the successive groups is at itsmaximum; it is largest when this interval is at its minimum; while ineach case a median value is presented by the relation of uniformityamong the intervals. In the second as well as the first of the ratiosincluded in the foregoing table the interval which separates adjacentgroups is felt to be distinctly longer than that internal to thegroup; in the third the relative durations of the two intervals arethose which support psychological uniformity. In the latter case, inconsequence of the freer passage from group to group, the continuityof the rhythmical series is more perfectly preserved than in theformer, and the integration of its elements into higher syntheses moreextended. 

The extension of the numerical limits of the rhythm group insubjective rhythm which appear in consequence of progressiveacceleration in the rate of succession is given for a series of sixdifferent values of the separating intervals in the following table, the figures of which represent the average for six observers:

TABLE V. 

 HIGHEST UNITS WHICH APPEAR. 

 Value of interval in secs. : 12/12 7/12 5/12 3/12 2/12 1/12 No. Of el's in rhythm group: 2. 5 3. 0 4. 0 7. 0 9. 0 11. 0 Average duration of group: 2. 500 1. 750 1. 666 1. 750 1. 500 0. 917

 SIMPLE UNITS. 

 No. Of els. In simplest group: 2. 5 2. 3 2. 9 3. 7 4. 7 5. 0 Duration of simplest group: 2. 50 1. 34 1. 21 0. 92 0. 78 0. 41

The rate of increase here presented in the number of elements is notsufficiently rapid to counterbalance the acceleration of speed andmaintain a constancy in the duration of the group. The greatest valueof this period is coördinated with the slowest rate of succession, thelowest with the most rapid. As the speed increases, the duration ofthe rhythmic unit is shortened. Its average duration for all rateshere included is 1. 680 sec. , or, without the first of the series(one-second intervals, at which only two of the observers received theimpression of rhythm), 1. 516 sec. These values are not for thesimplest combinations, but for the highest synthetical unit which wasimmediately apprehended in the series of stimulations. Thiscompounding becomes more pronounced as the rate of succession isaccelerated, but even at intervals of 5/12 and 7/12 sec. It is thecharacteristic mode of apprehension. 

The number of elements in the simple groups of which these higherunits are composed, and their average duration, are also given in thetable. These likewise show a progressive increase in number, but of amuch slower rate than that manifested by the total synthesis ofelements. That is to say, in subjective rhythm as well as inobjectively figured series, subordinate rhythmical differences in thematerial sink out of consciousness less rapidly than the inclusion offresh elements takes place; in other words, the organic complexity ofthe rhythmic unit increases with every acceleration in the rate ofsuccession. The duration of these simple structural groups, as may beinferred, decreases with such acceleration, but at a much more rapidrate than is the case with the total reach of rhythmical apprehension, the value of that unit which appears in connection with the highestspeed here included being less than half a second. The 'liveliness' ofsuch rapid measures is thus a resultant of several factors. It is nota consequence solely of the more rapid rate at which the individualstimuli succeed one another, but depends also on the shortening of theperiods of both these rhythmical units and on the progressivedivergence of the simple from the complex group. 

The influence of the rate of succession on the rhythmical unit is notconfined to its segregation from adjacent groups, but affects theinternal configuration of the measure as well. With every accelerationin rate the relative preponderance of the interval following theaccented element (in rhythms having initial stress) increases; as therate is retarded, smaller and smaller degrees of difference in thevalues of accented and unaccented intervals are discriminated. In thisregard the influence of reduction in the absolute value of theseparating intervals is analogous to that of increased accentuationwithin the group. In fast tempos and with high degrees of emphasis theinterval following the initial accent is relatively longer, thatfollowing the unaccented relatively shorter, than at slow tempos andwith weak emphasis. This is but another way of expressing the factthat as the elements of the auditory series succeed one another moreand more slowly the impression of rhythm fades out and that as theirsuccession increases in rapidity the impression becomes more and morepronounced. The following table presents these relations in aquantitative form for trochaic rhythm. The figures represent thenumber of times the second, or group interval, was judged to begreater than, equal to, or less than the first or internal interval ofthe group. Three rates were compared together, having averageintervals of 5/12, 3/12 and 2/12 sec. Six observers took part, butonly a small number of judgments was made by each, to which fact isprobably to be attributed the irregularities of form which appear inthe various curves:

TABLE VI. 

 Ratio of 1st to 2d 5/12 3/12 2/12 Interval + = - + = - + = - 1. 000: 1. 057 95. 0 0. 0 5. 0 100. 0 0. 0 0. 0 100. 0 0. 0 0. 0 1. 000: 1. 000 94. 7 5. 3 0. 0 86. 0 10. 5 3. 5 87. 5 12. 5 0. 0 1. 000: 0. 895 40. 0 60. 0 0. 0 46. 2 49. 6 3. 3 74. 1 18. 5 7. 4 1. 000: 0. 846 41. 0 50. 0 9. 0 39. 4 54. 6 6. 0 40. 0 52. 0 8. 0 1. 000: 0. 800 20. 0 60. 0 20. 0 13. 0 70. 0 17. 0 53. 8 46. 2 0. 0 1. 000: 0. 756 29. 4 23. 5 47. 1 21. 8 43. 4 34. 8 28. 0 72. 0 0. 0

 Av. For all ratios, 53. 3 33. 1 13. 5 51. 1 38. 0 10. 8 63. 9 33. 5 2. 6

Within the limits of its appearance, as the figures just presentedindicate, the force, definition and persistency of the rhythmicalimpression do not continue uniform. At the lowest rates at whichrhythm appears the integration of the successive groups is weak andtheir segregation indistinct. As the rate increases the definition ofthe rhythmic form grows more precise, group is separated from group bygreater apparent intervals, and the accentuation of the groupsbecomes more pronounced. In subjective rhythmization of anundifferentiated series, likewise, the impression of segregation andperiodic accentuation grows more forcible and dominating as the rateincreases. The sensitiveness to form and dynamic value in thesuccessive groups also increases up to a certain point in the processof acceleration. As expressed in the capacity to discriminatedepartures from formal equivalence among the groups, this functionreached its maximum, for those concerned in this investigation, atrates varying individually from 0. 3 sec. To 0. 6 sec. In the value oftheir intervals. 

It is in virtue of its nature as an impression, as opposed to aconstruction, that every structural unit, and every rhythmicalsequence into which it enters, possesses a distinct individualquality, by which it is immediately apprehended and discriminated fromother forms, as the face of an acquaintance is remembered andidentified without detailed knowledge of the character of any featureit possesses. For what persists from the reception of a rhythmimpression and becomes the basis of future recognition andreproduction of it, is not the number of beats in a unit or sequence, nor the absolute or relative intensity of the components of the group;it is the quality of the groups as individuals, and the form of thesequence as a whole. The phrase and verse are as vividly conceived asthe unit group; the stanza or the passage is apprehended asimmediately and simply as the bar or the measure. Of the number andrelation of the individual beats constituting a rhythmical sequencethere is no awareness whatever on the part of the ęsthetic subject. Isay this without qualification. So long as the rhythmical impressionendures the analytic unit is lost sight of, the synthetic unit, orgroup, is apprehended as a simple experience. When the rhythm functionis thoroughly established, when the structural form is well integratedor familiar, it becomes well-nigh impossible to return to the analyticattitude and discern the actual temporal and intensive relations whichenter into the rhythm. Even the quality of the organic units may lapsefrom distinct consciousness, and only a feeling of the form of thewhole sequence remain. The _Gestaltsqualität_ of the passage or thestanza is thus frequently appreciated and reproduced without anawareness of its sequential relations, though with the keenest senseof what is necessary to, or inconsistent with, its structure; so thatthe slightest deviation from its form is remarked and the wholesequence accurately reproduced. 

In order to isolate and exhibit the tendency toward rhythmization inregularly repeated motor reactions, one should examine series ofsimilar movements made at different rates both as an accompaniment toa recurrent auditory stimulus and as free expressions of the motorimpulse independent of such objective control. In the former of thesecases the series of stimuli should be undifferentiated in quality aswell as uniform in time. The rhythm which appears in such a case willcontradict the phases of an objective series which prescribes itsform, and the evidence of its existence, presented under such adverseconditions, should be indubitable. 

As preliminary to their special work the members of the experimentalgroup were tested in regard to the promptness and regularity of theirreactions (by finger flexion) in accompanying a periodically recurrentstimulus given by the beating of a metronome; records were taken alsoof their capacity to estimate and maintain constant time relations byfreely tapping at intervals of one, two and five seconds. Of thelatter type of reaction the records show that a temporal grouping ofthe reactions is presented in every rate of tapping. This, owing tothe large absolute intervals, is uniformly in groups of two, the firstmember of which is of shorter, the second of longer duration. There islikewise an intensive differentiation of the alternate reactions. Thusa double rhythmical treatment appears, but while with intervals of twoseconds the phases of temporal and intensive rhythm coincide, at ratesof one and five seconds they are opposed, that is, the accentuationfalls on the initial reaction which is followed by the shorterinterval. This doubtlessly marks the emergence of that tendency toinitial accentuation which was subsequently found to prevail in allexpression of rhythm. 

The types of reaction which these records afford leave no doubt that afuller investigation of the matter would show the constant presence, in all such forms of activity, of a rhythmical automatization of theseries. The special problems which such an investigation should firstresolve, relate to the dependence of the amount of rhythmicaldifferentiation on the rate of succession among the reactions; therelation of the form of this reaction series to factors of attentionand control; and the significance, in connection with the process ofrhythmization, of auditory stimuli produced by and accompanying thereaction series, that is, the comparison of soundless and soundedreactions. 

In the second set of experiments the reactor was directed simply toaccompany the beating of a metronome by a light tapping with theforefinger on a rubber-surfaced tambour connected with a pneumographicregistering pen, with which was aligned an electrical time-marker alsoactuated by the metronome. Three rates of tapping were adopted, 60, 90and 120 beats per minute. No specific instructions were given as todirection or keenness of attention on the part of the reactor; themost natural and simple accompaniment was desired. Occasionally, forcomparison, the reactor was directed to attend closely to eachsuccessive beat as it occurred. 

Certain questions as to the applicability of the material hereinterpreted to the point in question, and as to its relation to theobjective conditions of experimentation, must be met at the outset. The first of these is as to the actual uniformity of the metronomeseries. Objective determination of its temporal regularity isunnecessary (in so far as such a determination looks toward anexplanation of the form of tapping by reference to inequality in themetronomic intervals). That the rhythmical phases which appear in theaccompaniment are not due to inequality in the stimulation intervals, is shown by the reversal of relations between the metronome and itsaccompaniment which occur in the midst of a continuous series of taps. To speak roughly, a break occurs every twentieth beat. I do not referto minor irregularities occurring within the single group but notaffecting the form of the rhythmical accompaniment. The latterappeared with surprising rarity, but when found were included in thecontinuous calculation of averages. But in every score or so of beatsa stroke out of series would be interpolated, giving the form| 1 >2 [1] 2 >1 |; the accompaniment being coördinated during thesecond portion of the whole series with opposite phases of themetronome from those with which its elements were connected in theearlier part. Moreover, the dependence of this grouping of the soundson subjective attitudes may readily be made to appear. When attentionis turned keenly on the process its phases of rhythmicaldifferentiation decline; when the accompaniment becomes mechanicalthey mount in value. When the observer tries to mark the ticking asaccurately as possible, not only does the index of his motor reactionsbecome more constant, but the sounds of the instrument likewise appearmore uniform. The observers report also that at one and the same timethey are aware of the regularity of the metronome and the rhythmicalnature of their tapping, while yet the conviction remains that theaccompaniment has been in time with the beats. Furthermore, if thephases of ticking in the metronome were temporarily unlike, the motoraccompaniment by a series of observers, if accurate, should reproducethe time-values of the process, and if inaccurate, should present onlyan increase of the mean variation, without altering the characteristicrelations of the two phases. On the other hand, if the series beuniform and subjectively rhythmized by the hearer, there should beexpected definite perversions of the objective relations, presenting aseries of increasing departures from the original in proportion as thetendency to rhythmize varied from individual to individual. 

On the other hand, a rhythm is already presented in the sounds of themetronome, occasioned by the qualitative differentiation of themembers of each pair of ticks, a variation which it was impossible toeliminate and which must be borne in mind in estimating the followingresults. 

Five reactors took part in the experiment, the results of which aretabulated in the following pages. The figures are based on series ofone hundred reactions for each subject, fifty accompaniments to eachswing and return of the metronome pendulum. When taken in series often successive pairs of reactions, five repetitions of the series willbe given as the basis of each average. The quantitative results arestated in Tables VII. -XIV. , which present the proportional values ofthe time intervals elapsing between the successive reactions of anaccompaniment to the strokes of a metronome beating at the rates of60, 90 and 120 per minute. 

TABLE VII. 

 I. AVERAGES ACCORDING TO REACTORS OF ALL RATES FOR BOTH PHASES. 

 (_a_) In Series of Ten Successive Pairs of Beats. 

 Subject. I II III IV V VI VII VIII IX X

 J. 1. 000 1. 005 1. 022 1. 053 1. 044 1. 116 1. 058 1. 061 1. 055 1. 052 K. 1. 000 1. 027 1. 057 1. 111 1. 093 1. 086 1. 074 1. 096 1. 093 1. 071 N. 1. 000 1. 032 1. 062 0. 990 1. 009 0. 980 1. 019 1. 040 1. 067 1. 040

 Aver. 1. 000 1. 021 1. 047 1. 051 1. 049 1. 061 1. 050 1. 066 1. 072 1. 054

TABLE VIII. 

 (_b_) First and Second Halves of the Preceding Combined in Series of Five. 

 Subject. I II III IV V J. 1. 058 1. 031 1. 041 1. 054 1. 048 K. 1. 043 1. 050 1. 076 1. 102 1. 082 N. 0. 990 1. 025 1. 051 1. 028 1. 024

 Aver. 1. 030 1. 035 1. 056 1. 061 1. 051

TABLE IX. 

 AVERAGES OF ALL RATES AND SUBJECTS ACCORDING TO PHASES OF METRONOME. 

 (_a_) In Series of Ten Successive Reactions in Accompaniment of Each Phase. 

 Phase. I II III IV V VI VII VIII IX X First, 1. 000 1. 055 1. 102 1. 097 1. 082 1. 066 1. 053 1. 123 1. 120 1. 074 Second, 1. 000 0. 988 0. 992 1. 007 1. 016 1. 055 1. 015 1. 009 1. 024 1. 001

TABLE X. 

 (_b_) First and Second Halves of the Preceding Combined in Series of Five. 

 Phase. I II III IV V First, 1. 033 1. 054 1. 112 1. 108 1. 078 Second, 1. 027 1. 001 1. 000 1. 015 1. 008

TABLE XI. 

 AVERAGES OF ALL SUBJECTS ACCORDING TO RATES AND PHASES OF METRONOME. 

 (_a_) First Phase, Series of Ten Successive Reactions. 

 Rate. _I II III IV V VI VII VIII IX X_ 60 1. 000 1. 168 1. 239 1. 269 1. 237 1. 209 1. 265 1. 243 1. 237 1. 229 90 1. 000 1. 048 1. 063 1. 095 1. 086 1. 069 1. 102 1. 127 1. 168 1. 095 120 1. 000 1. 004 0. 942 1. 043 1. 057 0. 978 0. 949 1. 065 1. 065 0. 967

TABLE XII. 

 (_b_) Second Phase, Series of Ten Successive Reactions. 

 Rate. I II III IV V VI VII VIII IX X 60 1. 000 0. 963 0. 942 0. 947 1. 009 0. 695 0. 993 0. 995 1. 023 0. 996 90 1. 000 0. 893 0. 987 1. 018 1. 036 1. 005 0. 995 1. 000 0. 977 1. 000 120 1. 000 1. 000 0. 990 1. 048 1. 040 1. 007 0. 986 1. 030 1. 037 0. 962

TABLE XIII. 

 AVERAGES OF ALL SUBJECTS AND BOTH PHASES OF METRONOME ACCORDING TO RATES. 

 (_a_) In Series of Ten. 

 Rate. I II III IV V VI VII VIII IX X 60 1. 000 1. 065 1. 140 1. 108 1. 123 0. 952 1. 129 1. 119 1. 130 1. 112 90 1. 000 0. 970 1. 025 1. 056 1. 061 1. 037 1. 048 1. 063 1. 072 1. 047 120 1. 000 1. 000 0. 990 1. 048 1. 040 1. 007 0. 986 1. 030 1. 037 0. 962

TABLE XIV. 

 (_b_) Above Combined in Series of Five. 

 Rate. I II III IV V 60 0. 976 1. 097 1. 129 1. 119 1. 117 90 1. 018 1. 009 1. 044 1. 059 1. 054 120 1. 003 0. 993 1. 010 1. 042 1. 001

In the following table (XV. ) is presented the average proportionalduration of the intervals separating the successive reactions of thesesubjects to the stimulations given by the alternate swing and returnof the pendulum. 

TABLE XV. 

 Subject. Rate: 60. Rate: 90. Rate: 120. B. 0. 744 : 1. 000 0. 870 : 1. 000 0. 773 : 1. 000 J. 0. 730 : 1. 000 0. 737 : 1. 000 0. 748 : 1. 000 K. 0. 696 : 1. 000 0. 728 : 1. 000 0. 737 : 1. 000 N. 0. 526 : 1. 000 0. 844 : 1. 000 0. 893 : 1. 000

The corresponding intensive values, as measured by the excursion ofthe recording pen, are as follows:

TABLE XVI. 

 Subject. Rate: 60. Rate: 90. Rate: 120. B. (1. 066 : 1. 000) 0. 918 : 1. 000 (1. 010 : 1. 000) J. 0. 938 : 1. 000 0. 943 : 1. 000 0. 946 : 1. 000 K. 0. 970 : 1. 000 0. 949 : 1. 000 (1. 034 : 1. 000) N. 0. 883 : 1. 000 0. 900 : 1. 000 0. 950 : 1. 000

These figures present a double process of rhythmic differentiation, intensively into stronger and weaker beats, and temporally intolonger and shorter intervals. The accentuation of alternate elementshas an objective provocative in the qualitative unlikeness of theticks given by the swing and return of the pendulum. This phase is, however, neither so clearly marked nor so constant as the temporalgrouping of the reactions. In three cases the accent swings over tothe shorter interval, which, according to the report of the subjects, formed the initial member of the group when such grouping came tosubjective notice. This latter tendency appears most pronounced at thefastest rate of reaction, and perhaps indicates a tendency at rapidtempos to prefer trochaic forms of rhythm. In temporal grouping thecoördination of results with the succession of rates presents anexception only in the case of one subject (XV. B, Rate 120), and thevarious observers form a series in which the rhythmizing tendencybecomes more and more pronounced. 

Combining the reactions of the various subjects, the average for allshows an accentuation of the longer interval, as follows:

TABLE XVII. 

 Rate. Temp. Diff. Intens. Diff. 60 0. 674 : 1. 000 0. 714 : 1. 000 90 0. 795 : 1. 000 0. 927 : 1. 000 120 0. 788 : 1. 000 0. 985 : 1. 000

The rhythmical differentiation of phases is greatest at the slowesttempo included in the series, namely, one beat per second, and itdeclines as the rate of succession increases. It is impossible fromthis curve to say, however, that the subjective rhythmization ofuniform material becomes more pronounced in proportion as theintervals between the successive stimulations increase. Below acertain rapidity the series of sounds fails wholly to provoke therhythmizing tendency; and it is conceivable that a change in thedirection of the curve may occur at a point beyond the limits includedwithin these data. 

The introduction from time to time of a single extra tap, with theeffect of transposing the relations of the motor accompaniment to thephases of the metronome, has been here interpreted as arising from aperiodically recurring adjustment of the reaction process to theauditory series which it accompanies, and from which it has graduallydiverged. The departure is in the form of a slow retardation, thereturn is a swift acceleration. The retardation does not alwayscontinue until a point is reached at which a beat is dropped from, oran extra one introduced into, the series. In the course of a set ofreactions which presents no interpolation of extra-serial beatsperiodic retardation and acceleration of the tapping take place. Thistertiary rhythm, superimposed on the differentiation of simple phases, has, as regards the forms involved in the present experiments, aperiod of ten single beats or five measures. 

From the fact that this rhythm recurs again and again without theintroduction of an extra-serial beat it is possible to infer therelation of its alternate phases to the actual rate of the metronome. Since the most rapid succession included was two beats per second, itis hardly conceivable that the reactor lost count of the beats in thecourse of his tapping. If, therefore, the motor series in generalparallels the auditory, the retardations below the actual metronomerate must be compensated by periods of acceleration above it. Regardedin this light it becomes questionable if what has been called theprocess of readjustment really represents an effort to restore anequilibrium between motor and auditory processes after an involuntarydivergence. I believe the contrasting phases are fundamental, and thatthe changes represent a free, rhythmical accompaniment of theobjective periods, which themselves involve no such recurrentdifferentiation. 

Of the existence of higher rhythmic forms evidence will be afforded bya comparison of the total durations of the first and secondfive-groups included in the decimal series. Difference of some kind isof course to be looked for; equivalence between the groups would onlybe accidental, and inequality, apart from amount and constancy, isinsignificant. In the results here presented the differentiation is, in the first place, of considerable value, the average duration of thefirst of these groups bearing to the second the relation of1. 000:1. 028. 

Secondly, this differentiation in the time-values of the respectivegroups is constant for all the subjects participating. The ratios intheir several cases are annexed:

TABLE XVIII. 

 Subject. Ratio. J. 1. 000:1. 042 K. 1. 000:1. 025 N. 1. 000:1. 010

It is perhaps significant that the extent of this differentiation--andinferably the definition of rhythmical synthesis--corresponds to thereported musical aptitudes of the subjects; J. Is musically trained, K. Is fond of music but little trained, N. Is without musicalinclination. 

The relations of these larger rhythmical series repeat those of theirconstituent groups--the first is shorter, the second longer. The twosets of ratios are brought together for comparison in the annexedtable:

TABLE XIX. 

 Subject. Unit-Groups. Five Groups. J. 1. 000:1. 354 1. 000:1. 042 K. 1. 000:1. 388 1. 000:1. 025 N. 1. 000:1. 326 1. 000:1. 010

It is to be noted here, as in the case of beating out specificrhythms, that the index of differentiation is greater in simple thanin complex groups, the ratios for all subjects being, in simplegroups, 1. 000:1. 356, and in series of five, 1. 000:1. 026. 

There is thus present in the process of mechanically accompanying aseries of regularly recurring auditory stimuli a complex rhythmizationin the forms, first, of a differentiation of alternate intervals, andsecondly, of a synthesis of these in larger structures, a process heretraced to the third degree, but which may very well extend to thecomposition of still more comprehensive groups. The process ofreaction is permeated through and through by rhythmicaldifferentiation of phases, in which the feeling for unity andequivalence must hold fast through really vast periods as the longslow phases swing back and forth, upon which takes place a swift andyet swifter oscillation of rhythmical values as the unit groups becomemore limited, until the opposition of single elements is reached. 

III. THE CHARACTERISTICS OF THE RHYTHMICAL UNIT. 

A. _The Number of Elements in the Group and its Limits. _

The number of elements which the rhythmical group contains is related, in the first place, to the rate of succession among the elements ofthe sequence. This connection has already been discussed in so far asit bears on the forms of grouping which appear in an undifferentiatedseries of sounds in consequence of variations in the absolutemagnitude of the intervals which separate the successive stimuli. Insuch a case the number of elements which enter into the unit dependssolely on the rate of succession. The unit presents a continuousseries of changes from the lowest to the highest number ofconstituents which the simple group can possibly contain, and thesynthesis of elements itself changes from a succession of simple formsto structures involving complex subordination of the third and evenfourth degree, without other change in the objective series thanvariations in tempo. 

When objectively defined rhythm types are presented, or expression isgiven to a rhythm subjectively defined by ideal forms, these simplerelations no longer hold. Acceleration or retardation of speed doesnot unconditionally affect the number of elements which the rhythmgroup contains. In the rhythmization of an undifferentiated series therecurrence of accentuation depends solely on subjective conditions, the temporal relations of which can be displaced only within thelimits of single intervals; for example, if a trochaic rhythmcharacterizes a given tempo, the rhythm type persists under conditionsof progressive acceleration only in so far as the total duration ofthe two intervals composing the unit approximates more closely to thesubjective rhythm period than does that of three such intervals. When, in consequence of the continued reduction of the separating intervals, the latter duration presents the closer approximation, the previousrhythm form is overthrown, accentuation attaches to every thirdinstead of to alternate elements, and a dactylic rhythm replaces thetrochaic. 

In objective rhythms, on the other hand, the determination of specificpoints of increased stress makes it impossible thus to shift theaccentuation back and forth by increments of single intervals. Theunit of displacement becomes the whole period intervening between anytwo adjacent points of accentuation. The rhythm form in such cases isdisplaced, not by those of proximately greater units, but only by suchas present multiples of its own simple groups. Acceleration of thespeed at which a simple trochaic succession is presented results thus, first, in a more rapid trochaic tempo, until the duration of tworhythm groups approaches more nearly to the period of subjectiverhythmization, when--the fundamental trochaism persisting--theprevious simple succession is replaced by a dipodic structure in whichthe phases of major and minor accentuation correspond to theelementary opposition of accented and unaccented phases. In the sameway a triplicated structure replaces the dipodic as the accelerationstill continues; and likewise of the dactylic forms. 

We may say, then, that the relations of rate to complexity ofstructure present the same fundamental phenomena in subjectiverhythmization and objectively determined types, the unit of changeonly differing characteristically in the two cases. The wider range ofsubjective adjustment in the latter over the former experience is dueto the increased positive incentive to a rhythmical organicaccompaniment afforded by the periodic reinforcement of the objectivestimulus. 

An investigation of the limits of simple rhythmical groups is notconcerned with the solution of the question as to the extent to whicha reactor can carry the process of prolonging the series of elementsintegrated through subordination to a single dominant accentuation. The nature of such limits is not to be determined by the introspectiveresults of experiments in which the observer has endeavored to holdtogether the largest possible number of elements in a simple group. When such an attempt is made a wholly artificial set of conditions, and presumably of mechanisms, is introduced, which makes theexperiment valueless in solving the present problem. Both thedirection and the form of attention are adverse to the detection ofrhythmical complications under such conditions. Attention is directedaway from the observation of secondary accents and toward therealization of a rhythm form having but two simple phases, the firstof which is composed of a single element, while within the latterfall all the rest of the group. Such conditions are the worst possiblefor the determination of the limits of simple rhythm groups; for theobserver is predisposed from the outset to regard the whole group ofelements lying within the second phase as undifferentiated. Thus theconditions are such as to postpone the recognition of secondaryaccents far beyond the point at which they naturally arise. 

But further, such an attempt to extend the numerical scope of simplerhythm groups also tends to transform and disguise the mechanism bywhich secondary stresses are produced, and thereby to create theillusion of an extended simple series which does not exist. For wehave no right to assume that the process of periodic accentuation insuch a series, identical in function though it be, involves always thesame form of differentiation in the rhythmical material. If theprimary accentuation be given through a finger reaction, the fixatingof that specific form of change will predispose toward an overlookingof secondary emphases depending on minor motor reactions of adifferent sort. The variety of such substitutional mechanisms is verygreat, and includes variations in the local relations of the fingerreaction, movements of the head, eyes, jaws, throat, tongue, etc. , local strains produced by simultaneous innervation of flexor andextensor muscles, counting processes, visual images, and changes inideal significance and relation of the various members of the group. Any one of these may be seized upon to mediate the synthesis ofelements and thus become an unperceived secondary accentuation. 

Our problem is to determine at what point formal complication of therhythmical unit tends naturally to arise. How large may such a groupbecome and still remain fundamentally simple, without reduplication ofaccentual or temporal differentiation? The determination of suchlimits must be made on the basis of quantitative comparison of thereactions which enter into larger and smaller rhythmical series, onthe one hand, and, on the other, of the types of structure whichappear in subjective rhythmization and the apprehension of objectiverhythms the forms of which are antecedently unknown to the hearer. Theevidence from subjective rhythms is inconclusive. The prevailingtypes are of two and three beats. Higher forms appear which areintrospectively simple, but introspection is absolutely unable tosolve the problem as to the possible composite nature of theseextended series. The fact that they are confined to even numbers, themultiples of two, and to such odd-numbered series as are multiples ofthree, without the appearance of the higher primes, indicates theexistence in all these groups of secondary accentuation, and theresolution of their forms into structures which are fundamentallycomplications of units of two and three elements only. The process ofpositive accentuation which appears in every higher rhythmical series, and underlying its secondary changes exhibits the same reduction oftheir elementary structure to double and triple groups, has beendescribed elsewhere in this report. Here it is in place to point outcertain indirect evidence of the same process of resolution asmanifested in the treatment of longer series of elements. 

The breaking up of such series into subgroups may not be an explicitlyconscious process, while yet its presence is indispensable in givingrhythmical form to the material. One indication of suchundiscriminated rhythmical modification is the need of making oravoiding pauses between adjacent rhythmical groups according as thenumber of their constituents varies. Thus, in rhythms having units offive, seven, and nine beats such a pause was imperative to preservethe rhythmical form, and the attempt to eliminate it was followed byconfusion in the series; while in the case of rhythms having units ofsix, eight, and ten beats such a pause was inadmissible. This is theconsistent report of the subjects engaged in the presentinvestigation; it is corroborated by the results of a quantitativecomparison of the intervals presented by the various series ofreactions. The values of the intervals separating adjacent groups fora series of such higher rhythms are given in Table XX. As proportionsof those following the initial, accented reaction. 

TABLE XX. 

 Rhythm. Initial Interval. Final Interval Five-Beat, 1. 000 1. 386 Six " 1. 000 0. 919 Seven " 1. 000 1. 422 Eight " 1. 000 1. 000 Nine " 1. 000 1. 732 Ten " 1. 000 1. 014

The alternate rhythms of this series fall into two distinct groups invirtue of the sharply contrasted values of their final intervals orgroup pauses. The increased length of this interval in theodd-numbered rhythms is unquestionably due to a subdivision of theso-called unit into two parts, the first of which is formallycomplete, while the latter is syncopated. In the case of five-beatrhythms, this subdivision is into threes, the first three of the fivebeats which compose the so-called unit forming the primary subgroup, while the final two beats, together with a pause functionallyequivalent to an additional beat and interval, make up the second, thesystem being such as is expressed in the following notation:| . Q. Q q; >q. Q % |. The pause at the close of the group isindispensable, because on its presence depends the maintenance ofequivalence between the successive three-groups. On the other hand, the introduction of a similar pause at the close of a six-beat groupis inadmissible, because the subdivision is into three-beat groups, each of which is complete, so that the addition of a final pause wouldutterly unbalance the first and second members of the composite group, which would then be represented by the following notation:| >q. Q q; . Q. Q q % |; that is, a three-group would alternate with afour-group, the elements of which present the same simple timerelations, and the rhythm, in consequence, would be destroyed. Thesame conditions require or prevent the introduction of a final pausein the case of the remaining rhythm forms. 

The progressive increase in the value of the final interval, whichwill be observed in both the odd-and even-numbered rhythms, isprobably to be attributed to a gradual decline in the integration ofthe successive groups into a well-defined rhythmical sequence. 

This subdivision of material into two simple phases penetrates allrhythmical structuring. The fundamental fact in the constitution ofthe rhythmical unit is the antithesis of two phases which we call theaccented and the unaccented. In the three-beat group as in thetwo-beat, and in all more complex grouping, the primary analysis ofmaterial is into these two phases. The number of discriminableelements which enter each phase depends on the whole constitution ofthe group, for this duality of aspect is carried onward from its pointof origin in the primary rhythm group throughout the most complexcombination of elements, in which the accented phase may comprise anindefinitely great number of simple elements, thus:

 ______ __________ ______________ / \ / \ / \ > . > . >> . | q q ; q q |, | q q q; q q q |, | q q q q; q q q q |, etc. \_/ >

An indication of this process of differentiation into major and minorphases appears in the form of rhythm groups containing upwards of fourelements. In these the tendency is, as one observer expresses it, 'toconsider the first two beats as a group by themselves, with the otherstrailing off in a monotonous row behind. ' As the series of elementsthus bound up as a unit is extended, the number of beats which arecrowded into the primary subgroup also increases. When the attempt wasmade to unite eleven or twelve reactions in a single group, the firstfour beats were thus taken together, with the rest trailing off asbefore. It is evident that the lowest groups with which attentionconcerned itself here were composed of four beats, and that the actualform of the (nominally) unitary series of eleven beats was as follows:

 _______________________ / \ >> > > | q q q q; q q q q; q q q q |. . . . 

The subscripts are added in the notation given above because it is tobe doubted if a strictly simple four-beat rhythm is ever met with. Ofthe four types producible in such rhythm forms by variation in theaccentual position, three have been found, in the course of thepresent investigation, to present a fundamental dichotomy into unitsof two beats. Only one, that characterized by secondary accentuation, has no such discriminable quality of phases. Of this form two thingsare to be noted: first, that it is unstable and tends constantly torevert to that with initial stress, with consequent appearance ofsecondary accentuation; and second, that as a permanent form itpresents the relations of a triple rhythm with a grace note prefixed. 

The presence of this tendency to break up the four-rhythm intosubgroups of two beats explains a variety of peculiarities in therecords of this investigation. The four-beat rhythm with final accentis found most pleasant at the close of a rhythmical sequence. Thepossibility of including it in a continuous series depends on havingthe final interval of 'just the right length. ' If one keeps in mindthat a secondary initial accent characterizes this rhythm form, thevalue required in this final interval is explained by the resolutionof the whole group into two units of three beats each, the latter ofthe two being syncopated. The pause is of 'just the right length' whenit is functionally equal to two unaccented elements with theirsucceeding intervals, as follows: | . Q. Q q; . Q % % |. 

Likewise in four-rhythms characterized by initial stress there appearsa tendency to accent the final beat of the group, as well as that toaccent the third. Such a series of four may therefore break up ineither of two ways, into | >q. Q; . Q q | on a basis of two-beat units, or into | . Q. Q q; >q % %| on a basis of three-beat units. 

The persistence of these simple equivalences appears also in thetreatment of syncopated measures and of supplementary or displacedaccents. Of the form | >q. Q >q. | one reactor says, and hisdescription may stand for all, "This deliberate introduction of athird accent on the last beat is almost impossible for me to keep. Thesingle group is easy enough and rather agreeable, but in a successionof groups the secondarily accented third beat comes against the firstof the next group with a very disagreeable effect. " This is the casewhere no pause intervenes between the groups, in which case the rhythmis destroyed by the suppression, in each alternate simple group, ofthe unaccented phase; thus, | >q. Q >q. | alone is pleasant, becauseit becomes | . Q. Q; >q % |, but in combination with preceding andsucceeding groups it is disagreeable, because it becomes in reality| >q. Q; . Q % |, etc. A long pause between the groups destroys thisdisagreeableness, since the lacking phase of the second subgroup isthen restored and the rhythm follows its normal course. 

The amphibrachic form, | >q q. Q |, is more difficult to maintain thaneither the dactylic or the trochaic, and in a continuous series tendsto pass over into one of these, usually the former. 'With sufficientpause, ' the reactors report, 'to allow the attitude to die away, ' itis easily got. The same inability to maintain this form inconsciousness appears when a continuous series of clicks is given, every third of which is louder than the rest. Even when the beginningof the series is made coincident with the initial phase of theamphibrachic group the rhythmic type slips over into the dactylic, inspite of effort. In this, as in the preceding type of reaction, if theinterval separating adjacent groups be lengthened, the rhythm ismaintained without trouble. The 'dying away' of the attitude liesreally in such an arrangement of the intervals as will formallycomplete a phrase made up of simple two-beat units. 

The positive evidence which this investigation affords, points to theexistence of factors of composition in all rhythms of more than threebeats; and a variety of peculiarities which the results present can beexplained--and in my estimation explained only--on the basis of suchan assumption. I conclude, therefore, that strictly stated thenumerical limit of simple rhythm groups is very soon reached; thatonly two rhythmical units exist, of two and three beats respectively;that in all longer series a resolution into factors of one of thesetypes takes place; and, finally, that the subordination of higherrhythmical quantities of every grade involves these simple relations, of which, as the scope of the synthesis increases, the opposition ofsimple alternate phases tends more and more to predominate overtriplicated structures. 

Variation in the number of elements which enter into the rhythmicunit does not affect the sense of equivalence between successivegroups, so long as the numerical increase does not reach a point atwhich it lessens the definiteness of the unit itself. For the purposeof testing this relation the reactors beat out a series of rhythmforms from 'one-beat' rhythms to those in which the group consisted ofseven, eight and nine elements, and in which the units were eitheridentical with one another or were made up of alternately larger andsmaller numbers of elements. Two questions were to be answered in eachcase; the manner in which these various changes affected the sense ofrhythmical equivalence in the alternate groups, and the variations inaffective quality which these changes introduced into the experience. With the former of these problems we are here concerned. From'one-beat' to four-beat rhythms the increase in number of constituentsin no way affects the sense of rhythmical equivalence. Beyond thispoint there is a distinct falling off. 'The first part of the rhythmbegins to fade away before the end of the second, ' says one; andanother: 'The series then reverts to a monotonous succession withoutfeeling of rhythm. ' This decline marks those groups composed of an oddnumber of elements much earlier and more strongly than those whichcontain an even number. The sense of equivalence has fallen off atfive and practically disappears at seven beats, while groups of sixand eight retain a fairly definite value as units in a rhythmicalsequence. This peculiar relation must be due to the subconsciousresolution of the larger symmetrical groups into smaller units ofthree and four constituents respectively. 

Likewise the introduction of variations in the figure of thegroup--that is, in the number of elements which enter into the groupsto be compared, the distribution of time values within them, theposition of accents, rests, and the like--does not in any way affectthe sense of equivalence between the unlike units. Against a group oftwo, three, four, or even five elements may be balanced a syncopatedmeasure which contains but one constituent, with the sense of fullrhythmical equivalence in the functional values of the two types. Indeed, in the case of five-beat rhythms the definition of values isgreater when such opposition finds place than when the five-beatgroup is continuously repeated. This is to be explained doubtlessly bythe more definite integration into a higher rhythmical unity which isafforded under the former conditions. 

The number and the distribution of elements are factors variable atwill, and are so treated in both musical and poetical expression. Thecondition which cannot be transgressed is the maintenance of stricttemporal relations in the succession of total groups which constitutethe rhythmical sequence. These relations are, indeed, not invariablefor either the single interval or the duration of the whole group, butthey are fixed functions of the dynamic values of these elements andunits. Two identically figured groups (_e. G. _, | >q. Q q | >q. Q q |), no more possess rhythmically substitutionary values than does theopposition of a single beat to an extended series (_e. G. _, | >q. | >q. Q q | ), apart from this factor of temporal proportion. Those groups which are identical in figure must also be uniform induration if they are to enter as substitutionary groups into arhythmical sequence. [5] When the acatalectic type is alternatelydeparted from and returned to in the course of the rhythmicalsequence, the metrical equivalents must present total time-valueswhich, while differing from that of the full measure in direction anddegree, in dependence on the whole form of their structure, maintainsimilar fixed relations to the primary type. The changes which theseflexible quantities undergo will here only be indicated. If thesubstitutionary groups be of different figures, that which comprisesthe larger number of elements will occupy the greater time, that whichcontains fewer, the less. 

 [5] Theoretically and strictly identical; this abstracts from the coördination of such identical groups as major and minor components of a higher rhythmical synthesis, which is really never absent and in virtue of which the temporal values of the groups are also differentiated. 

I do not forget the work of other observers, such as Brücke, who findsthat dactyls which appear among trochees are of less duration than thelatter, nor do I impugn their results. The rhythmical measure cannotbe treated as an isolated unit; it must always be considered in itsstructural relations to the rhythmical sequence of which it forms apart. Every non-conforming measure is unquestionably affected by theprevailing type of the rhythmical sequence in which it occurs. Brückepoints out the converse fact that those trochees and iambs are longestwhich appear in dactylic or other four-measures; but this ignores thecomplexity of the conditions on which the character of these intrusivetypes depends. The time-values of such variants are also dependent onthe numerical preponderance of the typical form in the whole series. When a single divergent form appears in the sequence the dynamicrelations of the two types is different from that which obtains whenthe numbers of the two approach equality, and the effect of theprevailing form on it is proportionally greater. Secondly, thecharacter of such variants is dependent on the subordinateconfiguration of the sequence in which they appear, and on theirspecific functions within such minor rhythmical figures. The relativevalue of a single dactyl occurring in an iambic pentameter line cannotbe predicated of cases in which the two forms alternate with eachother throughout the verse. Not only does each type here approximatethe other, but each is affected by its structural relation to theproximately higher group which the two alternating measures compose. Thirdly, the quantitative values of these varying forms is related totheir logical significance in the verse and the degree of accentuationwhich they receive. Importance and emphasis increase the duration ofthe measure; the lack of either shortens it. In this last factor, Ibelieve, lies the explanation of the extreme brevity of dactylsappearing in three-rhythms. When a specific rhythm type is departedfrom, for the purpose of giving emphasis to a logically or metricallyimportant measure, the change is characteristically in the directionof syncopation. Such forms, as has been said elsewhere, mark nodes ofnatural accentuation and emphasis. Hence, the dactyl introduced intoan iambic or trochaic verse, which, so far as concerns mere number ofelements, tends to be extended, may, in virtue of its characteristiclack of accentuation and significance, be contracted below the valueof the prevailing three-rhythm. Conversely the trochee introduced intoa dactylic sequence, in consequence of its natural accentuation orimportance, may exceed in time-value the typical four-rhythm formsamong which it appears. The detailed examination of the relation oftemporal variations to numerical predominance in the series, tosubordinate structural organization, and to logical accentuation, inour common rhythms, is a matter of importance for the generalinvestigation which remains still to be carried out. In so far as theconsideration of these factors entered into the experimental work ofthe present research, such quantitative time relations are given inthe following table, the two types in all cases occurring in simplealternation:

TABLE XXI. 

 Rhythm. 1st Meas. 2d Meas. Rhythm. 1st Meas. 2d Meas. 

 . > > > > . Q q q; q q % 1. 000 1. 091 q q %; q q q 1. 000 1. 140 . > > . Q q q; q q % 1. 000 1. 159 q q %; q q q 1. 000 1. 021 . > > . Q q q; q q % 1. 000 1. 025 q q %; q q q 1. 000 1. 267 > . . > q q q; q q % 1. 000 0. 984 q q %; q q q 1. 000 1. 112 > . . > q q q; q q % 1. 000 0. 766 q q %; q q q 1. 000 1. 119

As the disparity in numerical constitution increases, so will also thedivergence in time-value of the two groups concerned. Whendifferentiation into major and minor phases is present, the durationof the former will be greater than that of the latter. Hence, inconsequence of the combination of these two factors--_e. G. _, in asyncopated measure of unusual emphasis--the characteristic time-valuesmay be inverted, and the briefer duration attach to that unit whichcomprises the greater number of elements. Intensive values cannot takethe place of temporal values in rhythm; the time form is fundamental. Through all variations its equivalences must be adhered to. Stressmakes rhythm only when its recurrence is at regular intervals. Thenumber of subordinate factors which combine with the accented elementto make the group is quite indifferent. But whether few or many, orwhether that element on which stress falls stands alone (as it may), the total time values of the successive groups must be sensiblyequivalent. When a secondary element is absent its place must besupplied by a rest of equivalent time-value. If these proper temporalconditions be not observed no device of intensive accentuation willavail to produce the impression of metrical equivalence among thesuccessive groups. 

B. _The Distribution of Elements Within the Group. _

(_a_) The Distribution of Intensities. 

In the analysis of the internal constitution of the rhythmic unit, asin other parts of this work, the investigation follows two distinctlines, involving the relations of rhythm as apprehended, on the onehand, and the relations of rhythm as expressed, on the other; theresults in the two cases will be presented separately. A word as tothe method of presentation is necessary. The fact that in connectionwith each experiment a group of questions was answered gives rise tosome difficulty in planning the statement of results. It is a simplematter to describe a particular set of experiments and to tell all thefacts which were learned from them; but it is not logical, since oneobservation may have concerned the number of elements in the rhythmicunit, another their internal distribution, and a third theircoalescence in a higher unity. On the other hand, the statement ofeach of these in its own proper connection would necessitate therepetition of some description, however meager, of the conditions ofexperimentation in connection with each item. For economy's sake, therefore, a compromise has been made between reporting resultsaccording to distribution of material and according to distribution oftopics. The evidence of higher grouping, for example, which isafforded by variations in duration and phases of intensity inalternate measures, will be found appended to the sections on theserespective classes of material. 

In all the following sections the hammer-clang apparatus formed themechanism of experimentation in sensory rhythms, while in reactiverhythms simple finger-tapping was employed. 

In comparing the variations in stress which the rhythmical materialpresents, the average intensities of reaction for the whole group hasbeen computed, as well as the intensities of the single reactionswhich compose it. This has been done chiefly in view of the unstableintensive configuration of the group and the small amount of materialon which the figures are based. The term is relative; in ascertainingthe relations of intensity among the several members of the group, atleast ten successive repetitions, and in a large part of the workfifty, have been averaged. This is sufficient to give a clearpreponderance in the results to those characteristics which are reallypermanent tendencies in the rhythmical expression. This is especiallytrue in virtue of the fact that throughout these experiments thesubject underwent preliminary training until the series of reactionscould be easily carried out, before any record of the process wastaken. But when such material is analyzed in larger and smaller seriesof successive groups the number of reactions on which each average isbased becomes reduced by one half, three quarters, and so on. In sucha case the prevailing intensive relations are liable to be interferedwith and transformed by the following factor of variation. When awrong intensity has accidentally been given to a particular reactionthere is observable a tendency to compensate the error by increasingthe intensity of the following reaction or reactions. This indicates, perhaps, the presence of a sense of the intensive value of the wholegroup as a unity, and an attempt to maintain its proper relationsunchanged, in spite of the failure to make exact coördination amongthe components. But such a process of compensation, the disappearanceof which is to be looked for in any long series, may transpose therelative values of the accented elements in two adjacent groups whenonly a small number of reactions is taken into account, and make thatseem to receive the major stress which should theoretically receivethe minor, and which, moreover, does actually receive such a minorstress when the value of the whole group is regarded, and not solelythat member which receives the formal accentuation. 

The quantitative analysis of intensive relations begins with triplerhythms, since its original object was to compare the relativestresses of the unaccented elements of the rhythmic group. Thesevalues for the three forms separately are given in Table XXII. , inwhich the value of the accented element in each case is represented byunity. 

TABLE XXII. 

 Rhythm. 1st Beat. 2d Beat. 3d Beat. 

 Dactylic, 1. 000 0. 436 0. 349 Amphibrachic, 0. 488 1. 000 0. 549 Anapęstic, 0. 479 0. 484 1. 000

The dactylic form is characterized by a progressive decline inintensity throughout the series of elements which constitute thegroup. The rate of decrease, however, is not continuous. There is amarked separation into two grades of intensity, the element receivingaccentual stress standing alone, those which possess no accent fallingtogether in a single natural group, as shown in the following ratios:first interval to third, 1. 000:0. 349; second interval to third, 1. 000:0. 879. One cannot say, therefore, that in such a rhythmic formthere are two quantities present, an accented element and twoundifferentiated elements which are unaccented. For the average is notbased on a confused series of individual records, but is consistentlyrepresented by three out of four subjects, the fourth reversing therelations of the second and third elements, but approximating moreclosely to equivalence than any other reactor (the proportional valuesfor this subject are 1. 000; 0. 443; 0. 461). Moreover, this reactor wasthe only musically trained subject of the group, and one in whom thecapacity for adhering to the logical instructions of the experimentappears decidedly highest. 

In the amphibrachic form the average again shows three degrees ofintensity, three out of four subjects conforming to the same type, while the fourth reverses the relative values of the first and thirdintervals. The initial element is the weakest of the group, and thefinal of median intensity, the relation for all subjects being in theratio, 1. 000:1. 124. The amphibrachic measure begins weakly and endsstrongly, and thus approximates, we may say, to the iambic type. 

In the anapęstic form the three degrees of intensity are stillmaintained, three out of four subjects giving consistent results; andthe order of relative values is the simple converse of the dactylic. There is presented in each case a single curve; the dactyl movescontinuously away from an initial accent in an unbroken decrescendo, the anapęst moves continuously toward a final accent in an unbrokencrescendo. But in the anapęstic form as well as in the dactylic thereis a clear duality in the arrangement of elements within the group, since the two unaccented beats fall, as before, into one naturalgroup, while the accented element is set apart by its widelydifferentiated magnitude. The ratios follow: first interval to second, 1. 000:1. 009; first interval to third, 1. 000:2. 084. 

The values of the three elements when considered irrespective ofaccentual stress are as follows: First, 1. 000; second, 1. 001; third, 0. 995. No characteristic preponderance due to primacy of positionappears as in the case of relative duration. The maximum value isreached in the second element. This is due to the coöperation of twofactors, namely, the proximity of the accentual stress, which in nocase is separated from this median position by an unaccented element, and the relative difficulty in giving expression to amphibrachicrhythms. The absolute values of the reactions in the three forms is ofsignificance in this connection. Their comparison is rendered possibleby the fact that no change in the apparatus was made in the course ofthe experiments. They have the following values: Dactylic, 10. 25;amphibrachic, 12. 84; anapęstic, 12. 45. The constant tendency, when anydifficulty in coördination is met with, is to increase the force ofthe reactions, in the endeavor to control the formal relations of thesuccessive beats. If such a method of discriminating types be appliedto the present material, then the most easily coördinated--the mostnatural--form is the dactyl; the anapęst stands next; the amphibrachis the most unnatural and difficult to coördinate. 

The same method of analysis was next applied to four-beat rhythms. Theproportional intensive values of the successive reactions for theseries of possible accentual positions are given in the followingtable:

TABLE XXIII. 

 Stress. 1st Beat. 2d Beat. 3d Beat. 4th Beat. 

 Initial, 1. 000 0. 575 0. 407 0. 432 Secondary, 0. 530 1. 000 0. 546 0. 439 Tertiary, 0. 470 0. 407 1. 000 0. 453 Final, 0. 492 0. 445 0. 467 1. 000

The first and fourth forms follow similar courses, each marked byinitial and final stress; but while this is true throughout in thefourth form, it results in the first form from the preponderance ofthe final interval in a single individual's record, and thereforecannot be considered typical. The second and third forms are preservedthroughout the individual averages. The second form shows a maximumfrom which the curve descends continuously in either direction; in thethird a division of the whole group into pairs is presented, a minorinitial accent occurring symmetrically with the primary accent on thethird element. This division of the third form into subgroups appearsalso in its duration aspect. Several inferences may be drawn from thisgroup of relations. The first and second forms only are composed ofsingly accented groups; in the third and fourth forms there ispresented a double accent and hence a composite grouping. Thisindicates that the position in which the accent falls is an importantelement in the coördination of the rhythmical unit. When the accent isinitial, or occurs early in the group, a larger number of elements canbe held together in a simple rhythmic structure than can becoördinated if the accent be final or come late in the series. In thissense the initial position of the accent is the natural one. The firsttwo of these four-beat forms are dactylic in structure, the formerwith a postscript note added, the latter with a grace note prefixed. In the third and fourth forms the difficulty in coördinating theunaccented initial elements has resulted in the substitution of adipodic division for the anapęstic structure of triple rhythms withfinal accent. 

The presence of a tendency toward initial accentuation appears whenthe average intensities of the four reactions are consideredirrespective of accentual position. Their proportional values are asfollows: First, 1. 000; second, 0. 999; third, 1. 005; fourth, 0. 981. Underlying all changes in accentuation there thus appears a resolutionof the rhythmic structure into units of two beats, which areprimitively trochaic in form. 

The influence exerted by the accented element on adjacent members ofthe group is manifested in these forms more clearly than heretoforewhen the values of the several elements are arranged in order of theirproximity to that accent and irrespective of their positions in thegroup. Their proportional values are as follows:

TABLE XXIV. 

 2d Remove. 1st Remove. Accent. 1st Remove. 2d Remove. 0. 442 0. 526 1. 000 0. 514 0. 442

This reinforcing influence is greater--according to the figures justgiven--in the case of the element preceding the accent than in that ofthe reaction which follows it. It may be, therefore, that the positionof maximal stress in the preceding table is due to the close averagerelation in which the third position stands to the accented element. This proximity it of course shares with the second reaction of thegroup, but the underlying trochaic tendency depreciates the value ofthe second reaction while it exaggerates that of the third. Thisreception of the primitive accent the third element of the groupindeed shares with the first, and one might on this basis alone haveexpected the maximal value to be reached in the initial position, wereit not for the influence of the accentual stress on adjacent membersof the group, which affects the value of the third reaction to anextent greater than the first, in the ratio 1. 000:0. 571. 

The average intensity of the reactions in each of the four forms--allsubjects and positions combined--is worthy of note. 

TABLE XXV. 

 Stress. Initial. Secondary. Tertiary. Final. Value, 1. 000 1. 211 1. 119 1. 151

The first and third forms, which involve initial accents--in therelation of the secondary as well as primary accent to thesubgroups--are both of lower average value than the remaining types, in which the accents are final, a relation which indicates, on theassumption already made, a greater ease and naturalness in the formertypes. Further, the second form, which according to the subjectivereports was found the most difficult of the group to execute--in sofar as difficulty may be said to be inherent in forms of motorreaction which were all relatively easy to manipulate--is that whichpresents the highest intensive value of the whole series. 

In the next group of experiments, the subject was required to executea series of reactions in groups of alternating content, the first tocontain two uniform beats, the second to consist of a single reaction. This second beat with the interval following it constitutes a measurewhich was to be made rhythmically equivalent to the two-beat groupwith which it alternated. The time-relations of the series weretherefore left to the adjustment of the reactor. The intensiverelations were separated into two groups; in the first the finalreaction was to be kept uniform in strength with those of thepreceding group, in the second it was to be accented. 

The absolute and relative intensive values for the two forms are givenin the following table:

TABLE XXVI. 

 Rhythm. 1st Beat. 2d Beat. 3d Beat. Value. 

 Syncopated Measures 13. 00 15. 12 16. 50 Absolute. Unaccented, 1. 000 1. 175 1. 269 Relative. 

 Syncopated Measures 10. 95 11. 82 16. 11 Absolute. Accented, 1. 000 1. 079 1. 471 Relative. 

These averages hold for every individual record, and thereforerepresent a thoroughly established type. In both forms the reaction ofthe syncopated measure receives the greatest stress. In the firstform, while the stress is relatively less than in the second, it is atthe same time absolutely greater. The whole set of values is raised(the ratio of average intensities in the two forms being 1. 147:1. 000), as it has already been found to be raised in other forms difficult toexecute. To this cause the preponderance is undoubtedly to beattributed, as the reports of every subject describe this form asunnatural, in consequence of the restraint it imposes on an impulse toaccent the final reaction, _i. E. _, the syncopated measure. 

In the next set of experiments the series of reactions involved thealternation of a syncopated measure consisting of a single beat with afull measure of three beats. The same discrimination into accented andunaccented forms in the final measure was made as in the precedinggroup. The series of absolute and relative values are given in thefollowing table. 

TABLE XXVII. 

 Rhythm. 1st Beat. 2d Beat. 3rd Beat. 4th Beat. Value. 

 Syncopated Measures 9. 77 8. 96 9. 61 13. 78 Absolute. Unaccented, 1. 000 0. 915 0. 983 1. 165 Relative. 

 Syncopated Measures 11. 57 11. 07 11. 53 21. 50 Absolute. Accented, 1. 000 0. 957 0. 996 1. 858 Relative. 

These averages hold for every subject where the syncopated measurereceives accentuation, and for two out of three reactors where it isunaccented. The latter individual variation shows a progressiveincrease in intensity throughout the series. 

Here, as in the preceding forms, a well-established type is presented. Not only when accentuation is consciously introduced, but also whenthe attempt is made--and in so far as the introspection of the reactorgoes, successfully made--to maintain a uniformity among the reactionsof the full and syncopated measures, the emphasis on the latter isunconsciously increased. In the accented form, as before, there is aclear discrimination into two grades of intensity (ratio of firstthree elements to final, 1. 000:1. 888) while in the unaccented no suchbroad separation exists (ratio of first three elements to final, 1. 000:1. 156). 

The type of succession in each of these forms of reaction is atransformed dactylic, in which group should now be included the simplefour-beat rhythm with final accent, which was found to follow the samecurve. The group begins with a minor stress in both of the presentforms, this stress being greater in the unaccented than in theaccented type. This preponderance I believe to be due to the endeavorto repress the natural accent on the syncopated measure. In both formsthe intensive value of the second element is less than that of thethird, while the intensity of the initial reaction is greater thanthat of either of these subsequent beats. This form of succession Ihave called a _transformed dactylic_. It adheres to the dactylic typein possessing initial accentuation; it departs from the normaldactylic succession in inverting the values of the second and thirdmembers of the group. This inversion is not inherent in the rhythmictype. The series of three beats decreasing in intensity represents thenatural dactylic; the distortion actually presented is the result ofthe proximity of each of these groups to a syncopated measure whichfollows it. This influence I believe to be reducible to moreelementary terms. The syncopated measure is used to mark the close ofa logical sequence, or to attract the hearer's attention to a strikingthought. In both cases it is introduced at significant points in therhythmical series and represents natural nodes of accentuation. Thedistortion of adjacent measures is to be attributed to the increase inthis elementary factor of stress, rather than to the secondarysignificance of the syncopation, for apart from any such change in therhythmical structure we have found that the reactions adjacent to thatwhich receives accentual stress are drawn toward it and increased inrelative intensity. 

Further quantitative analysis of rhythmical sequences, involving acomparison of the forms of successive measures throughout the highersyntheses of verse, couplet and stanza, will, I believe, confirm thisconception of the mutable character of the relations existing betweenthe elements of the rhythmical unit, and the dependence of theirquantitative values on fixed points and modes of structural changeoccurring within the series. An unbroken sequence of dactyls we shallexpect to find composed of forms in which a progressive decrease ofintensity is presented from beginning to end of the series (unless weshould conceive the whole succession of elements in a verse to takeshape in dependence on the point of finality toward which it isdirected); and when, at any point, a syncopated measure is introducedwe shall look for a distortion of this natural form, at least in thecase of the immediately preceding measure, by an inversion of therelative values of the second and third elements of the group. Thisinversion will unquestionably be found to affect the temporal as wellas the intensive relations of the unit. We should likewise expect therelations of accented and unaccented elements in the two-beat rhythmsto be similarly affected by the occurrence of syncopated measures, andindeed to find that their influence penetrates every order of rhythmand extends to all degrees of synthesis. 

To the quantitative analysis of the intensive relations presented bybeaten rhythms must be added the evidence afforded by the apprehensionof auditory types. When a series of sounds temporally andqualitatively uniform was given by making and breaking an electriccircuit in connection with a telephone receiver, the members of agroup of six observers without exception rhythmized the stimuli ingroups--of two, three and four elements according to rate ofsuccession--having initial accentuation, however frequently theseries was repeated. When the series of intervals was temporallydifferentiated so that every alternate interval, in one case, andevery third in another, stood to the remaining interval or intervalsin the ratio, 2:1, the members of this same group as uniformlyrhythmized the material in measures having final accentuation. Intriple groups the amphibrachic form (in regard to temporal relationsonly, as no accentuation was introduced) was never heard under naturalconditions. When the beginning of the series was made to coincide withthe initiation of an amphibrachic group, four of those taking part inthe investigation succeeded in maintaining this form of apprehensionfor a time, all but one losing it in the dactylic after a fewrepetitions; while the remaining two members were unable to hold theamphibrachic form in consciousness at all. 

(_b_) The Distribution of Durations. 

The inquiry concerning this topic took the direction, first, of aseries of experiments on the influence which the introduction of alouder sound into a series otherwise intensively uniform exerts on theapparent form of the series within which it occurs. Such a group ofexperiments forms the natural preliminary to an investigation of therelation of accentuation to the form of the rhythm group. Theapparatus employed was the fourth in the series already described. Thesounds which composed the series were six in number; of these, fivewere produced by the fall of the hammer through a distance of 2/8inch; the sixth, louder sound, by a fall through 7/8 inch. In thosecases in which the intensity of this louder sound was itself variedthere was added a third height of fall of two inches. The successionof sounds was given, in different experiments, at rates of 2. 5, 2. 2, and 1. 8 sec. For the whole series. The durations of the intervalsfollowing and (in one or two cases) preceding the louder sound werechanged; all the others remained constant. A longer intervalintervened between the close and beginning of the series than betweenpairs of successive sounds. After hearing the series the subjectreported the relations which appeared to him to obtain among itssuccessive elements. As a single hearing very commonly produced but aconfused impression, due to what was reported as a condition ofunpreparedness which made it impossible for the hearer to form anydistinct judgment of such relations, and so defeated the object of theexperiment, the method adopted was to repeat each series before askingfor judgment. The first succession of sounds then formed both a signalfor the appearance of the second repetition and a reinforcement of theapperception of its material. 

In order to define the direction of attention on the part of theobserver it was made known that the factors to be compared were thedurations of the intervals adjacent to the louder sound in relation tothe remaining intervals of the series, and that all other temporal andintensive values were maintained unchanged from experiment toexperiment. In no instance, on the other hand, did any subject knowthe direction or nature of the variation in those quantitiesconcerning which he was to give judgment. In all, five subjects sharedin the investigation, C. , E. , F. , H. And N. Of these C only hadmusical training. In the tables and diagrams the interval precedingthe louder sound is indicated by the letter B, that following it bythe letter A. Totals--judgment or errors--are indicated by the letterT, and errors by the letter E. The sign '+' indicates that theinterval against which it stands is judged to be greater than theremaining intervals of the series, the sign '=' that it is judgedequal, and the sign '-' that it is judged less. 

The first series of changes consisted in the introduction ofvariations in the duration of the interval following the loud sound, in the form of successive increments. This loud sound was at the thirdposition in the series. All intensive relations and the duration ofthe interval preceding the louder sound remained unchanged. Theresults of the experiment are presented in the following table. 

TABLE XXVIII. 

 Ratio of A to B A Errors Total Per cent. Other Intervals. + = - + = - B A T judgts. Of errors

 1. 000 : 0. 625 2 2 2 4 2 0 4 2 6 12 50 1. 000 : 0. 666 4 2 0 1 3 2 4 5 9 12 75 1. 009 : 0. 714 5 3 0 2 2 4 5 6 11 16 69 1. 000 : 0. 770 5 4 0 1 1 7 5 8 13 18 72 1. 000 : 0. 833 1 5 0 0 0 6 1 6 7 12 50

 Totals, 17 16 2 8 8 19 19 27 46 70

The value of the interval following the louder sound is correctlyreported eight times out of thirty; that preceding it is correctlyreported sixteen times out of thirty. The influence which such achange in intensive value introduced at a single point in a series ofsounds exerts on the apparent relation of its adjacent intervals tothose of the remainder of the series is not equally distributedbetween that which precedes and that which follows it, but affects thelatter more frequently than the former in a ratio (allowing latitudefor future correction) of 2:1. In the case of interval A the error isone of underestimation in twenty-seven cases; in none is it an errorof overestimation. In the case of interval B the error is one ofoverestimation in seventeen instances, of underestimation in two. Theinfluence of the introduction of such a louder sound, therefore, is tocause a decrease in the apparent duration of the interval whichfollows it, and an increase in that of the interval which precedes it. The illusion is more pronounced and invariable in the case of theinterval following the louder sound than of that preceding it, theproportion of such characteristic misinterpretations to the wholenumber of judgments in the two cases being, for A, 77 per cent. ; forB, 54 per cent. The effect on interval A is very strong. In the secondgroup, where the ratio of this interval to the others of the series is3:2, it is still judged to be equal to these others in 50 per cent. Ofthe cases, and less in 35 per cent. Further, these figures do not giveexhaustive expression to the whole number of errors which may berepresented in the judgments recorded, since no account is taken ofgreater and less but only of change of sign; and an interval might beunderestimated and still be reported greater than the remainingintervals of the series in a group of experiments in which therelation of the interval in question to these remaining intervalsranged from the neighborhood of equivalent values to that in which onewas double the other. If in a rough way a quantitative valuation oferrors be introduced by making a transference from any one sign tothat adjacent to it (_e. G. _, - to =, or = to +) equal to _one_, andthat from one extreme sign to the other equal to _two_, the differencein the influence exerted on the two intervals will become still moreevident, since the errors will then have the total (quantitative)values of A 46, and B 19, or ratio of 1. 000:0. 413. 

Next, the position of the louder sound in the series of six waschanged, all other conditions being maintained uniform throughout theset of experiments. The series of intervals bore the followingrelative values: A, 0. 900; B, 1. 100; all other intervals, 1. 000. Thelouder sound was produced by a fall of 0. 875 inch; all others by afall of 0. 250 inch. The louder sound occurred successively in thefirst, second, third, fourth and fifth positions of the series. In thefirst of these forms it must of course be remembered that no intervalB exists. The results of the experiment are shown in the followingtable:

TABLE XXIX. 

 Position Apparent Values. Errors. % of Errors Ditto in B A B A T in tot. Judg. Quant. Series + = - + = - B A B A 1 2 6 6 0 12 12 85. 7 85. 7 2 2 8 2 1 7 4 10 11 21 83. 3 91. 6 73. 3 91. 6 3 1 9 3 1 8 3 10 11 21 76. 9 91. 6 71. 9 91. 6 4 1 8 4 2 6 5 9 11 20 69. 2 84. 6 52. 8 84. 6 5 0 12 0 0 4 8 12 12 24 100. 0 100. 0 60. 0 100. 0 Totals, 4 37 9 6 31 26 41 57 98 82. 3 90. 7 64. 5 90. 7

 Total judgments, 113; Errors (B = 31), A = 57. 

The relatively meager results set forth in the preceding section arecorroborated in the present set of experiments. That such a variationof intensity introduced into an otherwise undifferentiated auditoryseries, while it affects the time-values of both preceding andfollowing intervals, has a much greater influence on the latter thanon the former, is as apparent here as in the previous test. The numberof errors, irrespective of extent, for the two intervals are: B, 82. 3per cent, of total judgments; A, 90. 7 per cent. When the mean andextreme sign displacements are estimated on the quantitative basisgiven above these percentages become B, 64. 5; A, 90. 7, respectively--aratio of 0. 711:1. 000. 

The direction of error, likewise, is the same as in the precedingsection. Since the actual values of the two intervals here arethroughout of extreme sign--one always greater, the other alwaysless--only errors which lie in a single direction are discriminable. Illusions lying in this direction will be clearly exhibited, since thedifferences of interval introduced are in every case above thethreshold of discrimination when the disturbing element of variationsin intensity has been removed and the series of sounds madeintensively uniform. In case of a tendency to underestimate B oroverestimate A, errors would not be shown. This problem, however, isnot to be met here, as the results show; for there is recorded aproportion of 82. 3 per cent. Of errors in judgment of interval B, andof 90. 7 per cent. In judgment of interval A, all the former beingerrors of overestimation, all of the latter of underestimation. 

The influence of position in the series on the effect exerted by sucha change of intensity in a single member can be stated onlytentatively. The number of experiments with the louder sound inposition five was smaller than in the other cases, and the relationwhich there appears cannot be absolutely maintained. It may be alsothat the number of intervals following that concerning which judgmentis to be given, and with which that interval may be compared, has aninfluence on the accuracy of the judgment made. If we abstract fromthis last set of results, the tendency which appears is toward anincrease in accuracy of perception of comparative durations from thebeginning to the end of the series, a tendency which appears moremarkedly in the relations of the interval preceding the louder soundthan in those of the interval which follows it. This conclusion isbased on the succession of values which the proportion of errors tototal judgments presents, as in the annexed table. 

TABLE XXX. 

 Percentage of Errors for Each Position. 

 Interval. I II III IV V B. 83. 3 76. 9 69. 2 (100) Irrespective A. 85. 7 91. 6 91. 6 84. 6 (100) of extent. B. 73. 3 71. 9 53. 8 (60) Estimated A. 85. 7 91. 6 91. 6 84. 6 (100) quantitatively. 

Next, the relation of the amount of increase in intensity introducedat a single position in such a series to the amount of error therebyoccasioned in the apprehension of the adjacent intervals was taken up. Two sets of experiments were carried out, in each of which five ofthe sounds were of equal intensity, while one, occurring in the midstof the series, was louder; but in one of the sets this louder soundwas occasioned by a fall of the hammer through a distance of 0. 875inch, while in the other the distance traversed was 2. 00 inches. Inboth cases the extent of fall in the remaining hammers was uniformly0. 25 inch. The results are given in the following table:

TABLE XXXI. 

 Interval B. ¹ Interval A. Ratio of Interval 0. 875 in. 2. 00 in. 0. 875 in. 2. 00 in. B to Interval A. + = - + = - + = - + = - 1. 000 : 1. 000 0 6 0 0 4 2 0 5 1 0 0 6 0. 909 : 1. 000 2 4 0 0 4 2 0 2 4 2 2 2 0. 833 : 1. 000 0 6 0 0 4 2 4 0 2 1 3 2 0. 770 : 1. 000 0 6 0 2 2 2 2 4 0 4 0 2 0. 714 : 1. 000 0 6 0 1 5 0 6 0 0 2 2 2 Totals, 2 28 3 19 8 12 11 7 9 7 14 T. E. , T. J. , 2 30 11 30 13 30 21 30 and per cent. , 6. 6% 36. 6% 60. 0% 70. 0%

 ¹Interval B in these experiments is of the same duration as all others but that following the louder sound; hence, judgments in the second column are correct. 

Again the markedly greater influence of increased intensity on theinterval following than on that preceding it appears, the percentageof errors being, for B (both intensities), 21. 6 per cent. ; for A, 56. 6per cent. Also, in these latter experiments the direction of error ismore definite in the case of interval A than in that of interval B. 

The influence of changes in intensity on the amount of error producedis striking. Two intensities only were used for comparison, but theresults of subsequent work in various other aspects of the generalinvestigation show that this correlation holds for all ranges ofintensities tested, and that the amount of underestimation of theinterval following a louder sound introduced into an otherwise uniformseries is a function of the excess of the former over the latter. Thelaw holds, but not with equal rigor, of the interval preceding thelouder sound. So far as these records go, the influence of such anincrease of intensity is more marked in the case of interval B than inthat of interval A. It is to be noted, however, that the absolutepercentage of errors in the case of A is several times greater than inthat of B. I conclude that A is much more sensitive than B to suchinfluences, and that there is here presented, in passing fromintensity I. To intensity II. , the rise of conditions under which theinfluence of the louder sound on B is first distinctly felt--that is, the appearance of a threshold--and that the rate of change manifestedmight not hold for higher intensities. 

Lastly, the rate at which the sounds of the series succeeded oneanother was varied, in order to determine the relation which theamount of influence exerted bore to the absolute value of theintervals which it affected. Three rates were adopted, the wholeseries of sounds occupying respectively 2. 50 secs. , 2. 20 secs, and1. 80 secs. The results are summed in the following table:

TABLE XXXII. 

 Rate: 2. 5 secs. Rate: 2. 2 secs. Rate: 1. 8 secs. 

 Ratio of Interval B B A B A B A to Interval A. + = - + = - + = - + = - + = - + = -

 1. 000 : 1. 000 2 8 0 0 8 2 0 8 2 0 2 8 0 4 0 0 2 2 0. 917 : 1. 000 0 8 2 4 6 0 3 8 0 0 8 3 2 2 0 0 2 2 0. 846 : 1. 000 1 9 0 5 4 1 3 8 0 3 7 1 6 5 0 1 8 2 0. 786 : 1. 000 1 10 0 11 0 0 6 6 0 7 3 4 6 2 2 2 6 2 0. 733 : 1. 000 4 2 0 4 0 2 4 6 0 8 0 2 0. 687 : 1. 000 5 3 1 6 1 2 2 6 0 7 0 1

 Totals 4 35 2 20 18 3 21 35 3 20 21 20 20 25 2 18 18 11*

 *Transcriber's Note: Original "1". 

These results are converted into percentages of the total number ofjudgments in the following table:

TABLE XXXIII. 

 Rate of B A Success. + = - Errors. + = - Errors. 2. 5 secs 10 85 5 15 49 44 7 51 2. 2 " 36 59 5 41 33 34 33 67 1. 8 " 43 53 4 47 38 38 24 62

In the case of interval A the direction of the curve of error changesin passing from Rate II. To Rate III. In the case of interval B theincrease is continuous. 

This increase in the percentage of error is, further, distinctly inthe direction of an accentuation of the overestimation of theinterval B, as is shown in the percentage of cases in which thisinterval appeared greater than the rest of the series for each of thethree rates. 

If the three rates be combined in the one set of results, thedifference in the effects produced on the interval following thelouder sound and on that which precedes it becomes again apparent. This is done in the table below. 

TABLE XXXIV. 

 B A B A Ratio + = - + = - T. E. T. J. % T. E. T. J. % I. 2 20 2 0 12 12 2 24 8. 5 12 24 50. 0 II. 5 18 2 4 16 5 5 25 20. 0 21 25 84. 4 III. 10 22 0 9 19 4 10 32 31. 0 23 32 72. 0 IV. 13 18 2 20 9 8 13 33 39. 0 17 37 46. 0 V. 8 8 0 12 0 4 8 16 50. 0 4 16 25. 0 VI. 7 9 1 13 1 3 7 17 41. 0 4 17 24. 0

The overestimation of the interval before the louder sound also tendsto increase in extent with the actual increase in duration of theinterval following that sound over the other intervals of the series. 

Thus, the form which the sensible time-relations of such a limitedseries of sounds present is found to be intimately dependent on theintensive preponderance of certain elements within it, on the degreeof increased stress which such elements receive, on their localposition in the series, and on the rate at which the stimulationssucceed one another. The knowledge of these facts prepares us for thewhole series of relations manifested in the special quantitativeinvestigations reported in the sections which follow. In the first ofthese is presented the time-relations obtaining among the successivereactions of the various rhythm types discussed in the precedingdivision of this part, the section, namely, on the distribution ofintensities. 

In the first group of reactions the series was not to be consciouslyaccented, nor to be divided into groups by the introduction of pauses. The reactor was required only to conceive it as a succession oftwo-beat groups continuously repeated, the way in which the groupsshould be defined, whether by counting or otherwise, being left to hisown discretion. The experimental group was composed of five subjects. 

The following table presents the quantitative results of an analysisof the material in series of ten successive pairs of reactions, uponthe basis of unity as the value of the first element. 

TABLE XXXV. 

 Quantities. I II III IV V VI VII VIII IX X Whole Meas. , 1. 000 0. 894 1. 035 0. 912 1. 000 0. 877 1. 070 0. 877 1. 070 0. 841 First Inter. , 1. 000 1. 142 1. 071 1. 142 1. 000 1. 285 1. 000 1. 214 1. 000 1. 214 Second Inter. , 1. 000 0. 837 1. 023 0. 860 1. 000 0. 744 1. 093 0. 767 1. 093 0. 790

Within the limits of the calculation no progressive change appears, either of acceleration or of retardation, whether in general or on thepart of individual reactors. In narrower ranges the inconstancy of theperiods is very marked, and their variations of clearly definedrhythmical character. The duration of the total measures of two beatsis throughout alternately longer and shorter, the average of theirvalues presenting a ratio of 1. 000:0. 847. The order of thisarrangement, namely, that the longer period precedes the shorter inthe larger group, is drawn from the fact that measurementsconsistently began with the initial reaction of the series. 

An analysis of the constituent intervals of the unit group, as shownin the second and third lines of the table, reveals the existence of acomplex subordinate rhythm. The two components of the rhythmical groupdo not increase and decrease concomitantly in temporal value incomposing the alternate long and short measures of the fluent rhythm. The movement involves a double compensating rhythmical change, inwhich the two elements are simultaneously in opposite phases to eachother. A measure which presents a major first interval contains alwaysa minor second; one introduced by a minor first concludes with a majorsecond. The ratios of these two series of periodic variations mustthemselves manifestly be different. Their values are, for the firstinterval of the measure, 1. 000:1. 214; and for the second interval, 1. 000:0. 764. The greater rhythmical differentiation marks the secondof the two intervals; on the variations of this second interval, therefore, depends the appearance of that larger rhythm whichcharacterizes the series. The ratios of these primary intervals areless consistently maintained than are those of the rhythmical measuresbuilt out of them. It will be noted that in both intervals there is atendency for the value of the difference between those of alternategroups to increase as the tapping progresses. This change I haveinterpreted as indicative of a progressive definition in the processof rhythmization, depending on an increase in coördination anddifferentiation of the reactions as the series advances. 

A simple stress on alternate elements was next introduced in theseries, forming a simple trochaic measure repeated withoutinterruption. The quantitative results follow, arranged as in thepreceding experiment. 

TABLE XXXVI. 

 Quantity. I II III IV V VI VII VIII IX X Measure, 1. 000 1. 035 1. 070 1. 035 1. 087 1. 070 1. 071 1. 052 1. 070 1. 070 1st Int. , 1. 000 1. 000 1. 111 1. 000 1. 055 1. 111 1. 166 1. 111 1. 111 1. 111 2d Int. , 1. 000 1. 025 1. 051 1. 051 1. 102 1. 051 1. 025 1. 025 1. 051 1. 051

Here again there is no progressive acceleration or retardation. Therhythmical differentiation of alternate measures is very slight--theaverage ratio of the first to the second being 1. 000:0. 993--but is ofthe same type as in the preceding. The excess in the amount of thisdifferentiation presented by the first type of reaction over thesecond may be due to the presence of a tendency to impart rhythmicalcharacter to such a series of reactions, which, prohibited in oneform--the intensive accent--finds expression through the substitutionfor this of a temporal form of differentiation. 

In this trochaic rhythm the phases of variation in the constituentintervals of the measure are concomitant, and their indices ofdifferentiation almost identical with each other. Their values are, for the first, 1. 000:0. 979; and for the second, 1. 000:0. 995. Thehigher index is that of the first interval, that, namely, whichfollows the accented beat of the measure, and indicates that therhythmical change is due chiefly to a differentiation in the elementwhich receives the stress. 

In iambic measures similarly beaten out there is likewise noacceleration nor retardation apparent in the progress of the tapping. The temporal differentiation of alternate measures is of the sameextent as in the preceding group, namely, 1. 000:0. 991. Theproportional quantitative values of the measure and its constituentintervals, taken in series of ten successive repetitions, are asfollow:

TABLE XXXVII. 

 Quantity I II III IV V VI VII VIII IX X Measure, 1. 000 0. 979 1. 000 0. 979 1. 020 0. 979 0. 979 1. 020 0. 979 0. 979 1st Int. , 1. 000 0. 941 0. 941 1. 000 1. 000 0. 941 8. 082 0. 941 0. 941 0. 941 2d Int. , 1. 000 1. 000 1. 032 0. 967 1. 032 1. 000 1. 000 1. 032 1. 000 0. 967

The alternation of greater and less duration in the rhythm groups isdue to a variation in the time-value of the second interval only, theindex of average change in the first member being zero. That is, thegreater index of instability again attaches to that element whichreceives the stress. Though this holds true throughout theseexperiments, the amount of difference here is misleading, since onaccount of the smaller absolute value of the first interval theproportional amount of change within it which passes unrecorded isgreater than in the case of the second interval. 

In general, the larger temporal variations of the trochaic and iambicrhythm forms are too slight to be significant when taken individually. The evidence of rhythmical treatment in such a series of reactions, which is strongly marked in the unaccented form, nevertheless receivesreinforcement from these inconsiderable but harmonious results. 

The proportional values of the variations in alternate measures foraccented and unaccented elements are given in the following table, inwhich the figures for the trochaic and iambic forms are combined:

TABLE XXXVIII. 

 Interval I II III IV V VI VII VIII IX X Accented, 1. 000 1. 000 1. 083 1. 000 1. 041 1. 000 1. 083 1. 000 1. 041 1. 000 Unacc. 1. 000 1. 000 1. 000 1. 035 1. 071 1. 000 0. 964 1. 000 1. 000 1. 000

It is perhaps worthy of note that in this table a still higherrhythmical synthesis of regular form appears in the accented elementsif the figures be taken in series of four consecutive pairs ofreactions. 

In the group of triple rhythms next taken up--the dactylic, theamphibrachic and the anapęstic--each type presents an increase in theduration of the unit group between the beginning and end of theseries, but without any regular curve connecting these terms. Neitherthe average results nor those of the individual subjects show anywherea decrease of duration in the progress of the tapping. Theproportional results for each of the three rhythm forms, and theiraverages, are given in the following table. 

TABLE XXXIX. 

 Rhythm. I II III IV V VI VII VIII IX X Datyl. , 1. 000 1. 062 1. 062 1. 087 1. 087 1. 075 1. 125 1. 112 1. 125 1. 112 Amphib. , 1. 000 1. 000 1. 000 1. 069 1. 085 1. 046 1. 046 1. 046 1. 046 1. 035 Anapęs. , 1. 000 1. 012 1. 023 1. 012 1. 037 1. 037 1. 023 1. 059 1. 023 1. 084

 Average, 1. 000 1. 024 1. 036 1. 060 1. 060 1. 060 1. 072 1. 072 1. 072 1. 084

When all types and subjects are thus combined the summation of theseinconstant retardations presents sharply differentiated terms and acurve uninverted at any point. 

A separate analysis of the components of the rhythmical group shows, for the dactylic form, an important increase in duration in only oneof the three intervals, namely, that following the element whichreceives accentual stress. The proportional values for these intervalsfollow. 

TABLE XL. 

Interval. I II III IV V VI VII VIII IX XFirst, 1. 000 1. 153 1. 153 1. 153 1. 153 1. 231 1. 193 1. 193 1. 231 1. 231Second, 1. 000 0. 917 0. 917 1. 000 0. 917 0. 917 0. 917 0. 917 0. 917 0. 917Third 1. 000 1. 000 1. 033 1. 066 1. 055 1. 066 1. 133 1. 066 1. 066 1. 066

Since the progressive variation does not penetrate the whole measure, but affects only a single constituent having a strongly markedfunctional character, the process of change becomes unlike that oftrue retardation. In such a case, if the increase in duration beconfined to a single element and parallel the changes in asimultaneous variant of a different order, we should regard them asfunctionally connected, and therefore interpret the successivelygreater periods of time occupied by the rhythmical measures asconstituting no real slowing of the tempo. The measure of relativetempo in such a case consists in the ratios of the successivedurations of the rhythmical units after the subtraction of thatelement of increase due to this extraneous source. Here, since theincrease is confined to that member of the group which receivesaccentual stress, and since the increase of accentuation is typicallyaccompanied by an extension of the following interval, the changespresented do fulfil the conditions of a progressively increasedaccentuation of the rhythm group, and to this origin I think it isundoubtedly to be attributed. It is to be noted that the finalinterval also undergoes a slight increase, while the median suffers asimilarly slight decrease in duration as the series progresses. 

In the amphibrachic form the changes manifested by the constituents ofthe unit group are more obscure. No progressive retardation of theaccented element is apparent. In the initial and final intervals thedifference in duration between the first and last members of theseries is small and appears early in the process. If we assume thegeneral application of the laws of change presented in the precedingsection, there should be here two influences concerned in thedetermination of the relations presented, the factors, namely, ofposition and accent. The falling of the accentual stress on the medianinterval eliminates one of the two factors of progressive reduction inthat element and replaces it by a factor of increase, thereby doingaway with the curve of change; while at the same time it decreases thechanges which occur in the bounding intervals of the group by removingthe accent from the first and by the proximate position of its ownaccent tending to reduce the last interval. 

Under this same assumption there should be expected in the anapęsticform of rhythm an exaggeration of the progressive increase in thefinal interval, together with a further reduction in the duration ofthe initial; since from the falling of the accent on the finalinterval two factors of increase combine, while in the initial, whichimmediately follows the accented interval in the series, a positivefactor of reduction appears. This is actually the type of changepresented by the quantitative relations, which are given asproportional values in the following table. 

TABLE XLI. 

 Interval. I II III IV V VI VII VIII IX X First, 1. 000 0. 950 1. 000 0. 950 1. 000 0. 950 1. 000 1. 000 1. 000 1. 050 Second, 1. 000 1. 100 1. 000 1. 050 1. 100 1. 000 1. 000 1. 050 1. 100 1. 000 Third, 1. 000 1. 073 1. 073 1. 024 1. 024 1. 122 1. 098 1. 098 1. 098 1. 146

Between its first and last terms the first interval shows a departureslightly less than that of the previous rhythm from the rate of changewhich characterizes the dactylic type; but if the average values ofthe whole series of intervals be taken in each of the three cases, theprogressive reduction will be seen clearly to continue in passing fromthe second to the third form. The figures annexed give these averagesas proportions of the first interval in the series. 

TABLE XLII. 

 1st Av. Of Rhythm. Interv. All others. Dactylic, 1. 000 : 1. 188 Amphibrachic, 1. 000 : 1. 019 Anapęstic, 1. 000 : 1. 000

The relations of the various intervals in the three forms are puttogether here for comparison:

TABLE XLIII. 

 Rhythm. 1st Interval. 2d Interval. 3d Interval. Dactylic, 1. 000 : 1. 231 1. 000 : 1. 000 1. 000 : 1. 066 Amphibrachic, 1. 000 : 1. 045 1. 000 : 1. 000 1. 000 : 1. 054 Anapęstic, 1. 000 : 1. 050 1. 000 : 1. 000 1. 000 : 1. 146

An analysis of the factors of accentual stress and of position in therhythmical group in isolation from each other, confirms theassumptions already made as to their influence in defining the form ofthe rhythmic unit. Table XLIV. Exhibits the series of temporal changestaking place in accented and unaccented intervals, respectively, forthe three forms combined, and therefore independent of position in thegroup. 

TABLE XLIV. 

 Interval. I II III IV V VI VII VIII IX X Accented. 1. 000 1. 064 1. 064 1. 064 1. 064 1. 094 1. 094 1. 064 1. 094 1. 129 Unaccented, 1. 000 1. 000 1. 000 1. 080 1. 040 1. 040 1. 040 1. 040 1. 040 1. 040

Similarly, in Table XLV. Are given the proportional values of theseries of intervals in order of their position in the group andindependent of accentual stress:

TABLE XLV. 

 Interval. I II III IV V VI VII VIII IX X First, 1. 000 1. 043 1. 087 1. 043 1. 087 1. 043 1. 043 1. 121 1. 043 1. 121 Second, 1. 000 1. 000 1. 000 1. 043 1. 000 0. 956 1. 000 0. 956 1. 000 0. 956 Third, 1. 000 1. 028 1. 028 1. 055 1. 028 1. 083 1. 083 1. 083 1. 083 1. 083

The former table makes clear the predominance of the increase in theaccented element over the average of all unaccented elements of theseries; the latter shows the independence of increase in the initialand final, and of decrease in the median interval, of any relation tothe position of the accentual stress. Both the intensive accentuationand the demarcation of successive groups thus appear to be factors ofdefinition in the rhythmic unit. Those types which are either markedby a more forcible accent or separated by longer pauses are moredistinctly apprehended and more easily held together than those inwhich the accent is weaker or the pause relatively less. It wouldfollow that the general set of changes which these series of reactionspresent are factors of a process of definition in the rhythmicaltreatment of the tapping, and are not due to any progressive change inthe elementary time relations of the series. 

The figures for measures of four beats are incomplete. They show anincrease in the average duration of the group from first to last ofthe series in three out of the four forms, namely, those havinginitial, secondary and final stress. 

Of the relative amounts contributed by the several elements to thetotal progressive variation of the measures in the first form, theleast marks those intervals which follow unaccented beats, thegreatest those which follow accented beats; among the latter, thatshows the greater increase which receives the primary accent, that onwhich falls the secondary, subconscious accent shows the less; and ofthe two subgroups which contain these accents that in which the majoraccent occurs contributes much more largely to the progressive changethan does that which contains the minor. 

When the phases of accented and unaccented elements are compared, irrespective of their position in the rhythmic group, the samefunctional differences are found to exist as in the case of triplerhythms. Their quantitative relations are given in the followingtable. 

TABLE XLVI. 

 Phase. I II III IV V VI VII VIII IX X Accented. 1. 000 1. 103 1. 069 1. 172 1. 241 1. 139 1. 206 1. 310 1. 241 1. 310 Unacc. , 1. 000 1. 083 1. 128 1. 169 1. 159 1. 208 1. 169 1. 250 1. 169 1. 169

The cause of the apparent retardation lies, as before, in a changeoccurring primarily in the accented elements of the rhythm, and thisprogressive differentiation, it is inferable from the results citedabove, affects adjacent unaccented elements as well, the wholeconstituting a process more naturally interpretable as a functionalaccompaniment of progressive definition in the rhythmical treatment ofthe material than as a mark of primary temporal retardation. 

The contribution of the several intervals according to position in theseries and irrespective of accentual stress is given in the tablefollowing. 

TABLE XLVII. 

 Interval. I II III IV V VI VII VIII IX X First, 1. 000 1. 136 1. 136 1. 182 1. 227 1. 227 1. 227 1. 273 1. 318 1. 318 Second, 1. 000 1. 042 1. 042 1. 125 1. 166 1. 042 1. 042 1. 083 1. 083 1. 166 Third, 1. 000 1. 150 1. 250 1. 250 1. 250 1. 250 1. 400 1. 400 1. 450 1. 450 Fourth, 1. 000 1. 059 1. 059 1. 147 1. 179 1. 147 1. 179 1. 294 1. 206 1. 179

A rhythmical alternation is here presented, the contributions of thefirst and third elements being far in advance of those of the secondand fourth. The values of the minor pair are almost equal; of themajor the third exceeds the first. Under the assumption already madethis would indicate the existence at these points of nodes of naturalaccentuation, of which the second marks the maximum reached in thepresent series. 

The determination of relative time-values for accented and unaccentedintervals was next sought by indirect experimentation, in which theaffective aspect of the experience was eliminated from consideration, and account was taken only of the perception of quantitativevariations in the duration of the successive intervals. Proceedingfrom the well-known observation that if every alternate element of atemporally uniform auditory series receive increased stress, the wholeseries will coalesce into successive groups of two elements in whichthe louder sound precedes and the weaker follows, while the intervalwhich succeeds the unaccented sound, and which therefore separatesadjacent groups, will appear of greater duration than that whichfollows the accented element, the investigation sought by employingthe method of right and wrong cases with a series of changingtime-values for the two intervals to determine the quantitativeproportion of the two durations necessary to produce the impression oftemporal uniformity in the series. 

Two rhythm forms only were tested, the trochaic and dactylic, sincewithout an actual prolongation of considerable value in the intervalfollowing the louder sound, at the outset, no apprehension of theseries as iambic or anapęstic could be brought about. The stimuli weregiven by mechanism number 4, the distance of fall being 2/8 and 7/8inch respectively for unaccented and accented sounds. The series ofchanges included extreme proportional values of 0. 714 and 1. 769 induration of the two intervals. Six persons took part in theinvestigation. In the following table is given the percentage of casesin which the interval following the unaccented element was judgedrespectively greater than, equal to, or less than that which followedthe accented element, for each of the series of ratios presented bythe time-values of the intervals in trochaic rhythm. 

TABLE XLIX. 

 Ration of Unaccented to Unaccented Interval Judged to be Accented Interval. + = - 1. 000 : 1. 769 0. 0 per cent. 100. 0 per cent 0. 0 per cent. 1. 000 : 1. 571 12. 5 " 50. 0 " 37. 5 " 1. 000 : 1. 400 22. 0 " 56. 0 " 22. 0 " 1. 000 : 1. 222 16. 0 " 84. 0 " 1. 000 : 1. 118 26. 0 " 74. 0 " 1. 000 : 1. 000 61. 6 " 38. 4 " 1. 000 : 0. 895 100. 0 " 1. 000 : 0. 800 88. 8 " 11. 2 " 1. 000 : 0. 714 100. 0 "

The anomalous percentage which appears in the first horizontal rowneeds explanation. The limit of possible differentiation in thetime-values of accented and unaccented intervals in a rhythmical groupis characteristically manifested, not by the rise of a perception ofthe greater duration of the interval following the accented element, but through an inversion of the rhythmical figure, the originaltrochee disappearing and giving place to an iambic form of grouping, the dactyl being replaced by an anapęst. In the case in question theinversion had taken place for all subjects but one, in whom theoriginal trochaic form, together with its typical distribution ofintervals, remained unchanged even with such a great actual disparityas is here involved. 

For this group of observers and for the series of intensities takenaccount of in the present experiment, the distribution of time-valuesnecessary to support psychological uniformity lies near to the ratio1. 400:1. 000 for accented and unaccented intervals respectively, sincehere the distribution of errors in judgment is arranged symmetricallyabout the indifference point. Overestimation of the interval followingthe louder sound appears by no means invariable. Under conditions ofobjective uniformity the judgment of equality was given in 38. 4 percent, of all cases. This cannot be baldly interpreted as a persistenceof the capacity for correct estimation of the time values of the twointervals in the presence of an appreciation of the series as arhythmical group. The rhythmic integration of the stimuli is weakestwhen the intervals separating them are uniform, and since the questionasked of the observer was invariably as to the apparent relativeduration of the two intervals, it may well be conceived that thehearers lapsed from a rhythmical apprehension of the stimuli in thesecases, and regarded the successive intervals in isolation from oneanother. The illusions of judgment which appear in these experiencesare essentially dependent on an apprehension of the series of soundsin the form of rhythmical groups. So long as that attitude obtains itis absolutely impossible to make impartial comparison of the durationof successive intervals. The group is a unit which cannot be analyzedwhile it continues to be apprehended as part of a rhythmical sequence. We should expect to find, were observation possible, a solution ofcontinuity in the rhythmical apprehension in every case in which thesedistortions of the normal rhythm form are forced on the attention. This solution appears tardily. If the observer be required to estimatecritically the values of the successive intervals, the attention fromthe outset is turned away from the rhythmical grouping and directedon each interval as it appears. When this attitude prevails very smalldifferences in duration are recognized (_e. G. _, those of 1. 000:1. 118, and 1. 000:0. 895). But when this is not the case, the changes ofrelative duration, if not too great for the limits of adaptation, areabsorbed by the rhythmical formula and pass unobserved, whilevariations which overstep these limits appear in consciousness only asthe emergence of a new rhythmic figure. Such inversions are not whollyrestricted by the necessity of maintaining the coincidence ofaccentuation with objective stress. With the relatively greatdifferences involved in the present set of experiments, the rhythmicalforms which appeared ignored often the objective accentuation ofsingle groups and of longer series. Thus, if the second interval of adactyl were lengthened the unaccented element which preceded itreceived accentuation, while the actual stress on the first sound ofthe group passed unobserved; and in a complex series of twelvehammer-strokes the whole system of accentuation might be transposed inthe hearer's consciousness by variations in the duration of certainintervals, or even by simple increase or decrease in the rate ofsuccession. [6]

 [6] Bolton found one subject apperceiving in four-beat groups a series of sounds in which increased stress fell only on every sixth. 

In the experiments on dactylic rhythm the changes introduced affectedthe initial and final intervals only, the one being diminished inproportion as the other was increased, so that the total duration ofthe group remained constant. The figures, arranged as in the precedingtable, are given in Table L. 

The percentage given in the case of the highest ratio is based on thereports of two subjects only, one of them the exceptional observercommented on in connection with two-beat rhythms; for all otherparticipants the anapęstic form had already replaced the dactylic. Thedistribution of values which supports psychological uniformity in thisrhythmic figure lies between the ratios 1. 166, 1. 000, 0. 800, and1. 250, 1. 000, 0. 755, since in this region the proportion of errors injudgment on either side becomes inverted. The two rhythmic forms, therefore, present no important differences[7] in the relations whichsupport psychological uniformity. A comparison in detail of thedistribution of judgments in the two cases reveals a higher percentageof plus and minus, and a lower percentage of equality judgmentsthroughout the changes of relation in the dactylic form than in thetrochaic. This appears to indicate a greater rhythmical integration inthe former case than in the latter. On the one hand, the illusion ofisolation from adjacent groups is greater at every point at which theintervening interval is actually reduced below the value of either ofthe internal intervals in the dactylic than in the trochaic rhythm;and on the other, the sensitiveness to differences in the whole seriesis less in the case of the trochee than in that of the dactyl, if wemay take the higher percentage of cases in which no discrimination hasbeen made in the former rhythm as a negative index of suchsensibility. 

 [7] The ratios of initial to final intervals in the two cases are, for trochaic measures, 1. 400:1. 000, and for dactylic, 1. 400(to 1. 666):1. 000. 

TABLE L. 

 Ration of Unaccented Unaccented Interval Judged to be to Accented Interval. + = - 1. 000 : 2. 428 100. 0 per cent 1. 000 : 2. 000 20. 0 per cent. 33. 3 per cent 46. 7 " 1. 000 : 1. 666 33. 2 " 23. 9 " 42. 9 " 1. 000 : 1. 400 39. 0 " 46. 0 " 15. 0 " 1. 000 : 1. 182 60. 0 " 37. 2 " 2. 8 " 1. 000 : 1. 000 85. 4 " 12. 2 " 2. 4 " 1. 000 : 0. 846 89. 2 " 10. 8 " 1. 000 : 0. 714 100. 0 " 1. 000 : 0. 660 96. 0 " 4. 0 "

The increase in the number of inverted forms which occur iscoördinated percentually in the following table with the successiveincrements of difference between the accented and unaccented intervalsof the group:

TABLE LI. 

 Rhythm. 2. 428 2. 000 1. 769 1. 666 1. 571 1. 400 1. 222 1. 182 1. 118 1. 000 Trochaic, 93. 7 74. 0 44. 2 25. 0 25. 0 2. 9 Datylic, 93. 6 54. 0 39. 4 18. 4

These figures are corroborative of the preceding conclusions. Thedactylic figure is maintained in the presence of much greaterdifferences in the relative durations of accented and unaccentedintervals than is the trochaic. In the latter, inversions not onlyappear earlier in the series, but become the (practically) exclusivemode of apprehension at a point where not fifty per cent, of thedactyls have suffered transformation. At a certain definite stage inthe process the tendencies toward the two forms of apprehensionbalance each other, so that with the slightest change in direction ofattention the rhythmical figure inverts and reverts to the originalform indifferently. These points are defined, in the case of the tworhythms here reported on, by the following (or intermediate) ratios:Trochaic-Iambic, (1. 400-1. 571): 1. 000; Dactylic-Anapęstic, (1. 666-2. 000): 1. 000. 

The temporal conditions of such equilibrium are a strict function ofthe degree of accentuation which the rhythm group presents. Thelocation of the indifference point must, therefore be independentlydetermined for each intensive value through which the accented elementmay pass. Its changes are given for five such increments in thefollowing table, in which the values of the various intervals arerepresented as proportions of the absolute magnitudes which appear inthe first, or undifferentiated series. 

TABLE LII. 

 Intensive Form. 1st Interval. 2d Interval. 3d Interval. 1/8 1/8 1/8 1. 000 1. 000 1. 000 3/8 1/8 1/8 1. 042 1. 010 0. 948 7/8 1/8 1/8 1. 142 1. 021 0. 862 15/8 1/8 1/8 1. 146 1. 042 0. 808 24/8 1/8 1/8 1. 291 1. 000 0. 708

IV. THE COMBINATION OF RHYTHMICAL GROUPS IN HIGHER SYNTHESES AND THEIREQUIVALENCES. 

In the elaboration of higher rhythmical forms the combination offormally identical groups is rather the rule than the exception, sincein poetical structures the definition of the metrical form and themaintenance of its proper relations depend on a clear preponderance ofits own particular unit-type over local variants. In the experimentalinvestigation of composite rhythm forms the temporal relations ofstructures presenting such likeness in their constituent groups werefirst taken up. In the conduct of the research those differences ofintensity which are actually expressed and apprehended in theutterance of a rhythmic sequence were uniformly employed. While thereis no doubt that a succession of perfectly identical forms would, under the requisite temporal conditions, be apprehended as presentingmajor and minor phases of accentuation, yet in the expression ofrhythmic relations the subordination of accents is consistentlyobserved, and all our ordinary apprehension of rhythm, therefore, issupported by an objective configuration which fulfils already the formof our own subjective interpretation. 

The temporal relations of these major and minor phases cannot beconsidered apart from the index of their respective accentuations. Asthe distribution of elements within the simple group fluctuates withthe changes in intensive accentuation, so does the form of temporalsuccession in larger structures depend on the relations of intensityin their primary and secondary accentuations. The quantitative valueshereafter given apply, therefore, only to those specific intensitiesinvolved in the experiment. Two types were chosen, the trochee and thedactyl. The series of sounds was given by successive hammer-falls of7/8 and 1/8 inch for the major, and 3/8 and 1/8 inch for the minorphase. The distribution of time-values within each group was made onthe basis of previous experimentation to determine those relationswhich support psychological uniformity. These internal relations weremaintained unchanged throughout the series of ratios which thedurations of the two groups presented. Four subjects took part in theexperiment. The quantitative results in the composition of trochaicforms are given in the following tables (LIII. , LIV. ), the figures ofwhich present, in the form of percentages of total judgments, theapprehension of sensible equality or disparity in the two groups. 

In the earlier set of experiments the series of ratios diverged inboth directions from unity; in the later it departed in one only, since every divergence in the opposite direction had, in the previousexperiments, been remarked at once by the observer. In this second setthe series of differences is more finely graded than in the former;otherwise the two sets of figures may be considered identical. Usingthe equilibrium of errors as an index of sensible equality, the twotrochaic groups are perceptually uniform when the temporal ratio ofmajor and minor lies between 1. 000:0. 757 and 1. 000:0. 779. 

TABLE LIII. 

 Ratio of Duration 2d Group Judged to be of 1st Group to 2d. + = - 1. 000 : 1. 250 100 per cent. 1. 000 : 1. 116 100 " 1. 000 : 1. 057 100 " 1. 000 : 1. 000 100 " 1. 000 : 0. 895 68 " 22 per cent. 1. 000 : 0. 800 25 " 75 " 1. 000 : 0. 714 100 per cent. 

TABLE LIV. 

 Ratio of Duration 2d Group Judged to be of 1st Group to 2d. + = - 1. 000 : 1. 000 100. 0 per cent. 1. 000 : 0. 973 87. 5 " 12. 5 per cent. 1. 000 : 0. 870 66. 6 " 33. 3 " 1. 000 : 0. 823 33. 3 " 22. 2 " 44. 4 per cent. 1. 000 : 0. 777 50. 0 " 50. 0 " 1. 000 : 0. 735 33. 3 " 33. 3 " 33. 3 " 1. 000 : 0. 694 33. 3 " 66. 6 "

In the dactylic form, as in the second trochaic series, ratios varyingfrom unity in one direction only were employed. The results follow:

TABLE LV. 

 Ratio of Duration Second Group Judged to be of 1st Group to 2d. + = - 1. 000 : 1. 000 100. 0 per cent. 1. 000 : 0. 946 62. 5 " 37. 5 per cent. 1. 000 : 0. 915 33. 3 " 66. 6 " 1. 000 : 0. 895 8. 3 " 33. 3 " 58. 3 per cent. 1. 000 : 0. 800 40. 0 " 60. 0 "

As in the preceding case, when relations of equality obtained betweenthe two subgroups, the secondary period in every instance appearedlonger than the primary. This prolongation was uniformly reported asdispleasing. The distribution of values which here supportpsychological uniformity lies between 1. 000:0. 915 and 1. 000:0. 895, that is to say, the difference of phases is less marked than in thecase of the simpler trochaic composite. This is a structural principlewhich penetrates all rhythmical forms. The difference in the case ofboth of these composites is less than in the opposition of phaseswithin the simple group, in which for identical intensities and(practically) the same group of observers these presented the ratio1. 000:0. 714. It is evident that the relative differentiation ofaccented and unaccented intervals due to specific variations inintensity is greater than is that of successive groups characterizedby similar differences of accentual stress; and if still moreextensive groups were compared it would unquestionably be found that afurther approximation to equality had taken place. 

In the integration of rhythmical groups this subordination of theintensive accents which characterize them is not the sole mechanism ofhigher synthesis with which we are presented. Another mode is theantithesis of rhythmical quantities through verse catalepsis. Suchvariation of the rhythmical figure can take place in two directionsand in two only: by an increase in the number of constituents, givingwhat may be called _redundancy_ to the measure, and by a decrease intheir number, or _syncopation_. Each of these forms of departure fromthe typical figure fulfils a specific rhythmic function whichdetermines its temporal and intensive characters, and its localposition in the rhythmical sequence. 

(_a_) _Redundant Measures. _--The position of such a measure isuniformly initial. On rare occasions individual observers reported aninversion of this order in the earlier portion of the series, [8] butin no case were subjectively formulated series concluded in this way;and when the objective succession ended with the redundant measure theexperience was rhythmically displeasing. In accentual stress theredundant measure is of secondary rank, the chief intensity fallingupon the shorter, typical groups. Variation from the type does not, therefore, unconditionally indicate a point of accentual stress, though the two are commonly connected. 

 [8] This was probably due to beginning the series of stimulations with the typical measure. Such beginning was always made by chance. 

In regard to the relative duration of the redundant measure thesubjective reports indicate a large variability. The dactylic formappears to be slightly longer than the trochaics among which itappears; but not infrequently it is shorter. [9] These variations areprobably connected with differences in stress due to the relationwhich the measure bears to the accentual initiation of the wholeseries; for this accent apparently may fall either within theredundant measure itself or on the first element of the succeeding ___ _____ >/ \ > | | > >group, thus: | q q q; q q; |, or | e e e q q; q q |. \_/

 [9] The only form taken up was the occurrence of dactylic measures in trochaic series. 

Two rhythm forms were analyzed, the trochaic and the dactylic, theseries of sounds being given by hammer-falls of 7/8 and 1/8 inch foraccented and unaccented elements respectively. In each experiment fulland syncopated measures alternated regularly with each other incontinuous succession, giving the forms

 > > > > | q. Q; q % | and | q. Q q; q. % % |. \_____/ \____________/

The initiation of the series was in every case determined by chance. Six observers took part in the work with trochaic forms, five in thatwith dactylic. The quantitative results are given in the followingtables, in each of which the relations of duration, position andstress are included. 

TABLE LVI. 

 TROCHAIC FORM. Apparent Accentuation Ratio of 1st Second Group Judged to be 2d Group of Second Group. To 2d Group. + = - Final + = - 1. 000:1. 000 55. 5% 44. 4% 100% 71. 5% 28. 5% 1. 000:0. 946 83. 3 16. 6% 100 30. 0 70. 0 1. 000:0. 895 66. 6 11. 1 22. 2 100 30. 0 60. 0 10. 0% 1. 000:0. 846 16. 6 41. 6 41. 6 100 40. 0 60. 0 1. 000:0. 800 16. 6 41. 6 41. 6 100 40. 0 60. 0 1. 000:0. 756 49. 9 24. 9 24. 9 100 40. 0 60. 0 1. 000:0. 714 16. 6 41. 6 41. 6 100 20. 0 80. 0

TABLE LVII. 

 DACTYLIC FORM. Apparent Accentuation Ratio of 1st Second Group Judged to be 2d Group of Second Group. To 2d Group. + = - Final + = - 1. 000:1. 000 100. 0% 100% 40. 0% 60. 0% 1. 000:0. 946 83. 3% 16. 6% 100 40. 0 60. 0 1. 000:0. 895 66. 6 33. 3 100 20. 0 80. 0 1. 000:0. 846 37. 5 62. 5 100 40. 0 60. 0 1. 000:0. 800 100. 0 100 40. 0 60. 0

The syncopated measure, like the redundant, bears to the acatalecticgroup specific relations of duration, accentual stress, and positionin the rhythmical sequence. In position it is final. This relation isindependent of the factor of duration, on which the order of elementsin the simple measure depends. Even the excessive shortening whichoccurs in the trochaic form, when the full measure has a durationalmost one and one half times as great as the syncopated, brings aboutno inversion of the order. 

In duration the syncopated group is a shortened measure. The amount ofreduction necessary to preserve rhythmical proportion with the rest ofthe sequence is greater in the trochaic than in the dactylic form, asin the relation of accented to unaccented elements in the simplemeasure it is greater than in the case of the trochaic, a principle ofstructure which has already been pointed out. 

There is similar evidence in beaten rhythms to show that when a fullmeasure is elided, the pause which replaces it is of less value thanthe duration of a syncopated measure. When trochaic rhythms werebeaten out with a distinct pause after each measure, the relativevalues of the two intervals were 1. 000:2. 046. Such a pause cannot beequivalent to a suppressed beat and its interval; I regard it asfunctionally equal to a whole measure. If that value be allowed forthe second interval which it possesses in the same rhythm type when nopause is introduced, namely, 1. 000:0. 920, the first two intervals willhave a value--in terms of linear measurement--of 1. 93 + 1. 77 or 3. 70. The value of the suppressed measure would therefore be 2. 15, a ratioof acatalectic to elided group of 1. 000:0. 581. 

Iambic rhythm beaten out without separating pauses presents thefollowing ratio between first and second intervals, 1. 000:1. 054; onthe introduction of a pause between the measures the ratio becomes1. 000:2. 131. The assignment of these proportional values gives 1. 68 +1. 77, or 3. 45, as the duration of the first two intervals, and 1. 81for the pause, a ratio of 1. 00:0. 524. 

In continuous dactylic tapping, the values of the successiveintervals are 1. 000; 0. 756; 0. 927; with a separating pause theirrelations are 1. 000; 0. 692; 1. 346. These being analyzed as before, theelided measure will have the relative value of 0. 419. This shows adecline in the proportional duration of the elision as the total valueof the measure elided increases. There can be little question thatthis principle applies also to the value of elisions of higherrhythmic structures as well. 

In intensity the syncopated measure is a point of increased accentualstress. This relation is not constantly maintained in the trochaicform, in which at one ratio the accent appears reduced;[10] in thedactylic form divergences are all in the direction of an apparentincrease in accentuation. In rhythms beaten out the form of succession > . > >was always prescribed (_e. G. _, | q. Q; q_% | or | q. %; q. Q|, but not \______/ \________/either at the subjects' preference), so that no material was thereafforded for a determination of the primacy of particular figures; butthe results must of course show any tendency which exists toward anincreased accentuation of the syncopated measure. It needs but acursory reference to the statements of these results in Pt. III. , B, of this paper, to observe how constant and pronounced this tendencyis. [11]

 [10] This result is clearly irregular, and is probably due to the effect of accidental variations on a meager series of judgments. The number of these was three for each observer, making eighteen judgments in all the basis of each percentage in the table. 

 [11] The subjective notes of the observers frequently refer to this as an explicitly conscious process, the nature of the rhythmical sequence requiring a greater stress at that point than elsewhere. Extracts are appended:

 _Trochaic Syncopation. _--"There is almost a necessity for an accent on the last beat. " ". . . An almost imperative tendency to emphasize the final syllable beyond the rest. " "The two taps were followed by a pause and then a tap with increased pressure. " "This was not satisfactory with any adjustment of time relations so long as the stress of all three beats was the same. In attempting to make them all equal I almost involuntarily fell into the habit of emphasizing the final one. "

 _Dactylic Syncopation. _--"In this series it was easy to lay stress on the last (beat) . . . This is the natural grouping; I unconsciously make such. " ". . . Of these the heavy one (accented syncopation) was much more satisfactory. " "It was constantly my tendency to increase the strength of the last tap. " "In this it is natural for me to make the final stroke heavy. To make the second group balance the first by equalizing the time alone is less satisfactory than by introducing elements of both time and force. " "I felt that the latter part of the rhythm (unaccented syncopation) was lacking in force. Something seemed continually to be dropped at the end of each group. "

 The reactors frequently repeated the full measure several times before introducing the syncopated measure, which thus brought a series to its close. It will probably be found that in the actual construction of poetic measures the syncopated or partially syncopated foot is systematically introduced coincidently with points of rhythmical or logical pause. 

Conclusive evidence of the integration of simple rhythm forms inhigher structures is presented by the process of increasing definitionwhich every rhythmical sequence manifests between its inception andits close. This process is manifested equally in the facts of sensoryapprehension and those of motor reproduction of rhythm forms. On theone hand, there is a progressive refinement in the discrimination ofvariations from temporal uniformity as the series of stimulationsadvances; and correspondingly, the sequence of motor reactionspresents a clearly marked increase in coördination taking placeparallel with its progress. A rhythmical form is thus given to thewhole succession of simple measures which are included within thelimits of the larger series, a form which is no less definite thanthat exhibited by the intensive and temporal relations of therhythmical unit, and which, there can be little doubt, is even moreimportant than the latter in determining the character of the rhythmexperience as a whole. 

The presentation of experimental results bearing on this point willfollow the lines already laid down. Only that part of the materialwhich is derived from the apprehension of sensory rhythm forms can beapplied to the determination of this formal curve for the ordinarymetrical types and their complications. The facts of progressivecoördination presented by beaten rhythms are based on the repetitionof simple forms only. The completion of the evidence requires aquantitative analysis of the temporal relations presented by the wholesequence of integrated measures which compose the common verse forms:dimeter, trimeter, etc. This matter was not taken up in the presentinvestigation. 

The perception of variations in the measures of an iambic pentameterline was first taken up. The series of sounds was produced by the fallof hammer, the distances traversed being, for the accented elements0. 875 inch, and for the unaccented, 0. 250 inch. The series wasfollowed by a pause equal to one and a half measures, and was repeatedbefore judgment was made. The time occupied by the series of soundswas 2. 62 seconds. The intervals between the successive sounds wereadjusted on the basis of previous experimentation concerning the mostacceptable relations between the durations of accented and unaccentedintervals. Their values were in the ratio 1. 000:0. 714 for accented andunaccented respectively. The variations were introduced in a singleelement, namely, the interval following the accented beat of thegroup, which, in this form of rhythm, is also the inter-groupinterval. This interval was changed by successive increments of oneseventh its original value, or one twelfth the duration of the wholemeasure. Four such additions were made, the final value of theinterval standing to its original duration in the ratio 1. 000:0. 636. The same series of changes in the duration of the accented intervalwas made successively in each measure of the pentameter series. In allthese experiments the subjects were in ignorance of the character andposition of the changes introduced. The results appear in the annexedtable. 

TABLE LVIII. 

 Position in Series. Percentage Values. Ratios. I II III IV I II III IV 1. 000 : 1. 000 0 0 0 0 0 0 0 0 1. 000 : 0. 874 4 4 4 7 40 40 40 70 1. 000 : 0. 777 6 6 8 10 60 60 80 100 1. 000 : 0. 700 6 6 10 10 60 60 100 100 1. 000 : 0. 636 6 6 10 10 60 60 100 100

In the five horizontal rows on the left of the table are set down thenumber of times, out of a total of ten judgments, the interval inquestion was perceived to be greater than the like interval in othergroups, under the original relation of uniformity and for the foursuccessive increments. On the right these numbers are given aspercentages of the whole number of judgments. These figures show anincrease of discriminative sensibility for such changes as the seriesadvances. The percentage of correct discrimination, as it stands inthe table, is the same for the first and second positions in theline, but this coincidence is to be attributed to accident, inconsequence of the relatively small number of judgments on which theresults are based, rather than to a functional indifference in the twopositions. I conclude that fuller experiments would show a curve ofcontinuous increase in the number of correct judgments for the wholeseries of measures here included. If we number the series of ratiosgiven above from one to five, the thresholds of perceptible change forthis series of positions, expressed in terms of this numerical series, would be: I. , 4. 1; II. , 4. 1; III. , 3. 9; IV. , 3. 6. 

Secondly, in a series of five trochaic measures, the intervalsseparating the groups--which in this case follow the unaccentedbeat--were successively lengthened by increments identical with thoseemployed in the preceding set of experiments. The results arepresented in the table below, arranged similarly to the previous one. 

TABLE LIX. 

 Position in Series. Percentage Values. Ratios. I II III IV I II III IV 1. 000 : 1. 000 0 0 0 0 0. 0 10. 0 0. 0 0. 0 1. 000 : 0. 874 1 1 3 4 16. 5 16. 5 50. 0 60. 0 1. 000 : 0. 777 4 4 5 6 66. 0 66. 0 83. 0 100. 0 1. 000 : 0. 700 6 6 6 6 100. 0 100. 0 100. 0 100. 0 1. 000 : 0. 636 6 6 6 6 100. 0 100. 0 100. 0 100. 0

These results are essentially identical with those of the precedingsection. The sensitiveness to small differences in duration within therhythmical series becomes continuously greater as that seriesproceeds. The thresholds of perceptible change in terms of thenumerical series of ratios (as in preceding paragraph) are as follows:I. , 4. 0; II. , 4. 0; III. , 3. 7; IV. , 3. 6. 

Finally, the intensity of the preceding sound was increased as well asthe duration of the interval separating it from the following stroke. The measure employed was the trochaic, the interval suffering changewas that following the accented beat--in this case, therefore, theintra-group interval. The relations obtaining among the unchangedmeasures were, as to duration of accented and unaccented elements, 1. 000:0. 714; as to intensity, 0. 875:0. 250 inch. Instead of a series, as in the preceding experiments, only one change in each directionwas introduced, namely, an increase in duration of a single accentedelement of the series from 1. 000 to 1. 285, and an increase of the sameelement in intensity from 0. 875 to 1. 875 inch fall. The results aregiven in the annexed table:

TABLE LX. 

 Duration. Stress. Position Interval Following Louder in Series. Judged to be Increased Stress. + = - Times Noted. Not Noted. I. 8 per cent. 92 per cent. 0 per cent. 40 per cent. 60 per cent II. 42 " 50 " 8 " 42 " 58 " III. 57 " 36 " 7 " 54 " 46 " IV. 67 " 26 " 7 " 62 " 38 " V. 30 " 40 " 40 " 60 " 40 "

The figures show that in regard to the discrimination of changes induration occurring in intervals internal to the rhythm group, as wellas in the case of intervals separating adjacent groups, there is aprogressive increase in sensibility to variations as the succession ofsounds advances. This increased sensitiveness is here complicated withanother element, the tendency to underestimate the duration of theinterval following a louder sound introduced into a series. Theinfluence of this second factor cannot be analyzed in detail, sincethe amount of underestimation is not recorded unless it be sufficientto displace the sign of the interval; but if such a quantitativemethod be applied as has already been described, the results show acontinuous decrease in the amount of underestimation of this intervalfrom the first position to the fourth, or penultimate, which presentsthe following relative values: 92, 66, 50, 40. A phase of rapidincrease in the amount of underestimation appears in the fifth orfinal position, represented on the above scale of relative values by120. This falling off at the end of the series, which appeared also inprevious experiments, can be attributed only to an interference withthe functions which the several measures bear in the process ofcomparison, and indicates that the accuracy of judgment is dependenton a comparison of the measure or element in question with those whichfollow as well as with those which precede it. 

The results presented in the preceding section form the statement ofbut one half the evidence of higher rhythmical synthesis afforded bythe material of the present investigation. We turn now to the secondset of results. It deals, in general, with the quantitative relationsof rhythmic forms which find expression through finger reactions. Portions of this evidence have already been presented, through motivesof economy, in connection with the discussion of the phases ofdifferentiation in intensity and duration which such beaten rhythmsmanifest. The burden of it, however, is contained in the results of ananalysis, form by form, of the proportional mean variations whichcharacterize these types of rhythmic expression. This method has beenapplied to a study (_a_) of the characters of the constituentintervals of the unit, in their relation to accentuation and position;(_b_) of the simple group which these elements compose; and (_c_) ofthe forms of higher synthesis manifested by the variations insuccessive groups. The first of these relations concerns, indeed, onlythe internal organization of the simple group, and has no directbearing on the combination of such groups in higher syntheses; but, again for the sake of economy, the items are included with the rest ofthe material. 

The application of such a method, as in all treatment of material bymean variations, involves much labor, [12] and on that account alonethe lack of its employment to any considerable extent in previousinvestigations may be excused; but to this method, as it seems to me, must the final appeal be made, as an indisputable means by which allquestions concerning the refined features of rhythmical organization, the definition of units and the determination of the forms in whichthey enter into larger rhythmic quantities, are to be settled. 

[12] In connection with this work some 48, 000 individual measurementswere made (for the transcription of which I am indebted to the patientassistance of my wife). Half of these were measurements of theintensity of the successive reactions; the other half, of theintervals which separated them. The former series has been employed inobtaining the averages which appear in the section on the distributionof intensities; the latter in that on the distribution of durations. The determination of mean variations was made in connection with thesecond series only (24, 000). These quantities were combined in seriesof single groups, and in series of two, four, eight and ten groups, and for each of these groupings severally the mean variation of theseries was computed. 

Of all the possible forms of rhythmic apprehension or expression, thematerial for such a statistical inquiry is most readily obtainable inthe form of a series of finger reactions, and to such material theapplication of the method in the present investigation has beenrestricted. 

In the first experiment of this group the reactor was asked to tap outa series in which temporal, but not intensive variations wereintroduced; the strokes were to be of uniform strength but separatedinto groups of two beats. No directions as to length of pause betweenthe successive groups were given, but the whole form of the groups wasto be kept absolutely constant. The reports of the subjects wereuniformly to the effect that no accent had been introduced. At acursory examination no intensive grouping was apparent. These recordswere the earliest analyzed, when only time relations were in mind, andno measurements were made of variations in strength. Only the meanvariations of the intervals, therefore, will here be taken up. 

A word first as to the relative value of the two intervals and itssignificance. The form of a rhythmical series is determined in everypart by subordination to principles of strict temporal arrangement. Every suppression of elements in such a series, every rest andsyncopated measure has as positive and well-defined a function as havethe successive reactions and their normal intervals. If such a pauseis made as we find introduced in the present case, its value must be afixed function of the system of durations of which it forms a part, whether it replace an element in a rhythmical unit, or a subgroup in ahigher rhythmical quantity. In general, the value of such a rest isless than the duration of a corresponding full measure or interval. For example, the syncopated forms | >q % | and | >q % %_| aredemonstrably of shorter average duration than the correspondingmeasures| >q q | and | >q q q_|; and the pause occurring at the closeof a syncopated line--such as that in the middle of a catalectictrochaic tetrameter--should be found of less value than that of theregular foot. 

In the present instance two reactions are made, a pause follows, thenthe reactions take place again, and so on. The intervals separatingsuccessive groups of reactions thus result from the coalescence of twoperiods, the interval which would regularly follow the reaction andthe additional pause at its close. The value of the latter I interpretas functionally equivalent to a group of two beats and not to a singleinterval; that is, the rhythm beaten out is essentially quadruple, thesecond member of each composite group being suppressed, as follows: > | q q; % % |. \______/

To estimate the proper value of such a rest the average relativeduration of first and second intervals was taken in a continuousseries of two-beat measures, in which the first member was accentedsufficiently to define the rhythmical groups. The ratio was1. 000:0. 760. In the present instance the values of the simple initialinterval and the composite interval which follows it are, in terms ofthe linear measurement, 1. 55 mm. And 3. 96 mm. Assuming the above ratioto hold, the duration of a period which included the secondbeat-interval and a group-rest should be 1. 16 + 1. 55 + 1. 16 = 3. 87 mm. This is slightly less than the actual value of the period, whereas itshould be greater. It must be remembered, however, that the disparitybetween the two intervals increases with initial accentuation, and inconsequence the proportional amounts here added for the secondinterval (1. 16 to 1. 55) should be greater. This interval is notrhythmically 'dead' or insensitive. The index of mean variation in allreactors is greater for the first than for the second interval (orinterval + pause) in the ratio 1. 000:0. 436, that is, the value of thelatter is more clearly defined than that of the former, and thereactor doubly sensitive to variations occurring within it. 

An analysis of the variations of these intervals separately in seriesof four groups reveals a secondary reciprocal rhythm, in which thechanges in value of the mean variation at any moment are in oppositedirections in the two intervals. These values in percentages of thetotal duration of the periods are given in the following table. 

TABLE LXI. 

 Interval. 1st Group. 2d. Group. 3d Group. 4th Group. First, 15. 4 per cent. 26. 4 per cent. 13. 8 per cent. 30. 3 per cent. Second, 12. 4 " 7. 0 " 9. 6 " 7. 5 "

Without measurement of their intensive values, interpretation of thesevariations is speculative. They indicate that the pairs of beats arecombined in higher groups of four; that the differences of meanvariation in the first interval are functions of an alternating majorand minor accentuation, the former occurring in the second and fourth, the latter in the first and third; and that the inversely varyingvalues of the mean variation in the second interval are functions ofthe division into minor and major groups, the reduced values of thesecond and fourth of these intervals being characteristic of thegreater sensitiveness to variations occurring in the group pause thanto changes occurring within the group. 

The fixity of the group is markedly greater than that of the simpleinterval. In the one case in which the mean variation of the group isgreater than that of the elementary period the material involved wasmeager (five instead of ten repetitions) and the discrepancy thereforeinsignificant. 

The difference in the mean variation of the first and second intervalsrespectively rises to an individual maximum of 3. 000:1. 000, andaverages for all subjects 2. 290:1. 000; the fixity, that is to say, ofthe inter-group interval in this form of tapping is more than twice asgreat as that of the intra-group interval. The fixity of the largerrhythmical quantities is greater than that of the smaller, whether therelation be between the elementary interval and the unit group, orbetween the synthetic unit and its higher composite. The average meanvariation of the beat intervals exceeds that of the whole group in therelation of 1. 953:1. 000. The differentiation of larger and smallergroups is less clear. When the material is taken in groups of eightsuccessive beats the mean variation is less in the case of everysubject than when taken in fours, in the ratio 1. 000:1. 521. Thecomparative values for groups of two and four beats is reversed in twothirds of the cases, yet so that an average for all subjects gives theratio 1. 000:1. 066 between groups of four and two beats. The wholeseries of values arranged on the basis of unity for the mean variationof the beat interval is given in Table LXII. 

TABLE LXII. 

 Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group. M. V. 1. 000 0. 512 0. 480 0. 320

The persons taking part in the investigation were next required tomake a series of reactions composed of unit groups of two beats, ineach of which the first member received accentuation, a simpletrochaic rhythm. In this type the relation of intra-group tointer-group interval remains unchanged. In all subjects but one themean variation of the first interval exceeds that of the second in theaverage ratio 1. 722:1. 000. The amount of difference is less than inthe preceding type of reaction. In the former there is presented notan intensively uniform series, but an irregularly rhythmical groupingof intensities, in dependence on the well-defined parallel types oftemporal differentiation; in the latter such intensive differentiationis fundamental and constant in its form. Assuming the character of thesecond interval to remain unchanged, there is in the intensive fixityof the initial accented element, on the one hand, and the alternateassertion of the impulse to accentuation and repression of it in theattempt to preserve uniformity, on the other, an occasion for thedifference in the relation of the mean variation of this interval tothat of the following in the two cases. It is to be expected thatthere should be less irregularity in a series of reactions each ofwhich represents an attempt to produce a definite and constantrhythmical accent, than in a series in which such an accent isspasmodically given and repressed. 

For a like reason, the difference in value between the mean variationsof the elementary interval and the unit group should be less in thecase of the positive rhythm form than in that of a series whichcombines a definite temporal segregation with an attempt to maintainintensive uniformity. The mean variation of the interval is still ofgreater value than that of the unit group, but stands to it in thereduced ratio 1. 000:0. 969. 

The relations of higher groups present certain departures from thepreceding type. In three cases out of five the unit has a greater > . Fixity than its immediate compound ( | q. Q; q q |), with an average \_______/ratio of 0. 969:1. 072. The original relation, however, is reėstablishedin the case of the next higher multiple, the eight-beat group, thewhole series of values, arranged on the basis of unity for the simpleinterval, being as follows:

TABLE LXIII. 

 Proportional Single Beat 2-Beat Group 4-Beat Group 8-Beat Group M. V. 1. 000 0. 969 1. 072 0. 859

An analysis of the material in successive pairs of two-beat groupsrevealed a pronounced rhythm in the values of the mean variations ofthe first and second members of the pair respectively, the fixity ofthe second group being much greater than that of the first, the meanvariation having a ratio for all subjects of 0. 801:1. 000. Theinterpretation of this rhythmical variation, as in the precedingreaction series, must be speculative in the absence of quantitativemeasurement of intensive changes, but is still not left in doubt. Therhythmic material is combined in larger syntheses than the groups oftwo beats, alternately accented and unaccented, which were avowedly inmind. This secondary grouping appears in at least a measure of fourbeats, into which the unit group enters as the elementary intervalentered into the composition of that unit. In this larger group theinitial period, or element of stress, is characterized by a greatermean variation than the unaccented period which follows it. There arepresent in this first interval two factors of instability: the factorof accent, that element which receives the stress, being in generalcharacterized by a greater mean variation than the unaccented; and thefactor of position, the initial member of a rhythmical group, independent of accentuation, being marked by a like excess of meanvariation over those which follow it. The interpretation of the latterfact lies in the direction of a development of uniformity in the motorhabit, which is partially interrupted and reėstablished with theending and beginning of each successive group, large or small, in theseries of reactions. 

Further, when the material is arranged with four unit groups in eachseries, the same relation is found to hold between the first periodcomposed of two unit groups and the second like period, as obtainedwithin these pairs themselves. The mean variation of the first periodof four beats is greater than that of the second in the case of allsubjects but one, with an average ratio for all subjects of1. 000:0. 745. The analysis was not carried further; there is, however, nothing which points to a limitation of the process of synthesis togroups of this magnitude; rather, to judge from the closeapproximation in definition of the two orders manifested here, thereis suggested the probability that it is carried into still highergroupings. 

In the next rhythmical type analyzed--the iambic form--that relationof the first to the second interval holds which was found to obtain inthe preceding forms. The excess of mean variation in the former overthe latter presents the ratio 1. 274: 1. 000. In amount it is less thanin either of the previous types (2. 290:1. 000 and 1. 722:1. 000). Forhere, though both elements have constant relations as accented orunaccented members of the group, the factor of stress has beentransferred from the initial to the final beat. Instead, therefore, ofcombining in a single member, the factors of inconstancy due to stressand to position are distributed between the two elements, and tend toneutralize each other. That the preponderance of irregularity is stillwith the initial interval leads to the inference that position is agreater factor of inconstancy than accentuation. 

Also, the group presents here, as in the preceding forms, a greaterfixity than does the individual interval. This relation holds for allsubjects but one, the average mean variations of the simple intervaland of the unit group having the ratio 1. 000:0. 824. 

In larger groupings irregularities in the relations of higher andlower again occur, and again the greater constancy obtains between thefirst and second orders of higher grouping (in which for only onesubject has the lower group a greater fixity than the higher, and theaverages for all subjects in the two cases are in the ratio1. 149:0. 951), and the lesser constancy between the unit group and thefirst higher (in which two subjects manifested like relations withthose just given, while three present inverted relations). The wholeseries of relations, on the basis of unity for the mean variation ofthe simple interval, is given in Table LXIV. 

TABLE LXIV. 

 Proportional. Single Beat. 2-Beat Group. 4-Beat Group. 8-Beat Group M. V. 1. 000 0. 824 1. 149 0. 951

There is also presented here, as in the preceding forms, a synthesisof the material into groups of four and eight beats, with similardifferences in the fixity of the first and last periods in each. Asingle subject, in the case of each order of grouping, diverges fromthe type. The ratio of difference in the mean variations of the firstand second members of the groups is, for series of four beats, 1. 000:0. 657, and for series of eight beats, 1. 000:0. 770. Thisindicates a diminishing definition of rhythmical quantities as thesynthesis proceeds, but a diminution which follows too gradual a curveto indicate the disappearance of synthesis at the proximate step inthe process. 

Three-beat rhythms were next taken up and the same method of analysiscarried out in connection with each of the three accentual forms, initial, median, and final stress. In these types of rhythm theintra-group intervals are more than one in number; for the purpose ofcomparison with the final, or inter-group interval, the average of thefirst and second intervals has been taken in each case. 

The results agree with those of the preceding types. The meanvariation of the interval separating the groups is less throughoutthan that of the average group-interval. The ratios for the variousrhythm types are as follows:

TABLE LXV. 

 Rhythm Form. Initial Stress. Median Stress. Final Stress. Ratios, 1. 000 : 0. 758 1. 000 : 0. 527 1. 000 : 0. 658

This relation, true of the average intra-group interval, is also trueof each interval separately. Among these ratios the greatest departurefrom unity appears in the second form which all subjects found mostdifficult to reproduce, and in which the tendency to revert to thefirst form constantly reasserts itself. The difference in value of themean variations is least in the first form, that with initial accent, and of intermediate magnitude in the third form when the accent isfinal. The contrary might be expected, since in the first form--as inthe second also--the factors of stress and initial position are bothrepresented in the average of the first two intervals, while in thethird form the factor of stress affects the final interval and should, on the assumption already made concerning its significance as adisturbing element, tend to increase the mean variation of thatinterval, and, therefore, to reduce to its lowest degree the index ofdifference between the two phases. That it does so tend is evidentfrom a comparison of the proportional mean variations of this intervalin the three forms, which are in order: initial stress, 4. 65 percent. ; median stress, 4. 70 per cent. , and final stress, 7. 15 per cent. That the consequent reduction also follows is shown by the individualrecords, of which, out of four, three give an average value for thisrelation, in forms having final stress, of 1. 000:0. 968, the least ofthe group of three; while the fourth subject departs from this type inhaving the mean variation of the initial interval very great, whilethat of the final interval is reduced to zero. 

If, as has been assumed, the magnitude of the average mean variationmay be taken as an index of the fixity or definition of the rhythmform, the first of these three types, the ordinary dactylic is themost clearly defined; the second, or amphibrachic, stands next, andthe third, the anapęstic, has least fixity; for in regard to the finalinterval, to the average of the first and second and also to each ofthese earlier intervals separately, the amount of mean variationincreases in the order of the accents as follows:

TABLE LXVI. 

 Interval. Initial Stress. Median Stress. Final Stress. First, 5. 82 per cent. 9. 95 per cent. 11. 95 per cent. Second, 6. 45 " 7. 87 " 9. 77 " Third, 4. 65 " 4. 70 " 7. 15 "

In these triple rhythms, as in the two-beat forms, the simple intervalis more variable than the unit group, and the lower group likewisemore unstable than the higher. The series of proportional values forthe three forms is given in the table annexed:

TABLE LXVII. 

 Rhythm Form. Single Interval. 3-Beat Group. 6-Beat Group. Initial Stress, 1. 000 1. 214 1. 037 Median " 1. 000 0. 422 0. 319 Final " 1. 000 0. 686 0. 524

A comparison of the second and third columns of the table shows anexcess of mean variation of the smaller group over that of the largerin each of the three forms. It is true also of the individual subjectsexcept in two instances, in each of which the two indices are equal. This proportion is broken in the relation of the primary interval tothe unit group in the dactylic rhythm form. A similar diversity of theindividual records occurred in the two-beat rhythms. 

The same indication of higher groupings appears here as in the case ofprevious rhythms. Rhythmical variations are presented in the amount ofthe mean variations for alternate groups of three beats. Chronologically in the records, as well as in dependence ontheoretical interpretation, the first member of each higher group ischaracterized by the greater instability. The amounts of thisdifference in coördination between the first and last halves in seriesof six beats is set down for the three rhythm forms in the followingtable:

TABLE LXVIII. 

 Stress. First Half. Second Half Initial, 1. 000 0. 794¹ Median, 1. 000 0. 668 Final, 1. 000 0. 770

 ¹These figures are made up from the records of three out of four subjects. In the exceptional results of the fourth subject no mean variation appears in the first half and 6. 3 per cent, in the second, making the average for the whole group 1. 000:1. 023. 

There is still other evidence of higher rhythmical grouping than theseoscillations in the amount of the mean variation of alternate groups. Exactness of coördination between the individual intervals ofsuccessive groups might undergo development without affecting therelative uniformity of such total groups themselves. But, throughoutthese results, an increase in coördination between the periods of thewhole group takes place in passing from the first to the second memberof a composite group. The relation here is not, however, so uniform asin the preceding case. The series of proportional values is given onpage 403. 

TABLE LXIX. 

 Stress. First Half. Second Half. Initial, 1. 000 0. 846¹ Median, 1. 000 1. 064 Final, 1. 000 0. 742

 ¹ Here also the records of three subjects only are involved, the results of the same reactor as in the preceding cases being discarded. Including this, the ratio becomes 1. 000:1. 016. 

The index of mean variation for the individual elements of the groupalso shows a progressive decrease from first to last as follows:

TABLE LXX. 

 Stress. Interval I. Interval II. Interval III. Initial, 5. 82 per cent. 6. 45 per cent. 4. 65 per cent. Median, 9. 95 " 7. 87 " 4. 70 " Final, 11. 95 " 9. 77 " 7. 15 "

The relation holds in all cases except that of I. To II. In the rhythmwith initial stress. From this table may be gathered the predominanceof primacy of position as a factor of disturbance over that of stress. Indeed, in this group of reactions the index of variation for theaccented element, all forms combined, falls below that of theunaccented in the ratio 6. 95 per cent. : 7. 91 per cent. 

In rhythms of four beats, as in those of three, the estimation ofvalues is made on the basis of an average of the mean variations forthe three intra-group intervals, which is then compared with the finalor inter-group interval. As in those previous forms, sensitiveness tovariations in duration is greater throughout in the case of the latterthan in that of the former. The proportional values of their severalmean variations are given in the annexed table:

TABLE LXXI. 

 Interval. Initial Stress. Secondary Stress. Tertiary Stress. Final Stress. Intra-group, 1. 000 1. 000 1. 000 1. 000 Inter-group, 0. 941 0. 775 0. 725 0. 713

This relation, true of the average of all intra-group intervals, isnot, as in the preceding forms, true of each of the three constituentintervals in every case. In the second and fourth forms, those markedby secondary and final stress, it holds for each member of the groupof intervals; in the first form it fails for the second and thirdintervals, while in the third form it fails for the last of the three. 

The proportional amount of this difference in mean variationcontinuously increases from beginning to end of the series ofrhythmical forms. This cannot be interpreted as directly indicative ofa corresponding change in the definition which the four forms possess. The absolute values of the several mean variations must simultaneouslybe taken into account. First, then, in regard to the final pause thereis presented the following series of values:

TABLE LXXII. 

 Stress. Initial. Secondary. Tertiary. Final. M. V. 6. 57 per cent. 9. 50 per cent. 4. 90 per cent. 15. 70 per cent. 

A very striking rhythmical alternation in the magnitude of the meanvariation thus occurs according as the accents fall on the firstmember of the subgroups when its amount is smaller or on the secondmember when it is larger. Further, the cases noted above, the secondand fourth forms, in which each of the intra-group intervals isseverally of greater mean variation than the final pause, are justthose in which the index of mean variation in the final pause itselfis at a maximum. 

The average mean variations of the earlier intervals thus presentchanges which are analogous to and synchronous with those of the finalpause. Their values in proportion to the whole duration of theintervals are as follows[13]:

 [13] In the second line of figures has been added the series of values of the average mean variation for all four intervals of the group. 

TABLE LXXIII. 

 Stress. Initial. Secondary. Tertiary. Final. M. V. 6. 98 per cent. 12. 25 per cent. 6. 57 per cent. 22. 0 per cent. M. V. 6. 87 " 11. 56 " 6. 15 " 20. 45 "

Those rhythmical forms having their accentual stress initial, or onthe initial elements of the subgroups, are marked by a sensitivenessalmost twice as great as those in which the stress is final, or on thefinal elements of the subgroups. 

Finally, if we take the whole series of intervals severally, we shallfind that this rhythmical variation holds true of each elementindividually as it does of their average. The whole series of valuesis given in the table annexed. 

TABLE LXXIV. 

 Stress. Interval. Initial. Secondary. Tertiary. Final. 

 First, 9. 57 per cent. 13. 23 per cent. 9. 00 per cent. 11. 45 per cent. Second, 5. 53 " 10. 60 " 8. 70 " 9. 00 " Third, 5. 83 " 12. 93 " 2. 00 " 12. 90 " Fourth, 6. 57 " 9. 50 " 4. 90 " 7. 85 "

It is an obvious inference from these facts that the position of theaccent in a rhythmical group is of very great significance in relationto the character of the rhythmical movement. The initial accent givesincomparably greater coördination and perfection to the forms ofuttered (produced) rhythm than does the final. It is in this sense thenatural position of the accent, because on the success and fluency ofthis coördination the ęsthetic value of the rhythm depends. 

In general, though not so unequivocally, the four-beat rhythms show aprogressive increase of stability in passing from the simple intervalto the group, and from the smaller group to the larger. The series ofvalues for the four accentual positions follows. 

TABLE LXXV. 

 Stress. Single Interval. 4-Beat Group. 2-Beat Group. Initial, 7. 27 per cent. 8. 20 per cent. 8. 17 per cent. Secondary, 11. 60 " 9. 60 " 6. 25 " Tertiary, 3. 20 " 3. 40 " 2. 25 " Final, 10. 22 " 6. 30 " 6. 00 " Average, 8. 07 " 6. 87 " 5. 67 "

Here, as in the preceding rhythmical forms, the most constant relationis that of smaller and larger groups, in which no exception occurs tothe excess of mean variation in the former over the latter. The casesin which this relation is reversed are found, as before, in comparingthe simple interval with the duration of the unit group; and theexceptional instances are just those, namely the first and thirdforms, in which the mean variation of this uncompounded interval isitself at a minimum. This means that the simple interval presents amore mobile character than that of the group; and while in general itis less stable than the latter, it is also the first to show theinfluence of increased coördination. Training affects more readily thesingle element than the composite measure, and in the most highlycoördinated forms of rhythm the simple interval is itself the mostperfectly integrated unit in the system of reactions. 

Here, as in the preceding rhythmical forms, evidence of highergrouping appears in the alternate increase and decrease of meanvariation as we pass from the first to the second subgroup when thematerial is arranged in series of eight beats. The proportional valuesof the indices are given in the following table:

TABLE LXXVI. 

 Subgroups Init. Stress Sec. Stress Tert. Stress Fin. Stress 1st Four, 1. 000 1. 000 1. 000 1. 000 2d Four, 0. 950 0. 762 0. 984 0. 790

The first member of the larger group, in the case of every rhythm formhere in question, is less exactly coördinated than the second, theinterpretation of which fact need not here be repeated. Severaladditional points, however, are to be noted. The differences instability of coördination which are encountered as one passes from thefirst to the last of the four rhythm forms, extends, when thereactions are analyzed in series of eight beats, to both members ofthe compound group, but not in equal ratios. The mean variation of thesecond and fourth forms is greater, both in the first and secondsubgroups, than that of the corresponding subgroups of the first andthird forms; but this increase is greatest in the first member of thecomposite group. That is, as the group grows more unstable it does somainly through an increase in variation of its initial member; or, inother words, the difference in variability of the beat intervals ofthe first and last subgroups reaches its maximum in those rhythmictypes in which the indices of mean variation for these intervals arethemselves at their maxima. 

This process of coördination, with its indication of a higherrhythmical synthesis, appears also in the transformations in the valueof the mean variations in duration of the total groups, when thematerial is treated in series of eight beats, as in table LXXVII. 

TABLE LXXVII. 

 Subgroups. Init. Stress. Sec. Stress. Tert. Stress. Final Stress. 1st Four, 1. 000 1. 000 1. 000 1. 000 2d Four, 0. 773 0. 768 0. 943 0. 579

The total initial group, therefore, as well as each of its constituentintervals, is less stable than the second. 

Within the unit group itself the values of the mean variation showhere, as in the preceding forms, a progressive increase insensitiveness to temporal variations from first to last of thecomponent intervals. The proportional values for the four intervals inorder are, 1. 000, 0. 786, 0. 771, 0. 666. The distribution of theserelative values, however, is not uniform for all four rhythmicalforms, but falls into two separate types in dependence on the positionof the accents as initial or final, following the discriminationalready made. The figures for the four forms separately are asfollows:

TABLE LXXVIII. 

 Stress. 1st Interval. 2d Interval. 3d Interval. 4th Interval. 

 Initial, 9. 57 per cent. 5. 53 per cent. 5. 83 per cent. 6. 57 per cent. Secondary, 13. 23 " 10. 60 " 12. 93 " 9. 50 " Tertiary, 9. 00 " 8. 70 " 2. 00 " 4. 90 " Final, 11. 45 " 9. 00 " 12. 60 " 7. 85 "

In the first type (Rhythms I. And III. ) appear a descending curvefollowed by an ascending; in the second type (Rhythms II. And IV. ) asecond descending curve follows the first. The changes in the firsttype are not coördinated with a similar curve of variation in theintensive magnitude of the beats. It is to be noted here that thesmallest mean variation presented in this whole set of results isfound in that element of the first form which receives the stress, anexception to the general rule. The variations in the contrasted typehave their maxima at those points on which the group initiation--primary or secondary--falls, namely, the first and third. 

As in preceding rhythmical forms, while the separation of accentualstress from primacy in the series tends to increase the mean variationof that element on which this stress falls and to raise the index ofmean variation for the whole group, yet the mean variation of theinitial element is also raised, and to a still greater degree, reinforcing the evidence that primacy of position is a more importantfactor of instability than the introduction of accentual stress. 

In the investigation of mean variations for units (if we may call themsuch) of more than four beats only a modicum of material has beenworked up, since the types of relation already discovered are of toodefinite a character to leave any doubt as to their significance inthe expression of rhythm. The results of these further experimentsconfirm the conclusions of the earlier experiments at every point. 

These higher series were treated in two ways. In the first the reactorbeat out a rhythm consisting in the simple succession of groups ofreactions, each of which contained one and only one accent. Theseunits in each case were marked by initial stress, and were composed offive, six, seven, eight and ten beats respectively. The results aregiven in the following table, which contains the series of meanvariations in duration both for single intervals and for total groups. 

TABLE LXXIX. 

 No. Med. Unac'td of Beats. Acc'td Beat. Beats. Final Beat. Average. Group. Five, 12. 2% 6. 8% 7. 1% 7. 9% 6. 3% Six, 9. 2 10. 6 6. 9 9. 7 8. 3 Seven, 7. 1 5. 2 7. 9 5. 8 3. 6 Eight, 12. 4 9. 5 8. 8 9. 7 8. 0 Ten, 7. 5 6. 6 7. 3 6. 8

The averages for the combined, median, unaccented intervals are givenseparately from those of the final interval, for the reason that themean variation of the latter is greater in three cases out of fivethan that of the former, a relation which apparently contradicts whathas already been said concerning the sensitiveness to variations whichmarks the intervals separating rhythmical groups. The reason for thisfinal increase in variation appears when the relative intensities ofthe series of reactions are considered. They are given in Table LXXX. 

TABLE LXXX. 

 No. Of Beats. Acc. Beat. Av. Unacc. Final. Pre-final. Five, 1. 000 0. 543 0. 518 0. 500 Six, 1. 000 0. 623 0. 608 0. 592 Seven, 1. 000 0. 515 0. 544 0. 437 Eight, 1. 000 0. 929 0. 949 0. 863 Ten, 1. 000 0. 621 0. 640 0. 545

In every case the final element is marked by an increase over thatwhich precedes it (see last two columns of table) of the average valuefor all rhythms of 1. 000:0. 900; an increase which raises it above theaverage value of the whole series of preceding unaccented beats inthree cases out of five. To this final accentuation the increase invariation is to be attributed. Yet despite the additional element ofdisturbance due to this increased final stress the average value ofthe mean variation for this final interval is lower than that of themedian unaccented intervals in the ratio (all rhythms combined) of0. 992:1. 000. 

Turning, then, to Table LXXIX. , there is presented, firstly, an excessof variation in the accented element over that of the averageunaccented elements in every case but one (the six-beat rhythm inwhich the values are nearly identical), which for the whole series ofrhythms has a value of 1. 000:0. 794. Secondly, in every completed case(part of the figures in the last rhythm are inadvertently lacking), the average mean variation of the single interval preponderates overthat of the total group. 

The second form of rhythmical tapping, in which the longer series werebeaten out as pairs of equal subgroups, was added in order todetermine the quantitative relations of the mean variations foralternate subgroups when such groups were purposely intended, insteadof appearing in the form of unconscious modifications of therhythmical treatment, as heretofore. At the same time the resultspresent an additional set of figures embodying the relations here inquestion. They are as follows:

TABLE LXXXI. Intervals. Groups. Number Av. 1st 2d 1st 2d of Beats. Acc. Unacc. Half. Half. Half. Half. Average Totals Six, 27. 9% 20. 9% 23. 4% 23. 0% 14. 6% 13. 3% 13. 9% 13. 8% Eight, 16. 6 14. 8 13. 2 17. 3 6. 2 3. 3 4. 7 2. 7 Ten, 7. 9 2. 6 3. 4 4. 0 5. 9 5. 2 5. 5 3. 1

No exception here occurs to the characteristic predominance ininstability of the accented element. As regards simple intervals, therelation of first and second groups is reversed, the reason for whichI do not know. It may be connected with the rapid speed at which theseries of reactions was made, and its consequent raising of thethreshold of perceptible variation, proportional to the value of thewhole interval, to which is also due the higher absolute value of thevariations which appear in both tables. 

These inversions disappear when we compare the relative stability ofthe first and second subgroups, in which the excess of variation inthe former over the latter is not only constant but great, presentingthe ratio for all three rhythms of 1. 000:0. 816. The characteristicrelation of lower to higher rhythmical syntheses also is herepreserved in regard to the two subgroups and the total which theycompose. 

The points here determined are but a few of the problems regarding thestructure of larger rhythmical sequences which are pressing forexamination. Of those proximate to the matter here underconsideration, the material for an analysis of the mean variation inintensity of a series of rhythmical reactions is contained in themeasurements taken in the course of the present work, and this may ata future time be presented. The temporal variations having once beenestablished it becomes a minor point. 

Such conclusions, however, are only preliminary to an investigation ofthe characteristic structure of the ordinary metrical forms, and tothese attention should next be turned. The configuration of the commonmeters should be worked out both in relation to the whole formalsequence, and to the occurrence within the series of characteristicvariations. There can be no question that each metrical structure, theiambic trimeter or dactylic tetrameter line, for example, composes adefinite rhythmical melody within which each measure is shortened orprolonged, subdued or emphasized, according to its position andconnections in the series of relations which constitute the rhythmicalsequence. 

These several metrical forms should be explored and the characters ofeach measure in the series quantitatively determined. Such aninvestigation would include an ascertainment of the proportionaltime-value of each successive measure, its average force, and itssensitiveness to variations, temporal and intensive. It should includean examination of the configuration of the single measure and thechanges in distribution of accents and intervals which it undergoes asthe rhythmical series advances. For the rhythm group must not beconceived as a simple unchanging form; both intensively and temporallyit is moulded by its function in the whole sequence, the earlieriambic of a heroic measure being unlike the later, the dactyl whichprecedes a measure of finality different from that which introducesthe series. Such a set of determinations will give the purecharacteristic curves of our common poetical meters. 

But these meters are no more simple forms than are their constituentmeasures. At every point their structure is subject to modification byfactors which appear in the rhythmic utterance in virtue of its use asa medium for the free expression of thought and emotion; and themanner in which the characteristic form is altered by these factors ofvariation must be studied. Of these variations the more important arethe effects of the introduction of variants--of spondees amongdactyls, of anapęsts among iambics, and the like--and the occurrenceof points of origin, emphasis, interruption, and finality in specialaccentuations, syncopated measures, cęsural pauses and elisions. Thesefactors influence the structure both of those measures within whichthey appear and of those adjacent to them. The nature and extent ofthis wave of disturbance and its relation to the configuration of thewhole sequence call for examination. 

Finally, this process of investigation should be applied to the largerstructures of the couplet and stanza, that the characteristicdifferences in the pair or series of verses involved may bedetermined. These characters include the whole time occupied by eachverse of the stanza, the relative values of acatalectic and catalecticverses occurring within the same stanza structure, differences inrhythmical melody between the latter forms, the variations of averageintensity in the accentual elements of such lines, and a determinationof the values of rests of higher and lower degrees--mid-line, verse, and couplet pauses--which appear in the various stanza forms, andtheir relation to other structural elements. 

 * * * * *

RHYTHM AND RHYME. 

BY R. H. STETSON. 

I. INTRODUCTION. 

The psychological theory of rhythm has its beginnings in the work ofHerbart, [1] who inaugurated the treatment of rhythm as a species oftime perception and suggested an explanation of its emotional effects. While Herbart had simply pointed out the effect of a whole rhythmicseries in giving rise to an emotion of expectation, delay, or haste, Lotze[2] applied the principle severally to each unit group (eachfoot) in the rhythm, and made the emotional effect of rhythm depend onthese alternate feelings of strain, expectation, and satisfactionproduced by every repetition of the unit group. Vierordt[3] did thefirst experimental work on rhythm, determining the period of greatestregularity in the tapping of rhythms. But the first importantexperiments were carried on by von Brücke. [4] By tapping out rhythmson a kymograph, he determined the well-known 'Taktgleichheit' of thefeet in scanned verse, and noted a number of facts about the timerelations of the different unit groups. Mach[5] added to the previousknowledge about rhythm certain observations on the subjectiveaccentuation of an objectively uniform series, and specially he notedthat the process is involuntary. With a much clearer understanding ofthe facts of rhythm than his predecessors had had, he really providedthe foundation for the theories which follow. His most importantcontribution, for some time overlooked, was his emphasis of theessentially motor nature of the phenomena of rhythm, and his motortheory therefor. 

 [1] Herbart, J. F. : 'Psychol. Untersuchungen' (Sämmt. Werk, herausgeg. Von Hartenstein), Leipzig, 1850-2, Bd. VII. , S. 291 ff. 

 [2] Lotze, R. H. : 'Geschichte der Ęsthetik, ' München, 1863, S. 487 ff. 

 [3] Vierordt, K. : 'Untersuchungen über d. Zeitsinn, ' Tübingen, 1868. 

 [4] von Brücke, E. W. : 'Die physiol. Grundlagen d. Neuhochdeutschen Verskunst, ' Wien, 1871. 

 [5] Mach, Ernst: 'Unters. ü. D. Zeitsinn d. Ohres, ' _Wiener Sitz. Ber. , mathem. Naturw. Classe_, 1865, Bd. 51, II. , S. 133. _Beiträge zur Physiol. D. Sinnesorgane_, S. 104 ff. 

Many of the recent theories of rhythm are based on Wundt's analysis. The work of Wundt and Dietze, [6] was concerned with rhythmic series;but it may be noted that the 'span of consciousness' and the'synthetic activity of consciousness' were the subjects actually underinvestigation. Rhythm was considered as a special temporal form ofthis 'psychic synthesis. ' There are three different elements in asound series, declared these writers, which contribute to thissynthesis: qualitative changes, intensive changes and melodic changes. Of these the intensive changes are the most important. Every increasein intensity, that is, every beat ('Hebung') is followed by adecrease, and the next increase which follows is recognized as arepetition of the preceding beat and as the forerunner of the beatwhich is to follow. From this comes the synthetic power of the rhythm. Just as the simple unit groups are built up by this synthesizingpower, so they in turn are combined into larger phrases and periods. The motor factor has little place in Wundt's own discussion, [7] the'mental activity' is the all-important thing. Bolton[8] also made avery important contribution to the experimental knowledge of rhythm. His work was based entirely on Wundt's theory. His method ofexperimentation was accurate and his observations copious. Thearrangement of his apparatus, however, led him to emphasize objectiveuniformity as a condition of rhythmic grouping; so that Meumann'scriticism of his application of this principle to poetry is quitejust. Nevertheless Bolton established the essential facts ofsubjective accentuation and apparent temporal displacement. It isnoteworthy that he laid great emphasis on the motor aspect of rhythm, and made many careful observations on the 'motor accompaniment. ' Whileinclining strongly to a motor interpretation he did not attempt to cutloose from the Wundtian 'apperceptive process' as the primary factor. 

 [6] Wundt, W. : 'Physiol. Psych. , ' 4te Aufl. , Leipzig, 1893, Bd. II. , S. 83. 

 [7] Wundt, W. : 'Physiol. Psych. , ' 4te Aufl. , Leipzig, 1893, II. , S. 89 ff. 

 [8] Bolton, T. L. : _Amer. Jour. Of Psych. _, 1894, VI. , p. 145 et seq. 

The most elaborate consideration of rhythm yet published is that ofMeumann. [9] He avowedly worked out and defended the theory of Wundt. The only important difference is the larger place which he gave to the'motor accompaniment, ' although he was always careful to emphasize itssecondary and derived character. He insisted that the 'mentalactivity' is always primary, and that without it there can be norhythmization; and he opposed vigorously the motor inclinations ofMach and Bolton. It is certainly unfortunate that rhythm has alwaysfallen into the hands of the investigators of the 'attention, ' or the'span of consciousness, ' or the 'perception of time. ' It is but anincident that judgments of time are often based on rhythms; andeverything that Meumann has said of a 'mental prius, ' or a'synthesizing activity' in the case of rhythms, may just as well besaid in the case of any coördinated act. 

 [9] Meumann, E. : _Phil. Stud. _, 1894, X. , S. 249 ff. 

Meumann discussed in detail the characteristics of the rhythm of asimple series of sounds, of music, and of verse. He assumed that inthe simple sound series we have rhythm in its barest form, and onlythe rhythmic synthetic activity is at work; while in music there is acontent which to some extent prescribes unities, and the objectiveregularity of the rhythm is broken. In verse we have much morecontent, and the rhythmization is no longer regular in its temporalrelations; it is entirely dominated at times by the 'logical unities'of the 'thought. '

One great difficulty with such a differentiation of the three types ofrhythms presents itself when one inquires into the objectiveregularity of the types; the fact is that music is by far the mostregular in its time values, though it has more content than the soundseries; and that just as great irregularities are possible in the baresound series as in the rhythm of verse with its rich and definitecontent. 

Later statements of the facts and theories relating to rhythm haveinclined more and more to an emphasis of the motor aspect, even on thepart of Wundtians. Since Meumann there has been some detailedlaboratory work published, but the amount of accurately measuredrhythmic material is astonishingly small. Meumann establishedexperimentally the well-known relation between the length of arhythmic element and its accent, and corroborated the earlier work onsubjective accentuation. The reports contain the measurements of butabout eighty individual unit groups (iambs, trochees, etc. ). Ebhardt[10] gave the measurements of from 150 to 300 taps from each ofthree subjects. But his work is vitiated, as far as any application torhythm is concerned, because he based everything on the judgment of_equality_, which has nothing to do with rhythm. 

 [10] Ebhardt, K. : _Zeilschr. F. Psych, u. Physiol. D. Sinnesorgane, _1898, Bd. 18, S. 99. 

Hurst, McKay and Pringle[11] published measurements of about 600individual unit groups from three different subjects; in severalcases, the material consists rather too much of records of theexperimenters themselves, but in general their results agree very wellwith those of other authors. Scripture[12] published the measurementsof a single stanza of poetry. It is but a single stanza and quite toolittle material on which to base any conclusions, but it is notable asa measurement of freely spoken rhythm. No experiments have beenpublished which bear on the nature of the rhythmic phrase, of theperiod, or of the stanza. 

 [11] Hurst, A. S. , McKay, J. , and Pringle, G. C. F. : _Univ. Of Toronto Studies, _ 1899, No. 3, p. 157. 

 [12] Scripture, E. W. : _Studies from the Yale Psych. Lab. , _ 1899, VII. , p. 1. 

Our problem is: What part do the recurrent qualitative factors, likerhyme, play in the grouping of rhythms? They function evidently, inthe main, as factors determining the periods or larger phrases of therhythm structure--the verses and stanzas of poetry and nonsense verse. As no work has been done on the nature of such larger rhythmicunities, a large share of the investigation was concerned with thenature of the verse unity. 

Two methods of investigation were used: Subjects listened to rhythmicseries, into which various modifications were introduced; andsecondly, rhythms of a prescribed type, produced by the subject, wererecorded and measured. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE IX. Opposite p. 417]

II. THE PERCEPTION OF A RHYTHMIC SERIES. 

Apparatus: A disc (Fig. 1, Plate IX. ) about 50 c. In diameter, rotating on a vertical pivot, was driven by a pulley-cone underneathmounted on the same spindle (not shown in the figure). On the face ofthe disc were four concentric rings of regularly spaced holes, whichreceived pegs of uniform height and provided with a shoulder. Corresponding holes of each circle lay on the same radius. On a platesupported by a bracket were mounted four levers whose heads stood inline radially to the movable disc. When the disc rotated to the rightunder the levers, the pegs forced up the lever heads and made anelectric contact. The dip of the levers was controlled by a screwadjustment. The apparatus was driven by a motor and reducing gear, which were isolated in a sound-proof box. The rate of speed wascontrollable. 

The apparatus was built for use with sounders connected with thebinding-posts, but in this investigation sounders were dispensed with, and the clicks from the apparatus itself were used, since but onequalitative difference was introduced. As a rule, the objective accentof the foot was not given; the subjective accentuation was nearlyalways sufficient. Subjects were quite unable to say whether theaccent was objective or not. If necessary, an accentuation wasproduced by raising the pegs representing the accentuated part of thefoot. The group elements were represented by single, simple clicksmade by a brass screw on the lever arm striking an iron plate (thenoise of the brass peg striking the lever head was eliminated bydamping with cloth). The rhyme was represented by a compound noiseconsisting of a click higher in pitch than the verse element click, made by the peg striking the lever head, and an almost simultaneousclick lower in pitch than the verse element click, made by the screwof the lever arm striking another iron plate. The rhyme noise was notlouder than the verse element click, and as a whole gave theimpression of being a lower tone because the first click was verybrief. Subjects did not analyze the rhyme noise, and had no difficultyin making it represent rhyming syllables. The pauses throughout hadno filling. 

The subject was always given a normal series until the type wasclearly established, and when the variations to be judged wereintroduced his attention was directed as far as possible to the factorto be introduced. This seemed the only way to obtain trustworthyjudgments. If the subject waits blindly for some perceptual change inthe whole complicated mass of sensations which the simplest rhythmicseries constitutes, he is apt to fit his attention on some irrelevantdetail, and the change may not be noted until greatly exaggerated, andhe may not judge that particular factor at all. 

The subject was always asked to choose a rate of delivery which wouldcorrespond to his natural rate of reading nonsense verse, and theclicks were always associated with syllables, though not with words. An effort was made to keep the series as colorless and devoid ofcontent as possible, to eliminate uncertain association. Beyondsuppressed articulation, the subject was not encouraged to mark therhythm with any part of the body, but a number of involuntarymovements of neck, body, hand, or foot were nearly always observed. Occasionally, when a subject's expression was doubtful, he was askedto say a nonsense series with the clicks. 

The nomenclature to be used in this paper is that of meter, but it isalways subject to the reservation that the material is only analogousto series of nonsense syllables. 

Records were kept in terms of the intervals on the revolving disc; thetime of revolution was also taken, so that the figures may betranslated in time intervals if desired. Thus, 34, 34, 34, 34, 34represents a series of iambs in which the unaccented click has thelength of three, and the accented click the length of four spacesbetween pegs. A uniform verse represented by a digit giving the numberof feet, followed by digits in parenthesis giving the character of thefoot, _e. G. _, 4 (34), is an iambic tetrameter. 

For convenience, the verse pause is written independently of the lastfoot of the verse, _e. G. _, 4 (34) p. 7 represents a tetrameter linehaving the intervals 34, 34, 34, 37. The interval of the last accentedsyllable is counted twice. 

Occasionally this is disregarded and vs. P. Equals o is written toindicate that the vs. P. Is equal to the foot pause. 

The results of the experiments may be grouped under three heads:

1. Why does a synthesizing factor such as rhyme occur at the end ofthe verse?

2. What is the relation between the verse pause and the rhyme?

3. What is the relation of rhyme to the cyclic movement of the unitgroup and of the verse?

_1. Why the Synthesizing Factor Occurs at the Close of the Verse_. 

To determine a possible difference in the sense of rhythm at thebeginning and the close of a verse, pauses ('lags') were introducedinto the earlier and later parts of the verse. These pauses were madebarely perceptible, _i. E. _, barely perceptible in any part of theverse. Usually in iambic verse the barely perceptible lag shows thefollowing proportions to the other pauses:

 34 _35_ 34 etc. , or 47 _48. 5_ 47. 

Most of the experiments were performed with iambic tetrameter. Thesubject was told to note the lags in the verse: these were introducedeither in both parts of the verse or at its close only. At least threeverses were given, and records were kept of the false judgments. Whenlags of identical duration were introduced between the first andsecond and between the third and fourth feet, it was found that nearlyalways the lag would not be detected in the earlier part of the versebut would be detected in the later part. Out of eighty-two cases, there were but six in which the same lag was recognized in the firstas well as in the last position. In two of these cases the subject'sattention had been called to the first part of the verse; and in thefour other cases the lag was still found more marked at the close thanat the beginning. 

There were no cases in which a lag detected in the earlier part of theverse was not also detected in the later part. False judgments, whenthey occurred, were made as to a lag in the earlier part of the verse. One subject falsely located a lag in the first of the verse fourtimes. Judgments as to the earlier part of the verse were uncertainand frequently changed. 

The maximum lag possible without breaking the unity of the verse wasdetermined for the earlier and later parts of the verse. The verseunity was tested by adding enough feet to make a full verse, after thebreak, and asking the subject to mark the close of the verse. In everycase this irregularity was introduced into the second verse, and thefirst verse was normal, _e. G. _ (pentameter), I. 5 (34). II. 34 lag 34 34 34 34 34. 

If the lag does not break the verse, the subject should hear the closeof the verse at the end of the fifth foot in II. If the verse isbroken he should ignore the first foot and make a new verse, endingwith the sixth foot. 

 J. Iamb. Tet. 1st pause of verse, max. Pos. Lag 9 3d 7 L. 1st 9 3d 7 R. 1st 11 3d 9 G. 1st 9 3d 7 Mi. 1st 10 3d 8 B. 1st 7 H. 1st 10 3d 6

Later, in the attempt to determine natural divisions, or nodes in theverse, the following were determined:

 L. Max. Pos. Lags in f. P. Of iamb. Pent. In order 8 13 9 6 G. 10 11 9 8 Mi. 15 18 17 14 Me. 7. 5 13 9. 5 6 R. 9 9 11 7 B. 12 8 15 7 H. 7. 5 8 10 7

 B. Max pos. Lags in dac. Let. , cat. , in order 12 16 8 S. 10 11 7 Mc. 7 10 6 G. 11 11 7 L. 19 16 7 H. 7 6 4

This shows that an irregularity in the time intervals may be greaterin the earlier than in the later part of the verse. This last table isfurther evidence of the increased exactness of the rhythmic perceptionat the close of the verse. As far as nodes are concerned, they showclearly two types: (1) A node after the second foot (L. , G. , Mi. , Mc. )and (2) a node after the third foot (R. , B. , H. ). For the tetrameterthere is some indication in the cases of B. , S. And Mc. , but the othercases are negative and further evidence is needed. 

With three of the subjects, Mi. , J. And K. , it was not always possibleto get records of the maximum lag, since it was impossible to definethe verse unity. When this was unbroken it was the unanimous testimonyof the subjects, corroborated by their unconscious movements, thatthere was a feeling of tension during the lag. But the subjects justreferred to got a type of unity, and there was no tension. The lagswere indefinite and very long (35-90). This unity must be of the samekind as the unity of the stanza, which includes long expressionalpauses, as well as rhythmic verse pauses. 

If a subject is asked to fall in at the beginning of a rhythmic serieshis first attempts are decidedly incoördinated. His earliest reactionsfollow the clicks which they are intended to represent, but presentlythe series of motor impulses generated by the sounds and the voluntarymovements which the subject makes fuse into a voluntary type ofreaction in which the cycle has become automatic and definite, and theclicks take their proper places as coöperating and controlling factorsalong with the motor cues of the process itself. The accuracy of thejudgments of time, if such judgments be made, or the estimation of thelikeness of the groups, depends on the definiteness with whichmovement sensations follow each other in a regular series. 

The following experiments (Table I. ) concern the perception of a lagin different parts not of a verse but of a stanza. It was a question, namely, whether a lag in the first rhythmic series (first verse) whichestablishes the motor cycle in the subject would be detected in thelater rhythmic series (later verses of the stanza) after the motorcycle in the subject has been inaugurated. This responsive motor cycleshould itself, of course, contain the lag given with the firstrhythmic series. 

A stanza of the form of A (Table I. ) was clicked out by theinstrument, but the subject had no clue as to the regularity orirregularity of any verse. The stanza was repeated as often as thesubject wished, but not without a pause of a few moments between eachrepetition. 

TABLE I. 

 THE INFLUENCE OF A LAG IN THE FIRST VERSE ON THE JUDGMENT OF IDENTICAL LAGS IN LATER VERSES. 

 A. Stanza given: I. 34 34 35 34 p. 7-9 II. " " " " " III. " " " " "

 In 14 cases the following was reported:

 I. Lag noted. II. " not noted. III. " " "

 In 9 cases the following was reported:

 I. Lag noted. II. " " but shorter than first. III. " " " " " "

 In 6 cases the following was reported:

 I. Lag noted. II. " " and equal to first. III. " " " " " "

 B. Stanza given: I. 35 34 34 34 p. 7-9 II. " " " " " III. " " " " "

 Any pause large enough to be noted in I. Was noted in II. And III. (This table contains the judgments made on all trials. )

Most of the judgments of the third set are due to the fact that thesubject first attended to the series on the second or third verse. Thelarge number of cases (83 per cent. ) in which the lags in the secondand third verses were concealed by the equal lag in the first verse, makes it very probable that the type of a verse is somehow altered bythe impression left by the preceding verse. 

The method of determining the maximal lags (as previously described)gave interesting evidence on the point at which the unity of the verseis actually felt. In the form

 I. 5 (34) II. 34 lag 34 34 34 34-34

as the lag increases, a point is reached at which the unity may bemade to include the first foot or to ignore it. Which of these is donedepends on the subject's attitude, or _on the point at which the verseis brought to a close. _ In either case the unity, the 'pentameterfeeling, ' is not experienced _until the end of the series unified isreached. _ This is the case with all the subjects. 

This development of the feeling of the particular verse form only atthe end of the verse, and the fact that the subject may be uncertainwhich form he will hear until the series has actually ceased, showsthat the verse-form movement is not of such a character that the closeof it may not be considerably modified. A form which may fit thepentameter can be broken off early, and become a satisfactorytetrameter. The feeling seems to depend on some total effect of theverse at the close. This effect is probably a blending of themass-effect of the impressions received thus far, which have adefinite character and feeling significance, and which form the motordisposition for the next verse. The essential thing in thedetermination of verse unity seems to be the dying out of theautomatism, the cessation of the coördination of the cyclic movement. The rhyme, it would seem, emphasizes the close of the automatic cycle. But it is probable that satisfactory phrasing has othercharacteristics, and a definite form as a movement whole. 

_2. The Relation of the Rhyme to the Verse Pause. _

Determinations of the minimal satisfactory verse pause were made witha view to comparing the minimum in unrhymed with that in rhymedverses. 

The stanza used was of the following form:

 I. 34 34 34 p. II. " " " " III. " " " "

The minimal satisfactory verse pauses were:

 Without Rhyme. With Rhyme. Subject. L. 6 4 " J. 5 4 " Mc. 6 4 " R. 7 4 " B. 6-7 3. 5 " G. 6 3. 5 " Mi. 6-7 3. 25

It thus appears that the minimal pause which is satisfactory, is lesswhen rhyme is present than when it is not present. Similardeterminations were made for the maximal satisfactory verse pauses, asfollows:

 Without Rhyme. With Rhyme. Subject. L. 9-10 11 " J. 8 9 " Mc. 9 9 " R. 10-11 10-11 " B. 9 9 " G. 11-12 11 " Mi. 10 10

(A few experiments were tried with verse pauses of different length inthe same stanza. A difference of one fourth the value of the pause isnot detected, and unless attention is called to them, the pauses mayvary widely from one another. )

This shows that the rhyme reduces the _necessary_ pause in verse tothe mere foot pause; while at the same time as great a pause is_possible_ with rhyme as without it. Aside from the table above, alarge number of the records made for other purposes support thisstatement: whenever rhyme was introduced, the verse pause was madeequal to the foot pause, or even slightly less than it, and was alwaysfound satisfactory. 

Numerous cases of introduction of lags into the verses of rhymedstanzas go to show that irregularities in such verses do not affectthe length of the pauses. 

Two hypotheses suggest themselves in explanation of the striking factthat the verse pause becomes unnecessary at the close of a rhymedverse. 

The unity is now a new kind of verse unity; the rhyme is a regularrecurrent factor like the accent of a foot, and the series of rhymesgenerates a new rhythm. In the rhymed stanza we are to see not a setof verses, like the verse of blank verse, but a new and enlarged verseunity. 

There are several decided objections to this conception. First, theverse pause _may_ be eliminated, but its elimination is _notessential_ to the rhyme effect; the verse pause may still be as long, if not longer, with rhyme. Secondly, the larger unity into which theverses enter is not in many cases a unity made up exclusively ofrhymed verses. Verses without rhyme alternate with rhymed verses, andhave the usual verse pause. Thirdly, the rhyme is not merely aregularly recurring element: it is essentially a recurring element ofwhich one may say what has been said falsely of the rhythm elements, that each rhyme is either a repetition of something gone before towhich it refers, or the anticipation of something to which it looksforward. In most cases, rhymes function in pairs. Such peculiaritiesdistinguish the rhyme from the accent of the foot. Lastly, the freedomof the whole stanza structure into which rhyme is introduced is muchgreater than that of the single verse; pauses much larger than theadmissible lags of a single verse are possible between the verses, andthere is no tension which persists throughout. There is no feeling ofstrain if the series halts at the verse ends. 

A second hypothesis is that there is some definite process at the endof the verse which marks the close of the verse and which takes moretime in the case of blank verse than in the case of rhymed verse. Ifwe conceive the end of the verse as a point where a dying out of thetension occurs, we may imagine that the rhyme brings an emphasis, andbecomes a qualitative signal for this release. The slight increase ofintensity on the rhyme contributes to the breaking up of thecoördination, and at the same time exhausts and satisfies the feelingof tension which the verse embodies. It is at the point for finishingand releasing the set of strains which constitute the motor image ofthe verse. A qualitative change may be supposed to produce the effectmore rapidly than the simple dying out of the tensions, which occursin blank verse without a differentiated end accent. 

3. _The Relation of the Rhyme to the Cyclic Movement of the Unit Groupand of the Verse_. 

A series was arranged in which the accent of an ordinary foot and arhyme occurred side by side; the distance between them was graduallylessened, and the effect on the rhyme and on the ordinary accentedelement was noted. 

A preliminary set of experiments on the effect of two accents whichapproach each other gave some very interesting results. Thus Table II. Shows the effect of gradually eliminating the verse pause from thecouplet. 

TABLE II. 

 Dactylic, catelectic couplet of the general form:

 ĶII ĶII ĶII Ķ / ĶII ĶII ĶII Ķ Without rhyme. 

 Each dactyl (ĶII) is, in terms of spaces between the pegs, 3 2 4; or in seconds, . 25, . 17, . 33. 

 The pause between the two verses was gradually lessened

 B. At 5 (. 42 sec. ) The verses are normal. 4. 5 The verses are normal, but first accent of II. Is fading. 4 The accent is less and less on first element of II. 3. 3 The accent is almost gone on first element of II. 3 (. 25 sec. ) First foot of II. Has quite lost accent. There is now but one verse. 'Amalgamation. ' Mc. 7 (. 58 sec. ) The verses are normal. 5. 3 Either first element of II. Has its normal accent, or it wavers to a secondary accent, and the verses become one. 5 (. 416 sec. ) First foot of II. Has quite lost accent. Amalgamation. 3 (. 25 sec. ) 'Last verse completely spoiled. ' Last verse ' ' ' ' becomes -- /- -, -- - -, -- - -, -- --. Unsatisfactory. 2 (. 16 sec. ) The II. Has become mere 'medley. ' H. 6 (. 5 sec. ) Normal. 5 First element of II. Attaches to I. , and its accent is lessened. 3 (. 25 sec. ) First element of II. Has lost its accent; the verses ' ' ' ' ' ' ' become --- --- --- - / - --- --- ---. But one verse. Amalgamation. J. 5 (. 42 sec. ) Normal. 4. 6 First element of II. Is losing accent. 3 (. 25 sec. ) First two elements of II. 'tumble over each ' ' ' ' ' ' ' other. ' --- --- --- - / ---- --- ---. Unsatisfactory. Amalgamation. L. 5 (. 42 sec. ) Normal. 4 Last element of I. Losing accent. 3. 3 Last element of I. And first of II. Have completely lost accent. Amalgamation. G. 7 (. 58 sec. ) Normal. ' ' ' ' ' ' 3 (. 25 sec. ) --- --- --- - / - ----- --- -. Amalgamation. 

 Mi. 4. 3(. 35 sec. ) Normal. 4 First two elements of II. Equal in accent. ' ' ' ' ' ' ' ' 3 (. 25 sec. ) --- --- --- - / - -- --- --- -. Amalgamation. 

As soon as the accents are within a certain distance they affect eachother. As a rule the first retains its original intensity and thesecond is weakened; rarely the first yields to the second. The tableshows that the distance at which this occurs is about . 42 seconds. Under many conditions it is quite possible for two accents to occur atthat distance, _e. G. _, in rapid rhythms, without any 'fusing. ' Thesubject has a type of rhythm very definitely in mind and the onlyhypothesis which will explain the difficulty in observing the type, inspite of the slight change in time values, is that somehow the cyclicautomatic movement has been affected and can no longer produce thenormal, limiting sensation at the accent. There is not time for thephase of relaxation before the next, objective, limiting sensationoccurs. We may figure the movement as follows:

[Illustration: FIG. 2. ]

_A_ is a curve in which _B_ is the relaxation phase. At _C_ thetensions are rapidly increasing in anticipation of the next limitingsensation at _A_. But if the objective factor appears too early, thetensions will be discharged prematurely, and the second accent will beweakened. Exactly the obverse of these phenomena is often noticed, when a slight retardation of the second accent produces a slightincrease in its intensity. When, finally, the second accent has beenmoved so near the first accent that it occurs within the phase of thefirst, it disappears as an independent accent. At the same time theobjective stimuli immediately following now appear at quite irregularintervals in the cycle, the coördination is broken up, and chaoswithout accentuation for some distance is the result. Occasionally theprocess does not right itself before the close of the verse. As thisprocess eliminates the verse pause, the two verses become one, as theaccents approach each other. In cases where the first accent is lost, one may suppose that the first accent functions as an anticipatorystimulus, while the second simply increases the effect (cf. Hofbauerand Cleghorn), and marks the culmination. The fact that the secondaccent is only lost at very close range favors this idea. 

TABLE III. 

 Dactylic, catalectic couplet of the general form: ĶII ĶII ĶII Ķ / ĶII ĶII ĶII Ķ (with rhyme). 

 Each dactyl (ĶII) is, in terms of spaces between the pegs, 324; or, in seconds, . 25, . 17, . 33. 

 The pause between the two verses was gradually lessened. 

 B. 

 At 4 (. 33 sec. ) Normal. 2 (. 17 sec. ) First accent of II. Is weakening. 1. 3(. 21 sec. ) Amalgamation. Rhyme retains the accent. Mc. 5 (. 42 sec. ) Normal. 4 II. Has become anapęstic. 2 (. 17 sec. ) Rhyme is lost. Amalgamation. J. 3 (. 25 sec. ) Normal. 2 (. 17 sec. ) Accent of rhyme is lost. Amalgamation. L. 4 (. 33 sec. ) Normal. 1. 6(. 18 sec. ) Rhyme retains accent, first accent of II. Is lost. Amalgamation. G. 4 (. 33 sec. ) Normal. 2 (. 17 sec. ) Accent of rhyme retained. Amalgamation. Mi. 2 (. 17 sec. ) Normal. 1. 6 First foot of II. Amphibrachic. . 4(. 03 sec. ) Accent of rhyme retained. Accent of first foot of II. Lost. Amalgamation. 

When the qualitatively different click representing the rhyme isintroduced, its most striking effect is decidedly to shorten thepossible distance between the two accents. This is in accord with thenotion suggested of the function of rhyme at the verse end. The rhymeseems greatly to hasten the relaxation phase, as compared with thetime required in the ordinary foot. 

There is a variety of forms possible to the unrhymed verse, but thatwith the climax at the close is decidedly the most frequent. When therhyme is introduced the climax goes with it, and the verse flows downas it were to the end. When the rhyme is put in the very first of theverse, however, a secondary or even a primary accent may be developedat the close of the verse. The natural place for the climax of theverse movement is apparently at the close, and the fact that not onlyis the earlier part of the verse more vague, but also that the end isthe natural, climactic position, makes the synthesizing and delimitingfactor, rhyme, preferable at the close. 

The records of the next table were obtained by asking the subjects torepeat the series with prescribed accents, until they decided whetheror not the rhyme could be felt under the conditions. 

TABLE IV. 

Rhymes under prescribed accentual conditions: iambic tetrameter. Heavy accent marked acute (“). Slight accent marked grave (`). Rhyme indicated by brace. 

 Ta ta ta ta ta ta ta dó) gņ) dņ dņ Hu. Rhymes imperfectly. Mc. Rhymes imperfectly. G. Rhymes imperfectly. Ha. Rhymes imperfectly. Hy. Rhymes fairly well. 

 Ta ta ta ta ta ta ta dņ) gó) dņ dņ Hu. Cannot get rhyme. Mc. Rhymes imperfectly. 'Produced by some sort of tension. ' G. Rhymes imperfectly. 

 Ta ta ta ta ta ta ta dņ) gņ) dó dņ Hu. Rhymes well. Mc. Rhymes well. G. Rhymes well. 

 Ta ta ta ta ta ta ta dņ gņ) dó) dņ) Hu. Cannot get rhyme. Hy. Cannot get rhyme. 'Accent spoils it. ' G. Cannot get rhyme. 'Accent breaks it all up. ' Mc. Rhymes imperfectly. 

The table shows that rhymes of syllables which have accents ofstrikingly different degrees are difficult to feel. In the last case, of the rhyming verses separated by a verse having a heavy end accent, it was practically impossible to hear the rhyme across the break madeby the heavy accent. Somehow the particular condition of the organismwhich constitutes the expectation of a rhyme is broken up by a heavyaccent. 

The material for the records of Table V. Was read to the subjects, thetones were in every case those of the speaking voice, and intervalshaving a definite speech character were chosen. The fifth is theinterval of the rising inflection of the question, the fourth is theinterval of the rising inflection of indifference or negation, and thesingle falling slide used is a descending interval of a third orfourth at the close of the sentence. The fifth appears in the table as5/, the fourth as 4/, and the single descending interval of finalityas the period (. ). Each verse was read on approximately the first toneof the interval, the rhyming syllable only had the second tone of theinterval. 

TABLE V. 

 RHYMES UNDER GIVEN PITCH CONDITIONS. 

 Iambic tetrameters: two-verse stanzas. 

 The body of the verse is omitted; the closing intervals alone are indicated. '1' is read 'good rhyme;' '2' is 'poor rhyme'; and '0' is 'no rhyme. '

 Couplets: --do 5/} 5/} . } . } 5/} --go . } 4/} 5/} . } 5/} G. 2 2 0 S. 0 0 2 1 R. 2 2 1 2 2 Mc. 0 0 0 1 1 Hu. 0 0 ? 1 Ha. 1 2 1 2

 Iambic tetrameters; four-verse stanzas. 

 Rhymes are indicated by 'a' and 'a, ' 'b' and 'b. ' Capital* letters are read 'poor rhyme;' 'o' is read 'no rhyme. '

 I. II. III. IV. I. II. III. IV. I. II. III. IV. I. II. III. IV. Do, no, go, so. Do, no, go, so. Do, no, go, so. Do, no, go, so. 5/ . 5/ . . 5/ . 5/ 5/ 5/ . . 5/ 5/ . 5/ G. A b a b a b a b a a b b a a a o R. A b a b a a b b Mc. A b a b a o a o Hu. A b a b a b a b a a b b a a o a Ha. A b a b o o o o a a B B a a o a

 5/ 5/ 5/ . . . . 5/ . . . . . 5/ . . G. A a a a a a a o a a a a o o a a Hu. A a a o a a a o a a a a a o a a Ha. A a a o a a A o a a a a a o a a Mc. A a a o a a a o A A A A A o A A R. A a a o a a a o a a a a A o A A

 5/ 5/ 4/ 5/ . . 5/ 5/ 5/ . 4/ . 5/ . . 5/ G. A a o o /a a b b /o a o a o o o o \a b a b \A A B B R. A A A A /o o a a\ a a b b \a a o o/ Hu. A a o a Mc. A a o a A A B B Ha. A A B B a a b b o a o a

 4/ 4/ 4/ . 5/ 5/ 5/ 5/ 5/ 4/ 5/ 4/ G. A a a a o a o a Mc. A a a o R. A a a o a a b b Ha. A A A A

 *Transcriber's Note: Original used italic lower case letters. 

The table shows that there is a decided tendency to prefer rhymes inwhich the members of the rhyme have the same interval. The onlyexception is in the case of couplets, where two contrasting slides 5/and . Rhyme, whenever the finality interval occurs last. Perhaps thesimilarity of pitch of the rhyming syllables is a part of the'Gestaltqualität' whose recognition brings about the release andsatisfaction of the state which we know as the 'feeling of expecting arhyme. ' Definite pitch relations in music seem to make rhyme of littlesignificance. We seldom notice the rhymes in a hymn or in a song ofany musical worth. In comic operas and popular ditties rhyme does nowand then figure. In such cases the pitch of the two or more rhymingsyllables is identical; often the whole phrase is repeated for eachrhyming verse. A few experiments in singing a rhyme to simpleintervals show that when the identical interval is used the twosyllables rhyme well, but if the interval be in the oppositedirection, or in another chord, the rhyme is very uncertain. It seemsthat in music we usually have 'feelings of expectation' (_i. E. _, tensions of some sort, central or peripheral), which are adequate tounite the phrases into larger unities. These tensions are so definiteand vivid that they quite obscure and swallow up the relatedcondition of rhyme expectation. These experiments on the modificationof the rhyme by the various pitch and accent factors are not at allexhaustive or conclusive. An extended series of experiments is needed. The study of sound records for pitch is peculiarly tedious, but itshould reveal some interesting relations between rhyme and speechmelody. 

III. THE SPEAKING OF A RHYTHMIC SERIES. 

I. _Methods of Making Speech Records. _

The study of spoken rhythm is of primary importance. Observations onwhat the subject really does are always open to the objections thatsubjective factors play a large part, and that the observer'sperception of a rhythm is after all _his_ perception of the rhythm, not the subject's. The voice is an important indicator of theactivities which generate the rhythms of verse and music, and someobjective method of measuring the sounds made is essential to a studyof the rhythm production. 

Methods of recording and studying the tones of the voice are asnumerous as they are unsatisfactory. In the main the work has beendone for purposes of phonetics, and but few of the methods are appliedin the psychological laboratory. 

Marage[13] has an excellent summary of the methods with practicalcomments on their applicability. Rousselot[14] (Histoire desapplications de phonétique expérimentale, 401-417: objets etappareils, 1-10 et 669-700) gives a careful history of the methodsfrom the phonetic point of view. Scripture[15] gives a convenientEnglish summary of the processes. 

 [13] Marage: _l'Année psychologique_, 1898, V. , p. 226. 

 [14] Rousselot: La Parole, 1899. 

 [15] Scripture, E. W. : _Studies from the Yale Psych. Lab. _, 1899, VII. , p. I. 

A few methods have been devised which avoid the difficulties incidentto the use of a diaphragm, but they are not applicable to themeasurement of rhythm material. The instruments which might be usedfor recording spoken rhythms are all modifications of two well-knownforms of apparatus, the phonautograph and the phonograph. Thephonograph record is incised in wax, and presents special difficultiesfor study. Boeke, however, has studied the wax record under amicroscope, with special arrangements for illumination. The work isquite too tedious to permit of its use for material of any length, though it is fairly satisfactory when applied to single vowels. Inorder to enlarge the record, and at the same time to obtain the curvesin the plane of the record surface, Hermann devised an attachment tothe phonograph (cf. Marage, loc. Citat. ) by which the movements of thestylus of the phonograph are magnified by a beam of light and recordedon photographic paper. The measurements of entire words by this methodwould be as tedious as by Boeke's. 

E. W. Scripture has chosen another type of talking machine from whichto obtain transcribed records. The permanent record of the gramophone(which makes a record in the plane of the surface, like thephonautograph) is carefully centered, and a lever attached to a styluswhich follows the furrow of the record transcribes the curve on thekymographic drum as the plate is slowly revolved. The method has theadvantage of using a record which may be reproduced (_i. E. _ theoriginal gramophone record may be reproduced), and of giving fairlylarge and well defined curves for study. It is too laborious to beapplied to extended research on speech rhythms, and has besidesseveral objections. The investigator is dependent on the manufacturerfor his material, which is necessarily limited, and cannot meet theneeds of various stages of an investigation. He knows nothing of theconditions under which the record was produced, as to rate, on whichtime relations depend, as to tone of voice, or as to muscularaccompaniments. There are also opportunities for error in the longlever used in the transcription; small errors are necessarilymagnified in the final curve, and the reading for intensity (amplitudeof the curve) is especially open to such error. 

The stylus of such a recording apparatus as is used by the gramophonemanufacturers, is subject to certain variations, which may modify thelinear measurements (which determine time relations). The recordingpoint is necessarily flexible; when such a flexible point is pressedagainst the recording surface it is dragged back slightly from itsoriginal position by friction with this surface. When the point iswriting a curve the conditions are changed, and it sways forward tonearly its original position. This elongates the initial part of thesound curve. This fact is of little importance in the study of asingle vowel, for the earlier part of the curve may be disregarded, but if the entire record is to be measured it is a source of error. Hensen[16] first turned the phonautograph to account for the study ofspeech. He used a diaphragm of goldbeater's skin, of conical shape, with a stylus acting over a fulcrum and writing on a thinly smokedglass plate. The apparatus was later improved by Pipping, who used adiamond in place of the steel point. The diamond scratched the recorddirectly on the glass. The Hensen-Pipping apparatus has the advantageof taking records directly in the plane of the surface, but it doesnot make a record which can be reproduced; in case of doubt as to theexact thing represented by the curve, there is no means of referringto the original sounds; and it involves working with a microscope. 

 [16] Hensen: Hermann's Handbuch d. Physiol. , 1879, Bd. I. , Th. II. , S. 187. 

[Illustration: FIG. 3. Diagrammatic section of recording apparatus. _a_, diaphragm; _s_, stylus; _g_, guide; _p_, section of plate. ]

The apparatus which was used in the following experiments consistedessentially of two recording devices--an ordinary phonograph, and arecorder of the Hensen type writing on a rotary glass disc (see Fig. 5, Plate X. ). Of the phonograph nothing need be said. The Hensenrecorder, seen in cross section in Fig. 3, was of the simplest type. Adiaphragm box of the sort formerly used in the phonograph was modifiedfor the purpose. The diaphragm was of glass, thin rubber, orgoldbeater's skin. The stylus was attached perpendicularly to thesurface of the diaphragm at its center. The stylus consisted of apiece of light brass wire bent into a right angle; the longer arm wasperpendicular to the diaphragm; the shorter arm was tipped with avery fine steel point, which pointed downward and wrote on the disc;the point was inclined a trifle to the disc, in order that it might'trail, ' and write smoothly on the moving disc. The stylus had nofulcrum or joint, but recorded directly the vibrations of thediaphragm. In early experiments, the diaphragm and stylus were usedwithout any other attachment. 

But a flexible point writing on smoked glass is a source of error. When the disc revolves under the stylus, the flexibility of thediaphragm and of the stylus permit it to be dragged forward slightlyby the friction of the moving surface. When the diaphragm is setvibrating the conditions are altered, and the stylus springs back tonearly its original position. The apparent effect is an elongation ofthe earlier part of the curve written, and a corresponding compressionof the last verse written. This error is easily tested by starting thedisc, and without vibrating the diaphragm stopping the disc; thestylus is now in its forward position; speak into the apparatus andvibrate the diaphragm, and the stylus will run backward to itsoriginal position, giving an effect in the line like _a_ (Fig. 4). Ifthe error is eliminated, the stylus will remain in positionthroughout, and the trial record will give a sharp line across thetrack of the stylus as in _b_. 

[Illustration: FIG. 4. ]

This source of error was avoided by fixing a polished steel rod or'guide' at right angles to the vertical part of the stylus, just infront of the stylus; the stylus trailed against this rod, and couldnot spring out of position. The friction of the rod did not modify therecord, and the rod gave much greater certainty to the details of thesound curve, by fixing the position of the vibrating point. This rodor guide is shown in Fig. 3 (_g_). 

The disc was driven directly from the phonograph by a very simplemethod. A fine chain was fixed to the shaft carrying the disc, andwrapped around a pulley on the shaft. The chain was unwound by theforward movement of the recording apparatus of the phonograph againstthe constant tension of a spring. When the phonograph apparatus wasbrought back to the beginning of a record which had been made, thespring wound up the chain, and the disc revolved back to its originalposition. 

A T from the speaking-tube near the diaphragm box was connected by arubber tube with the phonograph recorder, so that the voice of thespeaker was recorded both on the smoked glass plate and on thephonograph cylinder. The advantages of such a double record are thatthe possible error of a transcription process is eliminated, and yetthere is an original record to which it is possible to refer, and bywhich the record measured may be checked. 

An important feature in the method was the rate at which the discrevolved. The disc turned so slowly that the vibrations, instead ofbeing spread out as a harmonic curve, were closely crowded together. This had two great advantages; the measurements were not so laborious, and the intensity changes were much more definitely seen than in theelongated form of record. Each syllable had an intensity form, as a'box, ' 'spindle, ' 'double spindle, ' 'truncated cone, ' 'cone, ' etc. (cf. P. 446). 

The disc was run, as a rule, at a rate of about one revolution in twominutes. The rate could be varied to suit the purposes of theexperimenter, and it was perfectly possible to procure the usual formof record when desired. As a result of the low rate, the records wereexceedingly condensed. The records of the 300 stanzas measured are ontwo glass discs of about 25 cm. Diameter, and as much more could stillbe recorded on them. 

The diaphragm and the speaking tube were the great sources of error. For measurements of time values the particular component of the toneto which the diaphragm happens to vibrate is not important, but therecord of intensities depends on the fidelity with which the diaphragmresponds to a given component, preferably the fundamental, of thetone. The speaking tube has a resonance of its own which can be butpartly eliminated. For the records here recorded either glass orgoldbeater's skin was used as a diaphragm. Goldbeater's skin has theadvantage of being very sensitive, and it must be used if the subjecthas not a resonant voice. It has the great disadvantage of beingextremely variable. It is very sensitive to moisture, even when keptas loose as possible, and cannot be depended on to give the sameresults from day to day. The records marked Hu. , Ha. And G. Wereusually taken with a glass diaphragm, which has the advantage of beinginvariable. As the phonograph records show, glass does not modify thelower tones of the male voice to any extent. 

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT 17. PLATE X. Opposite p. 436. The apparatus is shown arranged for taking parallel records on thesmoked glass disc, and on the cylinder of the graphophone. On the leftis shown the microscope with which the records on the glass disc weremeasured. ]

The speaking-tube used was of woven material, not of rubber, and a padof felt was kept in the tube near the diaphragm box. As far aspossible more damping was used at the other end of the tube, but thishad to depend on the voices of the subjects. 

The best check on the performances of a diaphragm is the number persecond and character of the vibrations. The pitch may be calculatedfrom the rotation rate of the disc, which is very constant, as it isdriven at a low rate by the well-regulated high-speed motor of thephonograph. But it is better to place a fork in position to write onthe disc and take a parallel record. All the records were taken withthe vowel 'a' (sound as in father). This vowel has a verycharacteristic signature, which is easily seen, even in a very closelypacked curve, and the correctness of this is one of the bestguarantees that the fundamental of the tone is actuating the diaphragm(though that does not mean that the diaphragm is actually giving thevibration frequency of that fundamental). 

Every record was repeated at least twice, and both records weremeasured. In many of the experiments the intensities were fixed by theconditions of the experiment. There was always the corroborativetestimony of the phonograph diaphragm; for the two were not apt to errtogether. It was easy to determine if the actual intensity relationswere preserved in the phonograph (but it could not be taken forgranted). Each record was reproduced on the phonograph immediatelyafter it had been taken, and both subject and operator listened foranomalies. In practice it was not hard to get records of the singlevowel used (at a small range of pitch which was never more than athird or fourth and was nearly always much less) which representedfairly well the relative intensities. Beside the checks spoken ofabove, every record was repeated by a number of subjects, and thecomparison of the results of different voices shows uniformity. 

The recording of spoken verse is another matter. It is not difficultto test a diaphragm carefully through a small range, but to be certainof its action at all the pitches and qualities of the speaking voiceis impossible. A stable diaphragm, glass or mica, would have to beused, and careful corrections made for the different vowels. 

At best, when the records are satisfactory, nothing can be said forthe measurements of intensity but that they represent relations ofmore or less; the diaphragm has a minimum intensity, below which itdoes not vibrate, and a maximum intensity, above which the amplitudeof its vibrations does not materially increase without breaking intopartials and 'blasting. '

The disc recorder, which had for a mount a modified microscope stand, was placed on the shoe of the disc stand and clamped. The wax and discrecords were adjusted at known starting-points and the styluscarefully lowered, by the rack and pinion adjustment, to the surfaceof the disc. After a preliminary trial of the diaphragm the apparatuswas started, and when at full speed at least two satisfactory recordsof the material were taken. When the disc had made a singlerevolution--a record of some ten or fifteen stanzas--the recorder wasfed inward to a new circle on the disc. After the records were taken, a microscope with either 2 or 4 Leitz objective and a micrometerocular was substituted for the recorder. The phonograph recorder wasraised and drawn back to its starting point, and the disc came back toits original position. The microscope was focussed, and adjusted bythe screw of the shoe until it had the record line in its field; themicrometer furnished an object of reference in the field. Thephonograph, now carrying the reproducer--if possible without a horn, as the tones are truer--was started. At the first syllable of therecord the apparatus was stopped by the device furnished on the'Commercial' phonograph, and the plate was turned by adjusting thescrew at the phonograph carriage, which changed the length of thechain connecting the two records, until the record of the firstsyllable was at some chosen point in the field. In cases of recordsof poetry it was found better to have a set of syllables, say 'one, two, three' prefixed to the record, for this adjustment. Thephonograph was again started, and the curve-forms representing thespoken syllables filed past the point as the phonograph repeated eachsyllable. The rate was slow enough, with the objective 2, so thatthere was no difficulty in observing the passing syllables. After theconformity of the phonograph record had been noted by the operator, and the subject had passed judgment on the phonograph as sayingsatisfactorily what he had said, the curve-forms were measured withthe micrometer. The record was fed slowly through the field by meansof the chain screw on the phonograph carriage; and measurements of thelengths of syllables gave their time values. The micrometer was passedback and forth across the form by the shoe screw, for the measurementsof amplitude (intensity). The micrometer measurements in this casecould be made at least as rapidly as measurements of kymograph curves. The measurements, with the powers used, are accurate to. 01 sec. 

The smoked disc records are to be preferred to those scratched with adiamond, because of the superior legibility of the line, an importantitem if thousands of measurements are to be made. The records arefixed with shellac and preserved, or they may be printed out by aphotographic process and the prints preserved. The parallel set of waxrecords is preserved with them. There are several ways in which thewax records lend themselves to the study of rhythmic questions. It iseasy to change the rate, and thereby get new material for judgment, ina puzzling case. Consonant qualities are never strong, and it is easyso to damp the reproducer that only the vowel intensities are heard. The application in the study of rhyme is obvious. 

All the series consisted of regular nonsense syllables. The accentedand unaccented elements were represented by the single syllable 'ta'('a' as in father). Rhymes were of the form 'da, ' 'na, ' 'ga' and 'ka. 'In other parts of the work (cf. Table IV. ) the vowel o had been usedin rhymes for contrast; but the same vowel, a, was used in theserecords, to make the intensity measurements comparable. 

The records of the measurements were as complete as possible. Thesonant and the interval of each element were measured, and all thepauses except the stanza pause were recorded. The intensity of eachsyllable was recorded beneath the length of the syllable, and noteswere made both from the appearance of the curve and from thephonograph record. 

_2. The Normal Form of Unrhymed Verse. _

To determine the influence of a subordinate factor in rhythm such asrhyme, it is necessary to know the normal form of verse without thisfactor. It is natural to assume that the simplest possible form ofmaterial would be individual feet recorded seriatim. But on trial, such material turned out to be very complex; the forms changedgradually, iambs becoming trochees and trochees changing intospondees. It is very probable that the normal foot occurs only in alarger whole, the verse. 

To corroborate the conclusions from perceived rhythms as to theexistence of variations in earlier and later parts of the verse, atable of mean variations was prepared from the material recorded andmeasured for other purposes. 

TABLE VI. 

 MEAN VARIATIONS. 

 Iambic tetrameters; variations of each element from the average foot of the entire stanza. 

 [Label 1: Unaccented Element of Foot. ] [Label 2: Accented Element of Foot. ] [Label 3: Percentage M. V. Of Unac. El. ] [Label 4: Percentage M. V. Of Ac. El. ]

 Hu. 8 stanzas [1] [2] [3] [4] M. V. 1st foot 0. 9688 1. 3125 11. 1 7. 8 2d " 0. 8125 0. 6563 9. 3 3. 9 3d " 0. 8438 1. 1875 9. 7 7. 1 4th " 0. 9688 11. Av. Foot of all stanzas 8. 69 16. 88

 Geo. 10 stanzas, no accents or rhymes within the verse: M. V. 1st foot 2. 725 2. 775 24. 6 13. 3 2d " 1. 300 1. 325 11. 8 6. 4 3d " 1. 400 2. 050 12. 7 9. 8 4th " 2. 750 24. 9 Av. Foot of all stanzas 11. 05 20. 85

 Geo. 8 stanzas, accents and rhymes within the verse: M. V. 1st foot 1. 4843 2. 4687 13. 1 11. 5 2d " 1. 4219 2. 6875 12. 6 12. 6 3d " 1. 7031 2. 5312 15. 1 11. 8 4th " 1. 8594 16. 4 Av. Foot of all stanzas 11. 31 21. 38

The last element has the 'finality-form' and is not comparable to theother accented elements and therefore is not given. 

Dactylic tetrameters (catalectic); variations of each element from theaverage foot of the entire stanza:

 [Label 1: Accented elements of Foot] [Label 2: 1st Unaccented element of Foot] [Label 3: 2d Unaccented element of Foot] [Label 4: Percentage M. V. Of Ac. El. ] [Label 5: Percentage M. V. Of 1st Unac. El. ] [Label 6: Percentage M. V. Of 2d Unac. El. ]

 [1] [2] [3] [4] [5] [6] Me. , Ha. , 8 stanzas, normal: M. V. 1st foot 1. 6875 1. 2813 1. 8125 9. 70 9. 76 10. 5 " 2d " 1. 0613 1. 0613 1. 4061 6. 1 8. 0 8. 1 " 3d " 1. 6875 1. 3125 1. 3750 9. 7 9. 9 7. 9 Av. Foot 17. 38 13. 18 17. 31

 Geo. 4, stanzas, abnormal type of dactylic foot: M. V. 1st foot 1. 5000 1. 1250 1. 2813 11. 5 11. 0 8. 7 " 2d " 1. 5625 1. 1250 1. 1250 12. 0 11. 0 7. 6 " 3d " 1. 3437 1. 1873 0. 8737 10. 3 11. 5 5. 9 Av. Foot 13. 00 10. 25 14. 75

 Me. , Ha. , G. , Hu. , Am. , accent on 2d foot, 8 stanzas: M. V. 1st foot 2. 4688 1. 3125 2. 2813 12. 7 12. 7 11. 5 " 2d " 2. 3750 1. 1250 3. 8438 12. 2 8. 7 19. 3 " 3d " 2. 9688 1. 3750 2. 2500 15. 5 10. 7 11. 3 Av. Foot 19. 44 12. 88 19. 88

 Me. , Ha. , G. , Hu. , 19 stanzas, normal: M. V. 1st foot 1. 9474 1. 2500 2. 2763 10. 8 8. 6 11. 4 " 2d " 1. 3816 1. 2369 1. 7766 7. 7 8. 5 9. 3 " 3d " 1. 3158 1. 2105 1. 6382 7. 3 8. 4 8. 6 Av. Foot 18. 00 14. 24 19. 05

 Me. , Ha. , G. , 6 stanzas, normal: M. V. 1st foot 2. 0000 1. 2083 1. 8750 10. 5 10. 4 10. 7 " 2d " 2. 6250 1. 0416 2. 1666 13. 8 9. 1 12. 3 " 3d " 2. 1250 1. 3333 1. 3333 11. 3 11. 4 7. 6 Av. Foot 18. 92 11. 58 17. 50 The last foot (catalectic) is not comparable in these dactylic stanzas. 

The mean variations of the table (Table VI. ) were calculated asfollows: The average for all the elements of the stanza was obtainedand an average foot constructed (excluding the last sonant and thepause of the verse). From this average foot the variations of all thefirst feet were computed, then the variations of all the second feet, etc. Then the variations of the first feet of the stanza were averagedand percentages taken, etc. ; it is this last value which goes to themaking up of the tables. In inspecting the averages the correspondingelements of the feet should be compared. Any increased length due to aprescribed accent within the verse, etc. , appears in the averages as acorresponding increase in the mean variation at that point, and onlythe first and last feet can be compared as to the variations in theverse as a whole. In making up the tables the material was grouped, not by combining the records of each subject, but by combining all thestanzas of a single type, in order to eliminate individualpeculiarities. 

TABLE VII. 

 Verse pauses in unrhymed stanzas, together with the foot pause within the verse. Length of last foot, together with the average foot within the verse:

 Average first Last foot Average of first Verse Pause. 3 feet of verse. Of verse. 3 foot pauses of verse. Iambs: 36 56. 5 24 45. 5 57 122 35 100 68. 5 125 45 102 63. 5 111. 5 42 93 63. 5 117. 5 39 93. 5 66 135 42 110 53. 5 59 40 45 60 76 45 61 56. 5 68 41 54 55. 5 56 39 41 53 53. 5 37 41. 5 56 73 34 45 85 98 56 54 39 50 26. 5 36 37 43 17 30 42. 5 45 28 30 38. 5 49 26 36 40 79 26 55 31 72. 5 21 55 33 66 23 54 33 76 22 64 Dactyls, catalectic: 56 63 (The pauses cannot be 60 62 compared because of the 55 66 omission of elements in 51. 5 76 the final foot. ) 37 40 55 58. 5 53 59. 5 40 73 38 65 37. 5 56 37 73

Throughout the series of measurements made the accented element wasnearly always longer, and in no case did the accent fail to increasethe length of the sonant. Ebhardt's suggestion that there are twosignificant parts in each foot-element, viz. , sonant and pause, doesnot seem good. Although the sonant is much longer when accented, theratio between the sonant and the following interval is not definite. 

An examination of thirty-two stanzas of unrhymed iambic and dactylic(catalectic) tetrameters (cf. Table VII. ) shows that the verse pauseis always at least one fourth larger than the foot pause. In theunrhymed stanzas the verse pause varies widely, and may be as large asthree times the foot pause. A pause longer than the foot pause isabsolutely essential to the unity of the verse. All sorts of ratiosare presented; evidently the verse pause is not a function of the footpause. 

The next table (Table VIII. ) shows a variety of different dynamicshadings in the verse. It is noteworthy that in these nonsense versesthe type is uniform throughout the stanza. Representing theintensities by curves similar to those used by the subjects inlistening to rhythms, we have the forms shown in Fig. 6 (_a_). 

The general curve is like that in Fig. 6(_b_). 

[Illustration: FIG. 6. ]

When a special emphasis is prescribed on some particular accent in theverse, the type becomes invariable, not only in each stanza, but forall stanzas of all subjects. 

The records show that the accent is produced in a variety of ways. One, for example, gets the accent by a slight increase in intensity, but especially by a pause following the sonant. 

TABLE VIII. 

 THE INTENSITY RELATIONS WITHIN THE TOTAL, UNRHYMED VERSE. 

 UNRHYMED IAMBIC TETRAMETERS. Average Intensities. Length Length ' ' ' ' of first of last _ - _ - _ - _ - 3 sonants. Sonant. 

 Ha. 2 5 4 5 2 4 3 6 31 31s 4 4 2 4 2 5 3 7 33 36s 2 5 3 4 1 5 3 9 32 29s 2 4 2 5 2 5 3 7 31 22s 3 5 1 5 3 4 3 5 37 35s 2 5 2 4 2 4 3 6 35 27s 2 4 2 4 2 4 2 6 38 22s 1 4 3 4 1 5 3 6 34 23s Hu. 6 6 6 6 6 6 6 5 25 33 5 5 5 5 5 5 5 6 26 32 5 5 5 4 5 5 5 5 19 33 5 5 5 6 8 9 8 9 28 50 9 9 8 9 9 9 9 8 43 51 9 7 8 7 7 8 9 10 48 45s 6 7 7 7 6 7 6 7 43 43s 6 6 5 6 4 7 7 8 36 50 G. 9 14 7 14 4 12 6 10 20 25 7 12 7 14 7 10 6 10 16 26 7 12 6 11 4 12 5 10 17 26 6 13 6 11 1 9 7 12 16 26 10 8 7 30 6 15 7 16 18 25 7 14 8 12 6 15 10 13 15 28 7 16 9 15 4 14 7 12 16 25 7 15 7 13 5 13 6 12 17 25

 In verses marked 's' the last sonant is shorter than the average of the preceding sonants. 

 UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE THIRD FOOT. 

 ' \/ -- \/ -- \/ -- \/ -- Mc. Couplets. 4 6 6 7 4 6 4 4 5 8 5 6 2 12 8 5 4 6 5 10 4 11 5 3 4 6 5 10 4 10 4 4 7 11 5 9 9 15 5 5 5 19 20 22 21 24 6 6 12 22 16 22 20 22 8 7 12 22 14 31 10 26 6 7 Ha. Couplets. 4 7 4 8 8 9 5 7 5 7 4 6 6 8 2 7 2 6 2 6 5 6 3 6 2 7 3 6 2 10 3 4 3 7 3 7 4 6 4 6 4 5 3 6 4 7 2 6 5 7 1 6 4 8 2 5 2 7 3 5 3 7 2 6

 UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE SECOND FOOT. 

 ' \/ -- \/ -- \/ -- \/ -- Mc. Couplets. 13 22 22 30 22 18 15 18 11 20 22 26 15 19 15 10 10 25 20 26 20 24 12 23 10 19 17 26 19 11 9 10 12 23 18 26 22 17 10 15 8 23 20 27 16 22 15 16 12 23 26 30 22 21 10 17 14 28 26 34 11 28 11 21

 Ha. Couplets. 6 9 4 12 4 5 3 4 5 4 12 1 5 2 5 3 5 3 12 2 5 2 6 1 6 4 15 1 6 2 7 - 15 3 12 - 8 - 5 - 6 4 12 - 7 - 5 - 7 - 7 4 13 - 4 - 6 3 13 - 5 - 4

 G. Couplets. 9 19 11 20 4 12 3 10 5 13 6 16 5 10 6 11 8 16 10 18 5 10 6 11 6 12 6 16 6 10 6 10 8 16 13 19 5 13 8 12 9 17 11 19 3 10 6 12 9 16 9 18 6 10 7 9 7 15 7 15 5 10 5 10

Frequently the special accent seems to be made by a contrast betweenthe accented foot and the feet which follow. In most cases theinfluence of the special accent is to be seen, not merely within theaccented foot itself, but both before and after the accented foot. Often the appearance under the microscope is very striking; thesonants of the feet, both accented and unaccented, increase to thespecial accent and then decrease in a regular crescendo--diminuendoform. Much of this is not shown by the mere measurements. 

[Illustration: FIG. 7]

[Illustration: FIG. 8 Iambic Tetrameter Verse (with the accent on the second foot)]

In general the special accent may he said to be the climax of theverse movement. It is the crest of the wave, and, as noted above, thedynamic shading is not always made by an increase up to the accent, nor by a stress on a special accent, but by a sharp diminuendoimmediately following the accent. A study of the phonograph recordbrings out these forms of shading, especially when the record isrepeated slowly, exaggerating the dynamic variations and giving anopportunity for more careful observation. 

Within the verse the general form of the syllable as it appears in themass of closely written vibrations, often varies, but nearly alwaysshows a square end. Several very common shapes are noticed and appearin the record as (1) 'truncated cones, ' (2) 'boxes, ' and (3)'truncated spindles. ' (See Fig. 7. )

With the particular syllable used, 'ta, ' the beginning of curve formwas usually square and abrupt (4), and not gradual (5), although a fewof the latter type are found ('spindle'). 

One syllable form has an especial interest, because of its bearing onthe problem of 'finality' feeling at the close of the verse. At theclose of each verse, whether with or without rhyme, the syllable formis always a 'cone' (6) (cf. Fig. 8). Of about 600 verses measured notmore than 15 are exceptions to this rule. Of these 15 exceptions 10are under special conditions and confirm the hypothesis that this formis related to the finality process. The form very rarely occurs withinthe verse, and when it does it is usually before some cęsura, or underunusual conditions. 

This 'cone' form of the closing syllable of the verse indicates afalling of the intensity of the voice. It is often, though not always, associated with a fall in the pitch, showing relaxation of the vocalcords. It seems to be an indication of the dying out of the intensityfactor, a sinking of the tension, at the close of the verse. In thecase of unrhymed verses, with long verse pause, the cone is often verymuch elongated, and it is quite impossible to say where the soundceases. 

Special accentuation of the long syllable of the foot increases thelength of the sonant, of the accented element, and of the entire foot. There is probably a slight increase of the total length of anaccented verse as compared with the similar unaccented, but nocalculations were made to show that point. This is quite in accordwith other results (Meumann, Ebhardt). This special accentuation isconnected with an increased mean variation of the time values, asnoted above. It is in that sense a 'disturbing factor. '

TABLE IX. 

 VERSE PAUSES (INCLUDING FINAL SONANT) TOGETHER WITH THE AVERAGE OF THE CORRESPONDING ELEMENT WITHIN THE VERSE. 

 Average long Verse pause Verse pause Verse pause element of of 1st verse of 2d verse of 3d verse first 3 feet. Of stanza. Of stanza. Of stanza. End Rhymes. Mc. 26 34 104a 35 45 _45_a 80b 80a 31 33 64a 36 41 52a 51b 75a Ha. 41 _44_a _44_ 45a 43 47a _43_b 46a 39 _41_a 49b 46a 43 46a _45_b _45_a 36 44 41a 53 35 44a 58a 38b 33 40 73a ×30 Hu. 28 ×25a 50 28a

 Feminine Rhymes. Hu. 18 21a 37a 19b 19 _20_a 22a 16b 19 _21_a _21_a 16b Mc. 36 72a 64 51a 36 ×32 41a 40 22 _22_a ×18 29a Ha. 27 31a 44b _28_a 36 79 ×30 40 30 36 79a _30_b 31 38 50a 36 32 39a 42 40a Am. 34 70 95a 85 35 73a 94 89a 30 45 47a 86 28 54 53a 70 G. 19 64a 64 79a 19 73a 83b 76a 21 81 67a -- 19 61 83a 79

 The rhymes are marked 'a' and 'b'; _e. G. _, couplets a, a, b, b, etc. Verse pauses in italics are equal to the foot pause; those marked 'x' are _less_ than the foot pause. 

3. _Modification of the Normal Form of Verse due to Rhyme. _

Verse Pause in Rhymed Material. 

There are as wide, isolated variations as in the case of unrhymedmaterial. As compared with unrhymed verse, the pause is in generaldecidedly shorter. The verse pauses of the feminine rhymes aregenerally much like those of the end rhymed material. But there arevery few cases of the verse pause being as short as the footpause--only four cases in sixty (6. 6 per cent. ). See Table IX. 

This wide variation of the verse pause and its occasional equivalenceto the foot pause in rhymed verses is in accord with the notion thatthe rhyme in some way brings the verse to a close by a process morerapid than that in unrhymed material. 

The introduction of rhyme seems to be favorable to the division of astanza into two parts by producing an unusually long verse pause afterthe second verse. Of 43 unrhymed stanzas there are 19 which show adecidedly long pause at the close of some one of the verses. But ofthese 19 cases, only 8 (18 per cent. ) have the break at the close ofthe second verse. Of 64 rhymed stanzas, 29 show the division, and ofthis 29, 22 (34 per cent. ) have the break at the close of the secondverse. 

Influence of the Rhymes on Intensities. 

The intensities at the close of the verse, without rhyme, may beslightly greater than within the verse. The dynamic shading of theverse is elastic, and a variety of forms is possible, a decrescendo atthe close of the verse is not unusual (cf. Table VIII. ). But when therhyme is introduced the general dynamic form of the verse is fixed, and in the material measured this is true not only of the verses in astanza which contain the rhyme but of other verses in the same stanza. 

Of the 32 verses containing rhymes in Table X. , but four verses areexceptions to the rule of an increase of intensity on the rhyme. Thereare two cases of double, alternating rhymes where it is doubtful ifthe subject actually felt one of the alternating rhymes. This increaseof intensity on the rhyme is not confined to that particular syllableor foot; often, as indicated by the italics, the influence of theaccent makes itself felt earlier in the verse. 

TABLE X. 

 INTENSITIES OF IAMBIC TETRAMETER WITH END RHYME (SHOWING INCREASED INTENSITY OF THE RHYMING SYLLABLE). ALSO AVERAGE LENGTH OF THE FIRST THREE SONANTS, TOGETHER WITH THE LENGTH OF THE LAST SONANT. 

 Intensities. Average length of first 3 Length of last sonants. Sonant. \/ - \/ - \/ - \/ - Mc. -- 5 -- 5 -- 4 -- 5 19 27 -- 4 -- 4 -- 4 -- _11_a 34 -- 4 -- 4 -- 4 -- 7 21 -- 4 -- 5 -- 3 -- _8_a 23

 -- 6 -- 6 -- 5 -- 6 19 22 -- 8 -- 7 -- 6 -- _10_a 34 -- 4 -- 3 -- 4 -- 5 26 -- 3 -- 5 -- 4 -- _5_a 30

 2 3 5 4 4 5 6 _7_a 29 34 2 3 3 4 2 4 2 _7_b 48 1 2 3 2 2 2 1 _4_a 35 2 3 3 3 2 3 4 _5_b 20

 -- -- -- -- -- -- -- --a 25 40 3 4 4 14 3 4 5 _5_b 39 2 3 1 2 2 3 1 _3_a 25 1 3 2 2 1 3 3 _5_b 43

 Ha. 6 15 9 12 3 10 4 16 No increase in length. 3 5 3 7 3 5 5 15a 1 15 1 5 4 6 2 9 4 5 2 5 1 5 2 _14_a

 2 6 4 8 1 6 5 _11_a No increase in length. 1 7 5 7 3 6 7 _11_b 2 5 2 6 2 6 4 _12_a 1 5 1 5 2 6 3 _15_b 33 38

 4 9 5 9 1 3 6 _9_a 25 33 2 8 5 6 4 5 5 _10_b No increase in length. 2 5 2 5 2 5 5 _11_a 1 5 2 5 5 10 2 _12_b 32 34

The evidence of an increased intensity on the rhyme is not so positivein the case of rhymes in the third foot. Among the rhymes in thesecond foot there is but one exception. The rhymes in the second andthird feet were never given very satisfactorily by several of thesubjects. The rhymes within the verse determine a climax in the footin which they occur, and all the verses follow this well-defined type. It is interesting to note, in studying the phonographic record, thatin verses in which the accentuation of the rhythm is not verydefinite, the accentuation is perceived when the record is repeated atthe normal speed. If the record is repeated more slowly, andespecially at such a distance that the rhyming consonants cannot bedistinguished, then the accentuation seems to disappear. It isprobable that after a verse or stanza type has been established thevoice may deviate from the type, and the accentuation will be suppliedby the hearer. 

TABLE XI. 

 INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE THIRD FOOT (SHOWING INCREASE IN INTENSITY OF THE RHYME SYLLABLE). 

 ' ' ' ' \/ -- \/ -- \/ -- \/ -- Ha. 13 18 10 16 _7_ _9_a 6 12 9 10 4 11 7 _14_a 4 7 -- 12 5 10 7 9b 6 9 2 12 5 12 3 _14_b 4 6

 2 12 4 13 7 8a 4 9 6 8 4 14 4 _15_a 2 9 2 13 -- 12 8 8b -- -- 5 9 6 10 -- 3b 4 6

 Am. 10 10 4 12 6 _14_a 5 5 4 12 6 9 7 8a 4 4 5 12 8 9 7 _10_b 3 4 3 7 5 8 5 7b 2 4

 10 13 5 10 4 _10_a 4 6 1 9 4 9 3 5a 3 5 2 8 3 5 -- _8_b 1 5 1 7 2 7 5 _8_b 2 3

 G. 6 13 6 13 7 _12_a 1 10 6 10 6 6 _7_ _7_a 1 8 4 9 7 7 _6_ 9b 1 7 7 12 4 10 2 7b 1 7

 10 12 4 11 6 _10_a -- 8 5 12 5 11 6 _10_a -- 8 3 9 6 9 _7_ _9_b 3 8 2 8 5 9 5 5b 1 6

 D. 10 12 10 10 7 9a 7 11 5 8 6 9 7 7? 6 6 5 12 7 9 6 _10_b -- 8 6 9 7 10 7 7b 5 5

 10 15 5 11 6 9a -- 9 5 9 4 8 6 6a? 6 7 7 11 7 11 _11_ _13_b 8 10 8 11 8 10 7 9b 6 8

 INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE SECOND FOOT. 

 ' ' ' ' _ - _ - _ - _ - Hu. 5 6 6 6a 5 7 5 6 5 6 5 4a 5 4 5 6? 5 6 6 7b 5 6 4 7 5 6 4 4b 5 7 4 7 5 7 7 7a 6 7 6 6 5 7 5 5a 5 6 5 6? 5 7 _6_ 8b 6 7 6 7 6 7 6 5b 6 7 6 7 Mc. 5 7 6 _10a_ 5 4 3 5 1 6 6 _8a_ - 6 1 4 1 6 6 _10b_ 1 4 - 4 - 7 6 5b 3 3 - 3 Ha. 16 14 _8_ _10a_ 6 10 5 9 5 10 7 8a 5 9 5 7 2 8 4 _11b_ 4 7 2 8 2 8 4 6b 1 9 4 8 7 12 7 _10a_ - 10 6 10 3 10 5 8a 5 8 6 10 2 8 3 _11b_ 3 7 3 10 - 7 5 9b 4 8 6 12 Am. 4 9 _9_ _10a_ 4 7 4 5 4 8 _9_ _7a_ 5 7 4 6 1 8 5 _10b_ 4 6 3 6 - 10 _10_ 7b_ 3 5 2 7 15 15 _10_ 13a_ 9 11 - 11 5 12 7 9a 4 10 4 9 5 8 _8_ _9b_ 4 7 - 6 7 8 5 _9b_ 2 4 - 3 G. 2 6 _6_ _8a_ 1 7 2 3 - 10 _7_ _12a_ 1 9 4 8 4 9 _6_ _9b_ 8 8 2 7 - - - -b - - - - 4 9 _5_ _11_a - 7 4 6 - 8 6 7a 2 7 4 5 - 9 _7_ _6_b - 7 3 6 - 7 3 5 - 5 - 3 D. - - - - - - - - 7 11 _11_ _9_a 7 11 6 10 11 15 11 11a 8 11 9 14 6 10 _10_ 8b 7 8 7 11 12 13 10 10a 7 1? 8 11 6 10 9 8a 5 8 5 9 9 12 12 13b 8 10 7 9 7 11 _10_ 7b 4 8 4 8

 The values surrounded by '_'s (Transcriber's Note: Original italics) show the increase in intensity. Rhymes are indicated by 'a' and 'b. '

IV. SUGGESTIONS FOR A MOTOR THEORY OF RHYTHM. 

If the basis of rhythm is to be found in muscular sensations, ratherthan in the supposed activity of some special 'mental' function, thenature of the movement cycle involved is of the greatest interest. 

In every case where a rhythm comes to peripheral expression, there aretwo opposing sets of muscles involved. If a rhythmic movement beattempted with but a single set of muscles at work, it is veryunsatisfactory and soon ends in the tonic contraction of the muscleset. One may assume that in all cases of rhythm perception there is acycle of movement sensations involved, and that the simplest possiblecase of a peripheral rhythmic movement is the type of any rhythm. Intapping a rhythm with the finger, the flexors which bring the fingerdown become the positive muscle set, and the opposing extensor muscleswhich raise the finger for the next blow become the negative muscleset. 

In Fig. 9 the upper curve represents the actual movement of the fingertip, and the heavy lines _a_, _a'_, _a''_ represent thepressure-tension-sound sensation which we call the 'beat, ' and whichis the limiting sensation of the rhythm, and the regulating factor inthe movement cycle of the rhythm. The movement is divided into twophases; _B_, the phase of relaxation, during which the finger israised, and _A_, the phase of contraction, during which the fingerdelivers the blow which produces the beat. 

The curves below represent the changes in the two opposing sets ofmuscles whose interaction brings about the movement cycle. Thecontraction of the flexors, the positive muscle set, is represented bythe curve above the base line. It is obvious that during thecontraction phase, the contraction in the positive muscle set is atits height; it continues at a maximum during the limiting sensationand then dies away during the relaxation phase. The sensations fromthis positive muscle set have the principal place in consciousnessduring the rhythm experience. The curve below the base line representsthe contraction of the extensors, the negative muscle set. Thecontraction of the negative muscles reaches its climax very soon afterthe maximum contraction of the positive muscles, in the contractionphase. The sharp tension between the two opposing sets of muscles atthe limiting sensation may be made very apparent if the finger beatsthe rhythm entirely in the air; in that case the limiting sensationconsists entirely of the feeling of a sudden increase of tensionbetween the positive and negative muscle sets. During the relaxationphase the contraction of the negative muscles continues, but thetension between the two sets grows less and less, for the positivemuscles are rapidly relaxing. At the highest point in the movementeither muscle set is exerting but very little strain; the condition isrepresented in the figure by the approach of either curve to thebase-line; the amount of tension between the two sets is figured bythe distance of the two curves from each other. 

[Illustration: FIG. 9. ]

Assuming such a movement cycle, in which the tension between the twoopposing sets never comes to zero until the close of the series, it isnot difficult to arrange many of the facts of rhythmic perceptionunder the motor theory. 

1. The feeling of rhythm is more definite as we proceed in a verse, ora series of simple sound sensations. At first the cycle is notperfectly adjusted and complete automatism established. 

2. If an observer is listening to a series, and an unusually longpause is introduced between two beats, there is always a feeling ofsuspense or tension during the 'lag. ' As long as the tensions aremaintained there is a rhythmic continuity; the feeling of tension isthe strain of opposition between the opposing muscle sets. 

3. The continuity of the rhythmic series, whereby all the beats of aperiod seem to belong to a single whole, is due to the continuity ofthe muscle sensations involved and the continuous feeling of slighttension between the positive and negative muscle sets; nowhere withinthe period does the feeling of strain die out. 

4. But at the close of the period we have a pause which isdemonstrably not a function of any of the intervals of the period. During this pause the tension between the two sets 'dies out, ' and wehave a feeling of finality. This gradual dying out of the tension isclearly seen in the constant appearance of the cone-shaped finalsyllable at the end of each nonsense verse. 

5. The period composed of a number of unit groups (the verse, innonsense syllables) has a general form which suggests strongly that ithas the unity of a single coördinated movement. There is no morereason for assuming a transcendental mental activity in the case of arhythmic period than in the case of a single act which appears inconsciousness as a unity. Undoubtedly the breathing is correlated withthe rhythmic movements and may be a factor in determining the verseperiod. Meumann's principal accent, about which a number ofsubordinate accents are grouped, is characteristic not only of poetrybut of the simplest rhythms. At some point in the period there is adefinite climax, a chief accent; the movement 'rises' to that pointand then falls off. This is strikingly seen in nonsense verses spokenwith a heavy accent within the verse. The accent does not stand outfrom a dead level, but the verse culminates at that point. 

Unfortunately very little is known of the mechanism of so simple acoördinated muscular activity as that necessary for a simple rhythm. Sherrington[17] and Hering[18]have pointed out the primary characterof the grouping of the muscles in opposing sets and the reciprocalnature of almost all muscular activity, but in a review of the work ofcoördinated movements Hering denies any simultaneous stimulation ofthe two sets and considers the question of the innervation mechanismof opposing muscle-sets entirely unsettled. 

 [17] Sherrington, C. S. : _Proceedings Royal Soc. _, 1897, p. 415. 

 [18] Hering, H. E. : _Archiv f. D. Ges. Physiol. _ (Pflüger's), 1897, Bd. 68, S. 222; _ibid. _, 1898, Bd. 70, S. 559. 

That the connection between the positive and negative set of musclesin a rhythmic movement is very close, and that the reaction is of thecircular type, is evident from the automatic character of all rhythmicmovements, and it is evident that the limiting sensation is theprimary cue in the reaction. Anything further is mere hypothesis. Robert Müller's[19] thorough criticism of the Mosso ergograph throwsgreat doubt on the present methods of investigation and invalidatesconclusions from the various curves of voluntary movements which havebeen obtained. 

 [19] Müller, R. : _Phil. Stud. _, 1901, Bd. 17, S. 1. 

The curve of contraction and relaxation of a simple muscle is wellknown and is not affected by Müller's criticism. Its chiefcharacteristic, with or without opposing tension, is the inequalityof the intervals of the contraction and relaxation phases. As onemight expect, since a single set of muscles dominates in a rhythmicmovement, the typical rhythmic curve has the general character of thecurve of the simple muscle. The average values of the phases of curvesof simple rhythmic movement obtained by A. Cleghorn[20] from a largenumber of observations with at least three subjects, are as follows:phase of contraction, . 44 second; phase of relaxation, . 54 second. Itis very significant for a motor theory of rhythm that this generalform of the curve of rhythmic movement may easily be altered in allsorts of fashions by unusual stimuli to the two muscle sets. 

 [20] Cleghorn, A. : _Am. Journal of Physiol. _, 1898, I. , p. 336. 

While it is well recognized that a rhythm does not consist necessarilyof sound sensations, the 'rhythmization' of a series of soundsensations in the ordinary perceived rhythms is a matter of greatinterest. Ewald found strong reasons for believing that the ear ispeculiarly connected with the motor apparatus. The experiments ofHofbauer[21] and Cleghorn[22]show that any strong stimulus to eithereye or ear modifies decidedly the reactions of coördinated muscles. How shall we assume that the automatic movement cycle necessary torhythmic perception is set up when one listens to a series of sounds?

 [21] Hofbauer: _Archiv f. D. Ges. Physiol. _ (Pflüger's), 1897, Bd. 68, S. 553. 

 [22] Cleghorn, A. : _op. Cit. _

It must be assumed that any chance sound sets up a contraction in aset of muscles, however large or small. If but a single sound occurs, the phase of contraction in that muscle set is followed by a longerphase of relaxation, and the musculature is passive as before; it maybe that the stretching of the antagonistic set of muscles weaklystimulates them, and they then contract during the relaxation phaseand assist in restoring the original condition. 

But if a second sound occurs toward the end of the relaxation phase, before the tension is quite exhausted, the movement will be repeated;the negative set of muscles will be more definitely stimulated, forthe activity will not have been exhausted when the second soundoccurs. If the sound continues to recur at regular intervals, themovement cycle thus established will rapidly become coördinated. Thepositive set in its vigorous contraction furnishes a limitingsensation which becomes a cue for its own relaxation and for thereciprocal contraction of the negative muscle set. The contraction ofthe negative muscle set and the resulting changes in tension maybecome in turn a cue for the positive set. The reaction is now of thecircular type and the process has become self-regulative, thoughconstantly reinforced by the recurring sound (which has become a partof the limiting sensation of the rhythmic movement cycle). 

But it is very probable that the second sound may not be timed so asto come at the close of the relaxation phase in the set of musclesroused; moreover, in almost all rhythms there are secondary soundsoccurring between the main beats. What happens when a sound occurs outof place, early in the phase of relaxation, or just before or justafter the climax in the contraction phase? Does it make it impossibleto establish the coördination, or destroy it if already established?

Hofbauer demonstrated that a stimulus which appears in close proximityto the limiting sensation, _either before or after_, always increasesthe force of the reaction, so that such a slight displacement couldnot affect the rhythm, which would quickly readjust itself. Thepossibility of a stimulus occurring in the relaxation phase is of muchmore importance for a motor theory of the initiation of a rhythmicmovement. Cleghorn made the stimulus occur at the beginning of therelaxation phase. Instead of prolonging or reinstating the contractionphase, he found that the stimulus _intensified the relaxation processand shortened its period_. "The stimulated relaxation is not onlyquicker than the normal, but also more complete; the end of the normalrelaxation is slow; . . . Relaxation under the influence of thestimulus, on the contrary, shows nothing of this, but is a suddensharp drop directly to the base line and sometimes below it. " Acomparison of the normal phases with the same phases, when thestimulus occurs within the relaxation phase, follows:

 Normal: Contraction-phase, . 44 sec. ; relaxation-phase, . 54 sec. ; total, . 98 sec. With stim. : Contraction-phase, . 47 sec. : relaxation-phase, . 30 sec. ; total, . 77 sec. 

It will be noticed that the total time of the movement cycle isreduced. One may then assume that a sound which occurs too early tobecome a factor in the limiting sensation, functions as a stimulus tothe relaxation process and shortens the interval between the limitingsensations. Thus the movement cycle would be modified, but notdestroyed. It is impossible to say just how the relaxation process isaffected, and Cleghorn's own conclusions are open to criticism in thelight of Müller's comments on the method. The simplest assumptionwould be that the stimulus acted on the negative set of muscles. 

E. W. Scripture[23] objects to such a 'tonus theory, ' because somesubjects regularly react _before_ the signal. But in no case in thepublished records to which he refers is the error more than. 05 sec. Either before or after the signal. The investigation of Hofbauer showsconclusively that in such cases the effect of the external stimulussimply fuses with the limiting sensation. Scripture overlooks theautomatic character of the rhythmic movement. 

 [23] Scripture, E. W. : 'The New Psychology, ' London, 1897, p. 182. 

There is a striking difference between rhythmic movement from unitgroup to unit group within a period, and movement from period toperiod (_i. E. _, from verse to verse of nonsense syllables). Each footis simply the repetition of the movement cycle; all the tensions aremaintained, and each foot is an integral part of a larger act. At theclose of the period (verse) the active tensions die out, eitherbecause of the introduction of some unusual stimulus which causes thepositive muscle set to strike a heavy blow, and abruptly upset thebalanced tensions, or because a pause of indefinite length ensues inwhich the tensions die out. This is the process which we call'finality. '

In the stanza there is evidently a different type of unity from thatin the single verse. When we hear the first verse of the stanza, we donot know what the verse whole is, until the finality factor or theverse pause is reached, at its close. Then the verse has a certaindefinite cumulative effect, a synthetic effect which results from theechoes of the various movements and the total effect on the organism. One may call it the tetrameter feeling. The verse pause may varywithin large limits, but after a few verses there is a definitescheme, or 'Gestaltqualität, ' which represents the verse unity. It issome sort of a memory image, which functions as a cue to the motorprocess. This motor image, set of strains, or whatever it be, is morethan a mere standard by which we judge the present verse. The memoryimage fuses in some way with the living motor process. _The precedingverse affects the character of the following verse. _ An irregularity, easily noted in the first verse, is obscure in the second, and notdetected in the third verse, when the verses are identical. 

The experiments of Hofbauer and Cleghorn, and many facts about theunit groups themselves, make it evident that the function of stimuli, during the movement cycle, varies with the position of the stimulus inthat cycle. This offers a possible explanation of the strikingpeculiarities of the unit groups. The iamb [\/ _'] and the trochee [_'\/] should be quite alike for a general synthesizing process; but notonly is the experiential character of the two quite unlike, but theratio between their intervals is entirely different. 

A number of measurements by different observers show that in theiambic foot the unaccented syllable is proportionately much shorterthan the unaccented syllable in the trochaic foot. It is very easy tobeat a simple up-and-down accompaniment to a series of simple feet ofnonsense syllables; in the accompaniment the bottom of the downstroke, the limiting sensation of the movement cycle, coincides withthe accented syllable of the foot. It is not an unwarranted assumptionthat such a fundamental accompaniment represents the fundamentalmovement cycle of that rhythm. 

During the present investigation several observers were asked todetermine at just what point in the fundamental movement theunaccented syllable occurred, when the subject gave a series ofnonsense syllables. In the fundamental accompaniment the excursion ofthe hand and arm was at least. 4 meter. Four subjects were thus tested, and the results were uniform in the case of all the simple types ofunit groups. 

In the case of the iamb the unaccented syllable occurs at the top ofthe movement, at the very beginning of the contraction phase (A, inFig. 5). 

In the case of the trochee the unaccented syllable occurs in the firstthird of the relaxation phase (B). 

It is interesting to note that the unaccented element of the trocheecomes at the earlier part of the relaxation phase, where it mustintensify the relaxation process, and tend to shorten the total lengthof the cycle. This may be the reason for its peculiar buoyant, vigorous and non-final character. On the other hand the unaccentedelement of the iamb occurs at a point where it may initiate andintensify the contraction, which gives the limiting sensation; it is, therefore, more closely bound to the limiting sensation, and has thecharacter of intensifying the beat. There is a similar contrast in thecases of the dactyl and anapęst. The accented syllable of the dactylis longest, and the second unaccented syllable, the last in the group, is shortest. The accented syllable of the anapęst is much longer inproportion than that of the dactyl, and the unaccented syllables arevery short, and hence, very close to the accented syllable, ascompared with the dactyl. 

In the case of the dactyl the first unaccented syllable in themovement cycle occurs at the beginning of the relaxation phase (B), inthe same zone as the unaccented of the trochee. The second unaccentedsyllable of the dactyl appears at the beginning of the nextcontraction phase (A), in the zone of the unaccented syllable of theiamb. The group seems a sort of combination of the iamb and trochee, and has an element in every possible zone of the movement cycle. Likethe trochee the dactyl is a non-final foot. 

The unaccented syllables of the anapęst both occur at the beginning ofthe contraction phase (A). They are both within the zone of theunaccented syllable of the iamb. The group seems an iamb with aduplicated unaccented syllable. It is possible to form a unit group innonsense syllables where the unaccented syllable of the iamb shall berepresented not by two syllables, as in the anapęst, but by eventhree. 

The anapęst and dactyl, if they correspond to this construction, should show a decided difference as to the possibility of prolongingthe foot pause. The prolongation of the foot pause would make thedactyl but a modified trochee. 

It is significant that in poetry no other types of unit groups areoften recognized. The amphibrach, laid out on this scheme, wouldcoincide with the dactyl, as there are but three possible zones forfoot elements: the zone of the limiting sensation (always occupied bythe accented syllable), the zone of the contraction phase (occupied bythe unaccented syllables of the iamb and anapęst), and the zone of therelaxation phase (occupied by the unaccented syllable of the trocheeand the middle syllable of the dactyl). 

The simple sound series is fairly regular, because of its cyclic andautomatic character. It is not a matter of time estimation, and the'Taktgleichheit' is not observed with accuracy. The primary requisitefor the unit groups is that they shall be _alike_, not that they shallbe _equal_. The normal cycle with a heavy accent is longer than thenormal cycle with a lighter accent, for the simple reason that ittakes muscles longer to relax from the tenser condition. Time is notmysteriously 'lost'; the objective difference is not noticed, simplybecause there are no striking differences in the cycles to lead one toa time judgment. Ebhardt's notion that the motor reaction interfereswith the time judgment, and that a small amount of time is needed inthe rhythmic series in which to make time judgments, is a mere myth. 

An unusual irregularity, like a 'lag, ' is noted because of the senseof strain and because other events supervene in the interval. But suchlags may be large without destroying the rhythm; indeed cęsural andverse pauses are essential to a rhythm, and in no senserhythm-destroying. An unbroken series of unit groups is an abstractionto which most forms of apparatus have helped us. Between the extremeviews of Bolton[24] and Sidney Lanier, [25]who make regularity anessential of the rhythm of verse, and Meumann, on the other hand, whomakes the meaning predominate over the rhythm, the choice would fallwith Meumann, if one must choose. Bolton comes to the matter after aninvestigation in which regularity was a characteristic of all theseries. Lanier's constructions are in musical terms, and for that veryreason open to question. He points out many subtle and interestingrelationships, but that verse can be formulated in terms of music is atheory which stands or falls by experimental tests. 

 [24] Bolton, T. L. : _loc. Cit. _

 [25] Lanier, S. : 'The Science of English Verse. '

TABLE XII. 

 I saw a ship a sailing 50 16 20 13 9 18 32 23- 132 A sailing on the sea 10 16 45 22 8 15 49 -68 And it was full of pretty things 8 6 20 6 6 27 37 12 8 7 20 12 41 -34 For baby and for me 14 9 27 37 18 20 14 8 46 --

 Totals of the feet: --/66/60/187 26/45/45/117 14/59/49/47/75 23/64/60/46--

 Who killed Cock Robin 19 34 23 24 17-77 I said the sparrow 45 21 19 3 47 29 -- With my bow and arrow 22 36 25 49 11 38 12 23 33-42 I killed Cock Robin 33 12 33 21 22 5 21 16-95

 (The first stanza was measured in the Harvard Laboratory. The last is modified from Scripture's measurements of the gramophone record (1899). As the scansion of the last is in doubt with Scripture, no totals of feet are given. )

In the cases given in the above table there is an irregularity quiteimpossible to music. 

In the movement cycle of the simple sounds there is a perfectuniformity of the movements of the positive and negative sets ofmuscles from unit group to unit group. But in verse, the movements ofthe motor apparatus are very complicated. Certain combinations requiremore time for execution; but if this variation in the details of themovement does not break the series of motor cues, or so delay themovements as to produce a feeling of strain, the unit groups are feltto be alike. We have no means of judging their temporal _equality_, even if we cared to judge of it. It is a mistake, however, to say thattime relations ('quantity') play no part in modern verse, for thephases of the movement cycle have certain duration relations which canbe varied only within limits. 

Extreme caution is necessary in drawing conclusions as to the natureof verse from work with scanned nonsense syllables or with mechanicalclicks. It is safe to say that verse is rhythmic, and, if rhythmdepends on a certain regularity of movements, that verse will showsuch movements. It will of course use the widest variation possible inthe matter of accents, lags, dynamic forms, and lengths of sonant andelement depending on emphasis. The character of the verse as itappears on the page may not be the character of the verse as it isactually read. The verses may be arbitrarily united or divided. But inany simple, rhythmic series, like verse, it seems inevitable thatthere shall be a pause at the end of the real verse, unless some suchdevice as rhyme is used for the larger phrasing. 

There is a variety of repetitions in poetry. There may be a vague, haunting recurrence of a word or phrase, without a definite orsymmetrical place in the structure. 

Repetition at once attracts attention and tends to become a structuralelement because of its vividness in the total effect. There are twoways in which it may enter into the rhythmic structure. It may becomea well-defined refrain, usually of more than one word, repeated atintervals and giving a sense of recognition and possibly ofcompleteness, or it may be so correlated that the verses are boundtogether and occur in groups or pairs. Rhyme is a highly specializedform of such recurrence. 

The introduction of rhyme into verse must affect the verse in twodirections. 

It makes one element in the time values, viz. , the verse pause, muchmore flexible and favors 'run on' form of verses; it is an importantfactor in building larger unities; it correlates verses, andcontributes definite 'Gestaltqualitäten' which make possible therecognition of structure and the control of the larger movements whichdetermine this structure. Thus it gives plasticity and variety to theverse. 

On the other hand, it limits the verse form in several directions. Thegeneral dynamic relations and the individual accents must conform tothe types possible with rhyme. The expressional changes of pitch, which constitute the 'melody, ' or the 'inflections' of the sentences, play an important part. The dynamic and melodic phases of spoken versewhich have important relations to the rhyme are not determined by themere words. The verses may scan faultlessly, the lines may readsmoothly and be without harsh and difficult combinations, and yet thetotal rhythmic effect may be indifferent or unpleasant. When a criticdilates on his infallible detection of an indefinable somewhat, independent of material aspects of the verse and traceable to a mysticcharm of 'thought, ' it may very well be that the unanalyzed thing liesin just such dynamic and melodic conditions of rhythm and rhyme. 

The most primitive characteristic of music is the _ensemble_. Savagemusic is often little else than time-keeping. When the socialconsciousness would express itself in speech or movement in unison, some sort of automatic regulation is necessary. This is the beginningof music. The free reading of verse easily passes over into singing orchanting. When this happens, the thing most noticeable in the new formis its regulated, automatic and somewhat rigid character. It isstereotyped throughout. Not only are the intervals and accents fixed, but the pitch and quality changes are now definite, sustained andrecurrent. The whole sum of the motor processes of utterance hasbecome coördinated and regulated. Along with this precision of all themovements comes a tendency to beat a new rhythm. This accompanyingrhythm is simpler and broader in character; it is a kind of long swellon which the speech movements ripple. This second rhythm may expressitself in a new movement of hand, head, foot or body; when it hasbecome more conscious, as in patting time to a dance or chant, itdevelops complicated forms, and a third rhythm may appear beside it, to mark the main stresses of the two processes. The negro patting timefor a dance beats the third fundamental rhythm with his foot, whilehis hands pat an elaborate second rhythm to the primary rhythm of thedancers. 

The essential character of musical rhythm, as contrasted with therhythm of both simple sounds and of verse, is just this coördinationof a number of rhythms which move side by side. This is the reason forthe immense complexity and variety of musical rhythms. The processescheck each other and furnish a basis for a precision and elaboratenessof rhythmical movement in the individual parts which is quiteimpossible in a simple rhythm. 

Even when the concomitant rhythms are not expressed, as in anunaccompanied solo, an accompaniment of some sort is present in themotor apparatus, and contributes its effect to the consciousness. Thisregulation of the movement by the coincidence of several rhythms isthe cause of the striking regularity of the temporal relations. Atsome points in the musical series the several movement cycles mayappear in the same phase, and at these points the same irregularitiesas in verse are possible, as in the case of pauses at the ends ofperiods and the irregularities of phrasing. It is evident in cases ofexpressional variations of tempo that a single broad rhythm isdominating and serving as a cue for the other more elaborate rhythmicprocesses, instead of being regulated by them. 

 * * * * *

STUDIES IN SYMMETRY. [1]

BY ETHEL D. PUFFER. 

 [1] SOURCES OF ILLUSTRATIONS. 

 Fig. 1 was copied from Reiss u. Stübel, 'Todtenfeld v. Ancou, ' Berlin, 1880-1887. 

 Figs. 2, 3, 4, 5, 6, 7, 8 and 11 were copied from the publications of the American Bureau of Ethnology by the kind permission of the Direction. 

 Fig. 9. Was copied from A. C. Haddon, 'The Decorative Art of British New Guinea, ' Cunningham Memoir, N. , Royal Irish Academy, 1894. 

 Fig. 10 was copied from Franz Boas, 'The Decorative Art of the Indians of the North Pacific Coast, ' Bulletin of the Am. Mus. Of Nat. Hist. , Vol. IX. 

I. THE PROBLEMS OF SYMMETRY. 

The problem of ęsthetic satisfaction in symmetrical forms is easilylinked with the well-known theory of 'sympathetic reproduction. ' Ifthere exists an instinctive tendency to imitate visual forms by motorimpulses, the impulses suggested by the symmetrical form would seem tobe especially in harmony with the system of energies in our bilateralorganism, and this harmony may be the basis of our pleasure. But weshould then expect that all space arrangements which deviate fromcomplete symmetry, and thus suggest motor impulses which do notcorrespond to the natural bilateral type would fail to give ęstheticpleasure. Such, however, is not the case. Non-symmetrical arrangementsof space are often extremely pleasing. 

This contradiction disappears if we are able to show that theapparently non-symmetrical arrangement contains a hidden symmetry, andthat all the elements of that arrangement contribute to bring aboutjust that bilateral type of motor impulses which is characteristic ofgeometrical symmetry. The question whether or not this is the factmakes the leading problem of this paper, and the answer to it mustthrow light on the value of the theory itself. 

An exhaustive treatment of our question would thus divide itself intotwo parts; the first dealing with real (or geometrical) symmetry, thesecond with apparent asymmetry; the first seeking to show that thereis a real ęsthetic pleasure in geometrical symmetry, and that thispleasure is indeed based on the harmony of the motor impulsessuggested by symmetry, with the natural motor impulses of the humanorganism; the second seeking to show in what manner ęstheticallypleasing but asymmetrical arrangements conform to the same principles. Within these two groups of problems two general types of investigationare seen to be required; experiment, and the analysis of ęstheticobjects. 

The main question, as stated above, is of course whether the theorycan explain our pleasure in arrangements which are completely orpartly symmetrical. It is, however, an indispensible preliminary tothis question, to decide whether the pleasure in symmetricalarrangements of space is indeed immediate and original. If it wereshown to be a satisfaction of expectation, bred partly from theobservation of symmetrical forms in nature, partly from the greaterconvenience of symmetrical objects in daily use, the whole question ofa psychophysical explanation would have no point. If no originalęsthetic pleasure is felt, the problem would be transformed to ademand for the explanation of the various ways in which practicalsatisfaction is given by symmetrical objects and arrangements. Thelogical order, then, for our investigation would be: First, theappearance of symmetry in the productions of primitive life, as a(debatable) ęsthetic phenomenon emerging from pre-ęsthetic conditions;secondly, the experimental study of real symmetry; thirdly, theanalysis of geometrical symmetry in art, especially in painting andarchitecture, by means of which the results of the preceding studiescould be checked and confirmed. Having once established a theory ofthe ęsthetic significance of real symmetry, we should next have toexamine asymmetrical, beautiful objects with reference to the relationof their parts to a middle line; to isolate the elements which suggestmotor impulses; to find out how far it is possible to establish asystem of substitution of these psychological factors and how far suchsubstitution takes place in works of art--_i. E. _, to what extent asubstitutional symmetry or balance is found in pleasing arrangements. These investigations, again, would fall into the two groups ofexperiment and analysis. The products of civilized art are toocomplicated to admit of the complete analysis and isolation ofelements necessary to establish such a system of substitution ofpsychological factors as we seek. From suggestions, however, obtainedfrom pleasing asymmetrical arrangements, first, isolated elements maybe treated experimentally, and secondly, the results checked andconfirmed by works of art. 

With regard to the study of objects without a natural or suggestedmiddle line, as for instance sculpture, many types of architecture, landscapes, gardens, room-arrangements, etc. , we may fitly consider itas a corollary to the study of asymmetrical objects with artificiallimits which do suggest a middle. If we find, by the study of them, that a system of substitution of psychological factors does obtain, the whole field can be covered by the theory already propounded, andits application extended to the minutest details. The hypothesis, having been so far confirmed, may be then easily applied to the fieldof asymmetrical objects without a natural middle line. 

The set of problems here suggested to the student of symmetry will notbe fully followed out in this paper. The experimental treatment ofgeometrical symmetry, the analysis of the completely symmetricalproducts of civilized art, and the analysis of all forms of asymmetryexcept asymmetry in pictures will be omitted. If, however, the fact ofan original ęsthetic feeling for symmetry is established by the studyof primitive art, and the theory of the balance of motor impulsesthrough the substitution of factors is established by the experimentaltreatment of isolated elements, and further confirmed by the analysisof pictures, the general argument may be taken as sufficientlysupported. This paper, then, will contain three sections: anintroductory one on symmetry in primitive art, and two main sections, one on experiments in substitutional symmetry, and one onsubstitutional symmetry or balance in pictures. 

II. SYMMETRY IN PRIMITIVE ART. 

The question which this section will attempt to answer is this: Isthere in primitive art an original and immediate ęsthetic feeling forsymmetry? This question depends on two others which must precede it:To what extent does symmetry actually appear in primitive art? and, How far must its presence be accounted for by other than ęstheticdemands?

For the purpose of this inquiry the word _primitive_ may be takenbroadly as applying to the products of savage and half-savage peoplesof to-day, as well as to those of prehistoric races. The expression_primitive art_, also, requires a word of explanation. The primitiveman seldom makes purely ornamental objects, but, on the other hand, most of his articles of daily use have an ornamental character. Wehave to consider primitive art, therefore, as represented in the formand ornamentation of all these objects, constituting practically anhousehold inventory, with the addition of certain drawings andpaintings which do not appear to serve a definite practical end. Theselast, however, constitute only a small proportion of the material. 

The method of the following outline treatment will be to deduct fromthe object under consideration those symmetrical elements which seemto be directly traceable to non-ęsthetic influences; such elements asare not thus to be accounted for must be taken as evidence of a directpleasure in, and desire for symmetry on the part of primitive man. These possible non-ęsthetic influences may be provisionally suggestedto be the technical conditions of construction, the greaterconvenience and hence desirability of symmetrical objects forpractical use, and the symmetrical character of natural forms whichwere imitated. 

The first great group of objects is given in primitive architecture. Here is found almost complete unanimity of design, the conical, hemispherical or beehive form being well-nigh universal. The hut ofthe Hottentots, a cattle-herding, half-nomadic people, is a good typeof this. A circle of flexible staves is stuck into the ground, benttogether and fastened at the top, and covered with skins. But this isthe form of shelter constructed with the greatest ease, suitable tothe demands of elastic materials, boughs, twigs, reeds, etc. , andgiving the greatest amount of space with the least material. Thereare, indeed, a few examples of the rectangular form of dwelling amongvarious primitive races, but these seem to be more or less open toexplanation by the theory advanced by Mr. V. Mendeleff, of the U. S. Bureau of Ethnology. "In his opinion the rectangular form ofarchitecture which succeeds the type under discussion, must haveresulted from the circular form by the bringing together within alimited area of many houses. . . . This partition would naturally bebuilt straight as a two-fold measure of economy. "[2] This opinion isconfirmed by Mr. Cushing's observations among the Zuńi villages, wherethe pueblos have circular forms on the outskirts. Thus the shape ofthe typical primitive dwelling is seen to be fully accounted for asthe product of practical considerations alone. It may therefore bedismissed as offering no especial points of interest for this inquiry. 

 [2] Cushing, F. H. : 'Pueblo Pottery and Zuńi Culture-growth, ' Rep. Of Bur. Of Ethnol. , 1882-3, p. 473. 

Next in the order of primitive development are the arts of binding andweaving. The stone axe or arrow-head, for example, was bound to awooden staff, and had to be lashed with perfect evenness, [3] and whenin time the material and method of fastening changed, the geometricalforms of this careful binding continued to be engraved at the junctureof blade and handle of various implements. It should be noted, however, that these binding-patterns, in spite of their superfluouscharacter, remained symmetrical. 

 [3] Haddon, A. C. : 'Evolution in Art, ' London, 1895, pp. 84 ff. 

On the great topic of symmetry in weaving, monographs could bewritten. Here it is sufficient to recall[4] that the absolutelynecessary technique of weaving in all its various forms ofinterlacing, plaiting, netting, embroidering, etc. , implies order, uniformity, and symmetry. The chance introduction of a thread or witheof a different color, brings out at once an ordered pattern in theresult; the crowding together or pressing apart of elements, adifferent alternation of the woof, a change in the order ofintersection, all introduce changes by the natural necessities ofconstruction which have the effect of purpose. So far, then, as thesimple weaving is concerned, the ęsthetic demand for symmetry may bediscounted. While it may be operative, the forms can be explained bythe necessities of construction, and we have no right to assume anęsthetic motive. 

 [4] Holmes, W. H. : 'Textile Art in its Relation to the Development of Form and Ornament, ' Rep. Of Bur. Of Ethnol. , 1884-5, p. 195. 

The treatment of human and animal forms in weaving is, however, indicative of a direct pleasure in symmetry. The human form appearsalmost exclusively (much schematized) _en face_. When in profile, asfor instance in Mexican and South American work, it is doubled--thatis, two figures are seen face to face. Animal figures, on the otherhand, are much used as row-ornaments in profile. [5] It would seem thatonly the linear conception of the row or band with its suggestions ofmovement in one direction, justified the use of profile (_e. G. _, inPeruvian woven stuffs), since it is almost always seen under thoseconditions, indicating that a limited rectangular space is felt assatisfactorily filled only by a symmetrical figure. [6] Moreover, andstill more confirmatory of this theory, even these row-patternprofiles are immensely distorted toward symmetry, and every'degradation' of form, to use Professor Haddon's term, is in thedirection of symmetry. (See Fig. 1. )

 [5] Reiss, W. , und Stubel, A. : 'Todtenfeld von Ancon, ' Berlin, 1880-7, Bd. II. 

 [6] Hein, W. : 'Die Verwendung der Menschen-Gestalt in Flechtwerken, ' Mitteil. D. Anthrop. Gesellsch. In Wien, Bd. XXI. 

[Illustration: Fig. 1. ]

The shape of primitive pottery is conditioned by the followinginfluences: The shapes of utensils preceding clay, such as skins, gourds, shells, etc. , which have been imitated, the forms of basketmodels, and the conditions of construction (formation by the hands). For all these reasons, most of these shapes are circular. The only (inthe strict sense) symmetrical shapes found are of unmistakably animalorigin, and it is interesting to notice the gradual return of these tothe eurhythmic form; puma, bird, frog, etc. , gradually changing intohead, tail and leg excrescences, and then handles and nodes(rectangular panels), upon a round bowl or jar L, as shown in thefigures. In fact, in ancient American pottery, [7] at least, all thesymmetrical ornamentations can be traced to the opposition of head andtail, and the sides between them, of these animal forms. But beyondthis there is no degradation of the broad outline of the design. Thehead and tail, and sides, become respectively handles and nodes--butthe symmetry becomes only more and more emphasized. And as in the caseof textiles, the ornaments of the rectangular spaces given by thenodes are strikingly symmetrical. Many of these are from animalmotives, and nearly always heads are turned back over the body, tailsexaggerated, or either or both doubled, to get a symmetrical effect. Although much of the symmetrical ornament, again, is manifestly fromtextile models, its symmetrical character is so carefully preservedagainst the suggestions of the circular form that a direct pleasure inits symmetry may be inferred. (See Figs. 2-7. )

 [7] Cushing, F. H. : _op. Cit. _; Holmes, W. H. : three articles on pottery, Rep. Of Bur. Of Ethnol. , 1882-83, p. 265, p. 367, and p. 443. 

[Illustration: Fig. 2]

[Illustration: Fig. 3]

[Illustration: Fig. 4]

The subject of drawing can be here only touched upon, but the resultsof study go to show, in general, two main directions of primitiveexpression: pictorial representation, aiming at truth of life, andsymbolic ornament. The drawings of Australians, Hottentots andBushmen, and the carvings of the Esquimaux and of the prehistoric menof the reindeer period show remarkable vigor and naturalness; whilethe ornamentation of such tribes as the South Sea Islanders has arichness and formal beauty that compare favorably with the decorationof civilized contemporaries. But these two types of art do not alwayskeep pace with each other. The petroglyphs of the North AmericanIndians[8] exhibit the greatest irregularity, while their tattooing isextremely regular and symmetrical. The Brazilian savage [9] drawsfreehand in a very lively and grotesque manner, but his patterns areregular and carefully developed. Again, not all have artistic talentsin the same direction. Dr. Schurtz, in his 'Ornamentik der Aino, '[10]says: "There are people who show a decided impulse for the directimitation of nature, and especially for the representation of eventsof daily life, as dancing, hunting, fishing, etc. It is, however, remarkable that a real system of ornamentation is scarcely everdeveloped from pictorial representations of this kind; that, in fact, the people who carry out these copies of everyday scenes with especialpreference, are in general less given to covering their utensils witha rich ornamentive decoration. "[11] Drawing and ornament, as theproducts of different tendencies, may therefore be consideredseparately. 

 [8] Mallery, Garrick: 'Pictographs of the North American Indians, ' Rep. Of Bur. Of Ethnol. , 1882-3, p. 13. 

 [9] Von den Steinen, Karl: 'Unter den Naturvōlkern Zentral-Brasiliens, ' Berlin, 1894. 

 [10] _Internal. Archiv s. Ethnog. _, Bd. IX. 

 [11] Cf. Andrée, Richard: 'Ethnographische Parallelen, ' Neue Folge, Leipzig, 1889, S. 59. 

The reason for the divergence of drawing and ornament is doubtless theoriginal motive of ornamentation, which is found in the clan or totemideas. Either to invoke protection or to mark ownership, the totemsymbol appears on all instruments and utensils; it has been shown, indeed, that practically all primitive ornament is based on totemicmotives. [12] Now, since a very slight suggestion of the totem given byits recognized symbol is sufficient for the initiated, the extreme ofconventionalization and degradation of patterns is allowable, and isobserved to take place. The important point to be noted in thisconnection is, however, that all these changes are toward symmetry. The most striking examples might be indefinitely multiplied, and areto be found in the appended references (see Figs. 8 and 9). 

 [12] Haddon, _op. Cit. _; Frazer, J. G. : 'Totemism, ' 1887; Grosse, Ernst: Anfänge der Kunst, ' Freiburg i. B. U. Leipzig, 1894. 

[Illustration: Fig. 5. ]

[Illustration: Fig. 6. ]

[Illustration: Fig. 7. ]

We may distinguish here, also, between the gradual disintegration anddegradation of pattern toward symmetry, as seen in the examples justgiven, and the deliberate distortion of figures for a special purpose. This is strikingly shown in the decorative art of the Indians of theNorth Pacific coast. They systematically represent their totemanimals--their only decorative motives--as split in symmetricalsections, and opened out flat on the surface which is to becovered[13] (see Fig. 11). Dr. Boas argues that their purpose is toget in all the received symbols, or to show the whole animal, but, however this may be, every variation introduces symmetry even where itis difficult to do so, as in the case, for instance, of bracelets, hat-brims, etc. (Fig. 10). This may in some cases be due to thesymmetrical suggestions of the human body in tattooing, [14] but itmust be so in comparatively few. 

[13] Boas, Franz: 'Decorative Art of the Indians of the North PacificCoast, ' _Bulletin_ of Am. Mus. Of Nat. Hist. , Vol. IX. 

[14] Mallery, G. : _op. Cit. _; Haddon, A. C. : _op. Cit. _, p. 257;'Decorative Art of British New Guinea, ' Cunningham Memoir X. , RoyalIrish Acad. , 1894, p. 26. 

[Illustration: Fig. 8. ]

[Illustration: Fig. 9. ]

[Illustration: Fig. 10]

The primitive picture has for its object not only to impartinformation, but to excite the very definite pleasure of recognitionof a known object. All explorers agree in their accounts of thesavage's delight in his own naļve efforts at picture making. All suchdrawings show in varying degrees the same characteristics; first ofall, an entire lack of symmetry. In a really great number of examples, including drawings and picture-writing from all over the world, Ihave not found one which showed an attempt at symmetrical arrangement. Secondly, great life and movement, particularly in the drawings ofanimals. Thirdly, an emphasis of the typical characteristics, thelogical marks, amounting sometimes to caricature. The primitive mandraws to tell a story, as children do. He gives with real power whatinterests him, and puts in what he knows ought to be there, even if itis not seen, but he is so engrossed by his interest in the imitatedobject as to neglect entirely its relation to a background. 

[Illustration: FIG. 11]

Now, this very antithesis of ornament and picture is enlightening asto the dawn of ęsthetic feeling, and the strongest confirmation of ourhypothesis of an original impulse to symmetry in art. In theornamentation of objects the content or meaning of the design isalready supplied by the merest hint of the symbol which is thepractical motive of all ornamentation. The savage artist need, therefore, concern himself no more about it, and the form of hisdesign is free to take whatever shape is demanded either by theconditions of technique and the surface to be ornamented, or by thenatural ęsthetic impulse. We have found that technical conditionsaccount for only a small part of the observed symmetry in pattern, andthe inference to a natural tendency to symmetry is clear. Pictorialrepresentation, on the other hand, is enjoyed by the primitive manmerely as an imitation, of which he can say, 'This is that animal'--toparaphrase Aristotle's Poetics. He is thus constrained to reproducethe form as it shows meaning, and to ignore it as form, or as hisnatural motor impulses would make it. 

To sum up the conclusions reached by this short survey of the field ofprimitive art, it is clear that much of the symmetry appearing inprimitive art is due (1) to the conditions of construction, as in theform of dwellings, binding-patterns, weaving and textile patternsgenerally; (2) to convenience in use, as in the shapes of spears, arrows, knives, two-handled baskets and jars; (3) to the imitation ofanimal forms, as in the shapes of pottery, etc. On the other hand (1)a very great deal of symmetrical ornament maintains itself _against_the suggestions of the shape to which it is applied, as the ornamentsof baskets, pottery, and all rounded objects; and (2) all distortion, disintegration, degradation of pattern-motives, often so marked as allbut to destroy their meaning, is in the direction of geometricalsymmetry. In short it is impossible to account for more than a smallpart of the marked symmetry of primitive art by non-ęstheticinfluences, and we are therefore forced to conclude an originaltendency to create symmetry, and to take pleasure in it. A strongnegative confirmation of this is given, as noted above, by the utterlack of symmetry of the only branch of art in which the primitive manis fully preoccupied with meaning to the neglect of shape; and by thecontrast of this with those branches of art in which attention tomeaning is at its minimum. 

The question put at the beginning of this section must thus beanswered affirmatively. There is evidence of an original ęstheticpleasure in symmetry. 

III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY. 

_A. Method of Experiment. _

A certain degree of original ęsthetic pleasure in symmetry may beconsidered to have been established by the preceding section, and, without considering further the problems of real or geometricalsymmetry, it may now be asked whether the pleasure aroused by the formof asymmetrical objects is not at bottom also pleasure in symmetry;whether, in other words, a kind of substitution of factors does notobtain in such objects, which brings about a psychological statesimilar to that produced by real symmetry. 

The question what these substituted factors may be can perhaps beapproached by a glance at a few pictures which are accepted asbeautiful in form, although not geometrically symmetrical. Let ustake, for instance, several simple pictures from among the well-knownaltar-pieces, all representing the same subject, the _MadonnaEnthroned_ with _Infant Christ_, and all of generally symmetricaloutline. It seems, then, reasonable to assume that if the variationsfrom symmetry show constantly recurring tendencies, they represent thechief factors in such a substitutional symmetry or balance, supposingit to exist. The following pictures are thus treated in detail, M. Denoting Madonna; C. , Child; and Cn. , Central Line. The numbers referto the collection of reproductions used exclusively in thisinvestigation, and further described in section IV. 

1. 56, Martin Schöngauer: _Madonna in Rose-arbor. _ M. Is seatedexactly in Cn. , C. On Right, turning to Right. M. Turns to Left, andher long hair and draperies form one long unbroken line down to Leftlower corner. All other details symmetrical. 

2. 867, Titian: _Madonna_. The picture is wider than it is high. M. Stands slightly to Right of Cn. ; C. On Right. Both turn slightly toLeft, and the drapery of M. Makes a long sweep to Left. Also a deepperspective occupies the whole Left field. 

3. 248, Raphael: _Madonna_ (The Bridgewater Madonna). M. Sits in Cn. , turning to Left; C. Lies across her lap, head to Left, but his faceturned up to Right, and all the lines of his body tending sharply downto Right. 

In 1, all the elements of the picture are symmetrical except theposition of C. On the Right, and the long flowing line to Left. In 2, there is a slightly greater variation. The mass of the figures is toRight, and the C. Entirely over against the deep perspective and theflowing line on the Left, and the direction of both faces toward thatside. In 3, the greater part of C. 's figure on Left is opposed by thedirection of his lines and movement to Right. Thus these threepictures, whether or not they are considered as presenting a balance, at least show several well-defined factors which detach themselvesfrom the general symmetrical scheme. (1) Interest in C. Is opposed byoutward-pointing line; (2) greater mass, by outward-pointing line, deep vista, and direction of attention; and (3) again interest bydirection of line and suggestion of movement. 

This analysis of several ęsthetically pleasing but asymmetricalarrangements of space strongly suggests that the elements of largesize, deep perspective, suggested movement, and intrinsic interest arein some way equivalent in their power to arouse those motor impulseswhich we believe to constitute the basis of ęsthetic response. It isthe purpose of these experiments to follow up the lines of thesesuggestions, reducing them to their simplest forms and studying themunder exact conditions. 

But before describing the instruments and methods of this experimentaltreatment, I wish to speak of the articles on the 'Ęsthetics of SimpleForm, ' published as Studies from the Harvard Psychological Laboratory, by Dr. Edgar Pierce. [15] These articles, sub-entitled 'Symmetry' and'The Functions of the Elements' seem at first sight to anticipate thediscussions of this paper; but a short analysis shows that while theypoint in the same direction, they nevertheless deal with quitedifferent questions and in a different manner. In the statement of hisproblem, indeed, Dr. Pierce is apparently treading the same path. 

 [15] Pierce E. : PSYCH. REV. , 1894, I. , p. 483; 1896, III. , p. 270. 

He says: "Can a feeling of symmetry, that is, of ęsthetical equalityof the two halves, remain where the two sides are not geometricallyidentical; and if so, what are the conditions under which this canresult--what variations of one side seem ęsthetically equal to thevariations of the other side?" Some preliminary experiments resultedin the conclusion that an unsymmetrical and yet pleasing arrangementof a varied content rests on the pleasure in unity, thus shutting outthe Golden Section choice, which depends on the pleasure in variety. That is, the choices made will not in general follow the goldensection, but 'when the figure consists of two halves, the pleasuremust be a feeling of ęsthetical symmetry. '

The final experiments were arrangements of lines and simple figures ona square, black background in which the center was marked by a whitevertical line with a blue or a red line on each side. On one side ofthese central lines a line was fixed; and the subject had to place onthe other side lines and simple figures of different sizes anddifferent colors, so as to balance the fixed line. The results showedthat lines of greater length, or figures of greater area must be putnearer the center than shorter or smaller ones--'A short line must befarther than a long one, a narrow farther than a wide, a line fartherthan a square; an empty interval must be larger than one filled, andso on. ' And for colors, "blue, maroon and green, the dark colors, arethe farthest out; white, red and orange, the bright colors, arenearest the center. This means that a dark color must be farther outthan a bright one to compensate for a form on the other side. Thebrightness of an object is then a constant substitute for its distancein satisfying our feeling of symmetry. "

Now from these conclusions two things are clear. By his extremelyemphasized central line, and his explicit question to the subjects, 'Does this balance?' the author has excluded any other point of viewthan that of mechanical balance. His central fulcrum is quiteoverpowering. Secondly, his inquiry has dealt only with size andcolor, leaving the questions of interest, movement, and perspectiveuntouched. But just the purpose of this experimental study is to seekfor the different and possibly conflicting tendencies in composition, and to approximate to the conditions given in pictorial art. It isevident, I think, that the two studies on symmetry will not trespasson each other's territory. The second paper of Dr. Pierce, on 'TheFunctions of the Elements, ' deals entirely with the relation ofhorizontal and vertical positions of the ęsthetic object and of thesubject to ęsthetic judgments, and has therefore no bearing on thispaper. 

For his apparatus Dr. Pierce used a surface of black cloth stretchedover black rubber, 1 m. Square. Now an investigation which is to dealwith complicated and varied relations, resembling those of pictures, demands an instrument resembling them also in the shape of thebackground. A rectangle 600 mm. Broad by 400 mm. High seemed to meetthis requirement better than the square of Dr. Pierce. Other parts, also, of his instrument seemed unfitted for our purpose. The tin, 5cm. Broad and confined to the slits across the center of the square, gave not enough opportunity for movement in a vertical direction, while the scale at the back was very inconvenient for reading. Tosupply these lacks, a scale graduated in millimeters was attached onthe lower edge of the board, between a double track in which ranslides, the positions of which could be read on the scale. To theslides were attached long strips of tin covered with black cloth. Onthese strips figures glued to small clamps or clasps could be slippedup or down; this arrangement of coördinates made it possible to placea figure in any spot of the whole surface without bringing the handsinto the field of view. The experiments were made in a dark room, inwhich the apparatus was lighted by an electric globe veiled by whitepaper and hung above and behind the head of the subject, so as not tobe seen by him and to cast no shadow: in this soft light of course theblack movable strips disappeared against the black background. A graypaper frame an inch and a half wide was fitted to the black rectangleto throw it up against the black depths of the dark room--thus givingin all details the background of a picture to be composed. 

The differences in method between the two sets of experiments werefundamental. In Dr. Pierce's experiments the figures were pulled fromone side to the other of the half-square in question, and the subjectwas asked to stop them where he liked; in those of the writer thesubject himself moved the slides back and forth until a position wasfound ęsthetically satisfactory. The subject was never asked, Doesthis balance? He was indeed requested to abstract from the idea ofbalance, but to choose that position which was the most immediatelypleasing for its own sake, and so far as possible detached fromassociations. 

I have said that Dr. Pierce intentionally accentuated the center. Theconditions of pictorial composition suggest in general the center onlyby the rectangular frame. Most of my experiments were, therefore, madewithout any middle line; some were repeated with a middle line of finewhite silk thread, for the purpose of ascertaining the effect of theenhanced suggestion of the middle line. 

But the chief difference came in the different treatment of results. Dr. Pierce took averages, whereas the present writer has interpretedindividual results. Now, suppose that one tendency led the subject toplace the slide at 50 and another to place it at 130 mm. From thecenter. The average of a large number of such choices would be 90--aposition very probably disagreeable in every way. For such aninvestigation it was evident that interpretation of individual resultswas the only method possible, except where it could be conclusivelyshown that the subjects took one and only one point of view. They werealways encouraged to make a second choice if they wished to do so, asit often happened that one would say: 'I like both of these ways verymuch. ' Of course, individual testimony would be of the highestimportance, and a general grouping into classes and indication of themajority tendency would be the only way to treat the resultsstatistically. And indeed in carrying out the experiments this cautionwas found absolutely necessary. In all but one or two of the sections, the taking of averages would have made the numerical resultsabsolutely unintelligible. Only the careful study of the individualcase, comparison of various experiments on the same person to findpersonal tendencies, and comparison of the different tendencies, couldgive valuable results for the theory of symmetry. 

The first question to be taken up was the influence of right and leftpositions on choice. A long series of experiments was undertaken witha line 80×10 mm. On one side and a line 160×10 mm. On the other, inwhich the positions of these were reversed, and each in turn taken asfixed and variable, with a view to determining the effect of right andleft positions. No definite conclusions emerged; and in the followingexperiments, most of which have been made for both right and leftpositions, the results will be treated as if made for one side alone, and, where averages are taken, will be considered as indifferentlyleft or right. 

The experiments of Dr. Pierce were made for only one position of thefixed line--at 12 cm. Distance from the center. The characteristic ofthe following experiments is their reference to all positions of thefixed line. For instance a fixed line, 10 cm. In length at 12 cm. Distance from the center, might be balanced by a line 5 cm. In lengthat 20 cm. Distance. But would the distance be in the same proportionfor a given distance of the fixed line of say 20 or 25 cm. ? It isclear that only a progressive series of positions of the fixed linewould suggest the changes in points of view or tendencies of choice ofthe subject. Accordingly, for all the experiments the fixed line orother object was placed successively at distances of 20, 40, 60 mm. , etc. , from the center; or at 40, 80 mm. , etc. , according to thecharacter of the object, and for each of these fixed points thesubject made one or two choices. Only an understanding of thedirection in which the variable series moved gave in many cases anexplanation for the choice. 

Each choice, it should be added, was itself the outcome of a longseries of trials to find the most pleasing position. Thus, eachsubject made only about ten choices in an hour, each of which, as itappears in the tables, represents a large number of approximations. 

_B. Experiments on Size. _

I have said that different tendencies or types of choice inarrangement appeared. It will be convenient in the course ofexplaining in detail the method of experiment, to discuss at the sametime the meaning of these types of choice. 

From analysis of the pictures, the simplest suggestion of balanceappeared in the setting off against each other of objects of differentsizes;--an apparent equivalence of a large object near the center witha small object far from the center; thus inevitably suggesting therelations of the mechanical balance, or lever, in which the heavyshort arm balances the light long arm. This was also the result ofDr. Pierce's experiments for one position of his fixed line. Theexperiments which follow, however, differ in some significant pointsfrom this result. The instrument used was the one described in thepreceding section. On one side, in the middle of the vertical strip, was placed the 'fixed' line, denoted by F. , and the subject moved the'variable' line, denoted by V. , until he found the arrangementęsthetically pleasing. The experimenter alone placed F. At the givenreading, and read off the position of V. After the choice F. Wasplaced at the next interval, V. Was again tried in differentpositions, and so on. In the following tables the successive positionsof F. Are given in the left column, reading downward, and thecorresponding positions of V. In the right column. The differentchoices are placed together, but in case of any preference the secondchoice is indicated. The measurements are always in millimeters. Thus, F. 40, V. 60, means that F. Is 40 mm. To one side of the center, andV. 60 mm. To the opposite side. F. 80×10, V. 160×10, means that thewhite cardboard strips 80 mm. ×10 mm. , etc. , are used. The minus signprefixed to a reading means that the variable was placed on the sideof the fixed line. An X indicates ęsthetic dislike--refusal to choose. An asterisk (*) indicates a second choice. 

The following tables are specimen sets made by the subjects _C, O_, and _D_. 

I. (a) F. 80×10, V. 160×10. 

 F. V. C. O. D. 

 40 62, 120 166, 130 28, 24 80 70, 110 104, 102 80, 126 120 46, X 70, 46 68, --44, 128* 160 26, 96 50, 25 85, 196, --88* 200 20, X 55, X --46, 230, * 220, --110*

I. (b) F. 160×10, V. 80×10. 

 F. V. C. O. D. 

 40 74, 64 60, 96 27, 34 80 76, 65 72, 87 55, 138 120 60, 56 48, 82 70, 174 160 29, 74 16, 77 --114, 140, 138, 200 200 96, 36 25, 36 177, --146, --148, 230

Now, on Dr. Pierce's theory, the variable in the first set should benearer the center, since it is twice the size of the fixed line;--butthe choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F. 80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, showthat other forces are at work. If these variations from the expectedwere slight, or if the presence of second choices did not show acertain opposition or contrast between the two positions, they mightdisappear in an average. But the position of F. 40, over against V. 120, 166, 130, is evidently not a chance variation. Still morestriking are the variations for I. (_b_). Here we should expect thevariable, being smaller, to be farther from the center. But for F. 40, we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60, 56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V. 96, 36, 25, 36, 177--while several positions on the same side of thecenter as the constant show a point of view quite irreconcilable withmechanical balance. 

II. (a) F. 2 LINES 80×10. V. SINGLE LINK 80×10. 

 F. V. C. O. P. 

 40- 60 58, 114* 138, 20 96, 84 166 60- 80 48 40, 138* 100, 56 150 80-100 64 70, 162* 47, 87 128 100-120 70 to 80 60 53, 53 X 120-140 58 82 50, 48 35 140-160 74 95 to 100 22, 32 37 160-180 72 102 X, X 42 180-200 90 X X, X 50

Here the variable should supposedly be the farther out; but we have V. 58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80;no larger choice for F. 100-120; indeed, from this point on everythingnearer, and very much nearer. We can trace in these cases, moreclearly perhaps than in the preceding, the presence of definitetendencies. _O_ and _P_, from positions in accord with the mechanicaltheory, approach the center rapidly; while _C_ is seldom 'mechanical, 'but very slowly recedes from the center. The large number of refusalsto choose assures us that the subjects demand a definitely pleasantarrangement--in other words, that every choice is the expression of adeliberate judgment. 

Taking again the experiments 1. (a) and 1. (b), and grouping theresults for nine subjects, _C_, _O_, _A_, _S_, _H_, _G_, _D_, and _P_, we obtain the following general types of choice. The experiments wererepeated by each subject, so that we have eighteen records for eachposition. I should note here that preliminary experiments showed thatnear the frame the threshold of difference of position was 10 mm. , ormore, while near the center it was 4 or 5 mm. ; that is, arrangementswere often judged symmetrically equal which really differed by from 4to 10 mm. , according as they were near to or far from the center. Ingrouping types of choice, therefore, choices lying within these limitswill be taken as belonging to the same type. 

 EXP. 1. (a) F. (80 X 10). V. (160 X 10). 

 1. F. 40. V. 40. ¹

 Types of Choice for V. (1) 24 24 25 28 (2) 40 42 45 45 40 40 40 (3) 62 65 (4) 100 105 1O9 120 130 136 120 (5) 166 180 200 200 200 200 160 160

 ¹This table is obtained by taking from the full list, not given here, of 1. (b) F. (l60 X 10), V. (80 X 10), those positions of 160 X 10 where the variable 80 X 10 has been placed at or near 40, thus giving the same arrangement as for 1. (a). 

It might be objected that a group 40-65 (2-3) would not be larger thanone of 100-136 (4), but the break between 45 and 62 shows the zonesnot continuous. Moreover, as said above, the positions far from thecenter have a very large difference threshold. 

 I. (a) 2. F. 80:--(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95 85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V. 80:--(2) 40 40, (4) 80, (5) 120 120, (6) 160 160. 

 I. (a) 3. F. 120:--(1) 44 46, (2) 64 48 70 70, (3) 85 95 97 91, (4) 113 113 118, (5) 168 169 178;--44, X; also V. 120:--(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160. 

 I. (a) 4. F. 160:--(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*, (4) 114 115 130, (5) 145 145 156 162, (6) 196, (7)--88*--150*--105. 

 I. (a) 5. F. 200:--(1) 20 23 28 36, (2) 55, (3) 108 124 130*, (4) 171 189 199 195, (5) 220 230*, (6)--46--90--110*. 

On comparing the different groups, we find that in 1 and 2 there is adecided preference for a position somewhat less than half way betweencenter and frame--more sharply marked for 1 than for 2. From 3 onwardthere is a decided preference for the mechanical arrangement, whichwould bring the larger strip nearer. Besides this, however, there aregroups of variations, some very near the center, others approaching tosymmetry. The maintenance of geometrical symmetry at a pretty constantratio is to be noted; as also the presence of positions on the sameside of the center as the fixed line. Before discussing thesignificance of these groups we may consider the results of ExperimentII. (F. Double line 80×10, V. Single line 80×10) without givingcomplete lists. 

We notice therein, first of all, the practical disappearance of thesymmetrical choice; for F. 40-60, 60-80, 80-100, a tendency, decreasing, however, with distance from the center, to the mechanicalarrangement; for F. 100-120, and all the rest, not one mechanicalchoice, and the positions confined almost entirely to the region35-75. In some cases, however, the mechanical choice for (1) 40-80, (2) 60-80, was one of two, _e. G. _, we have for (1) 20 and 138, for (3)70 and 162; in the last two cases the mechanical being the secondchoice. 

Now the reversals of the mechanical choice occur for Exp. I. In 1 and2 (F. 40 and F. 80); that is, when the small fixed line is near thecenter, the larger variable is distant. For Exp. II. The reversals, which are much more marked, occur in all cases _beyond_ F. 40, F. 60and F. 80; that is, when the double constant line is far from thecenter, the single variable approaches. If the mechanical theoryprevailed, we should have in Exp. I. The lines together in the center, and in Exp. II. Both near the fringe. 

From the individual testimony, based both on I. (_a_) and I. (_b_), itappears that subject _M_ is perfectly uniform in mechanical choicewhen the fixed line is the small line--_i. E. _ when it moves out, thelarger is placed near the center; but when the conditions ofmechanical choice would demand that, as the larger fixed line movesout, the small variable one should move out farther, he regularlychooses the reverse. Nevertheless, he insists that in just thesecases he has a feeling of equilibrium. 

_A_ also takes the mechanical choice as the small fixed line goesfarther from the center; but when the fixed line is large and leavesthe center, he reverses the mechanical choice--evidently because itwould take the small line too far out. As he says, 'he is alwaysdisturbed by too large a black space in the center. '

_G_ almost always takes the mechanical choice;--in one whole set ofexperiments, in which the fixed line is the large line, he reversesregularly. 

_H_ takes for F. (80×10) the mechanical choice only for the positionsF. 160 and F. 200--_i. E. _, only when F. Is very far from the centerand he wishes V. (160×10) nearer. For F. (160×10) he makes six suchchoices out of ten, but for positions F. 160 and F. 200 he has V. 44, 65 and 20. 

_S_ takes for F. (160×10) at F. 120, V. 185 and-70; says of V. 185, which is also his choice for F. (160×10) at F. 80, 'I cannot go outfurther, because it is so hard to take in the whole field. ' For F. (160×10) at F. 200, he has V. 130 and 60; says of V. 60, 'Veryagreeable elements in connection with the relation of the two lines. '

_C_ takes for F. (80×10) only one mechanical choice until it is at F. 120. Then always mechanical, _i. E. _, nearer center; for F. (160×10)makes after the position F. 40 no mechanical choice, _i. E. _, V. Isnearer center. 

It is evident from the above tables and individual cases that thereversals from the mechanical choice occur only when the mechanicalchoice would bring both lines in the center, or both near the edges, and the subjective testimony shows from what point of view thisappears desirable. The subjects wish 'to take in the whole field, 'they wish 'not to be disturbed by too large a black space in thecenter'; and when, in order to cover in some way the whole space, thesmall line is drawn in or the large one pushed out, they have, nevertheless, a feeling of equilibrium in spite of the reversal ofmechanical balance. 

Accepting for the present, without seeking a further psychologicalexplanation, the type of 'mechanical balance, ' in which amount ofspace is a substitute for weight, as the one most often observed, wehave to seek some point of view from which this entire reversal isintelligible. For even the feeling that 'the whole field must becovered' would hardly account for an exact interchanging of positions. If size gives 'weight, ' why does it not always do so? A simple answerwould seem to be given by the consideration that we tend to give mostattention to the center of a circumscribed space, and that any objectin that center will get proportionately more attention than on theoutskirts. The small line near the center, therefore, would attractattention by virtue of its centrality, and thus balance the largeline, intrinsically more noticeable but farther away. Moreover, allthe other moments of ęsthetic pleasure, derived from the even fillingof the space, would work in favor of this arrangement and against themechanical arrangement, which would leave a large black space in themiddle. 

The hypothesis, then, that the demand for the filling of the wholespace without large gaps anywhere enters into competition with thetendency to mechanical balance, and that this tendency is, nevertheless, reconciled with that demand through the power of acentral position to confer importance, would seem to fit the facts. Itis, of course, clear that neither 'mechanical balance' nor the balanceof 'central' with 'intrinsic' importance have been yet accounted foron psychological grounds; it is sufficient at this point to haveestablished the fact of some kind of balance between elements ofdifferent qualities, and to have demonstrated that this balance is atleast not always to be translated into the 'mechanical' metaphor. 

_C. Experiments on Movement. _

In the preceding experiments the element of size was isolated, and itwas sought to discover, in pleasing combinations of objects ofdifferent sizes, the presence of some kind of balance and the meaningof different tendencies of arrangement. The relative value of the twoobjects was taken as determined on the assumption, supported by commonsense, that under like conditions a large object is given moreattention than a small one. If the unequal objects seem to balanceeach other, then the only other condition in which they differ, theirdistance from the center, must be the cause of their balancing. Thusthe influence of relative position, being the only unknown quantity inthis balance-equation, is easily made out. 

The following experiments will deal with the as yet quite undeterminedelements of suggested movement, perspective and intrinsic interest. Bycombining objects expressing them, each with another simple object ofthe same size, another equation will be obtained in which there isonly one unknown quantity, the sizes of the objects being equal andthe influence of relative position being at least clearly indicated. 

1. Movement. 

The experiments on suggestion of movement were made by _C_, _O_ and_P_. Suggestions of movement in pictures are of two kinds--given bylines pointing in a direction which the eye of the spectator tends tofollow, and by movement represented as about to take place andtherefore interpreted as the product of internal energy. Thus, thetapering of a pyramid would give the first kind of suggestion, thepicture of a runner the second kind. Translated into terms ofexperiment, this distinction would give two classes dealing with (A)the direction of a straight line as a whole, and (B) the expression ofinternal energy by a curve or part of a line. In order to be able tochange the direction of a straight line at a given point, a strip oftin two inches long was fastened by a pivot to the usual clasp whichslipped up and down on the vertical black strip. The tin strip couldbe moved about the pivot by black threads fastened to its perforatedends. A strip of cardboard glued upon it would then take itsdirection. The first experiments, made with the usual 80×10 strip, proved very disagreeable. The subject was much disturbed by the bluntends of the strip. The variable (pivoted) line was then slightlypointed at the upper end, and in the final experiments, in which bothare oblique, both strips were pointed at each end. In Exp. III. A linepointing at an angle from the perpendicular was set over against aline of the same dimensions in the ordinary position. 

 Exp. III. (_a_) F. (80×10) pointed up toward center at 145°, V. (80×10). 

 F. 40:--(1) 39 48 48, (2) 60 66 68, (3) 97 97, (4) 156* 168*. 

 F. 60:--(1) 45, (2) 60 62 65 68 90, (3) 90 94, (4) 117 128 152 155. 

 F. 80:--(1) 50 44*, (2) 74 76 77, (3) 94 100 106 113 115 116, (4) 123 124* 140 165* 169*. 

 F. 100:--(1) 36 58 60 65* 65 74 77 80 87, (2) 98 108 118, (3) 114* 168 186* 170 136*. 

 F. 120:--(1) 40 46 54 60 63 76 96 97 111, (2) 115 120 126* 137*, (3) 170 170*. 

 F. 140:--(1) 45 52 65 65 76 76 86 90, (2) 109 111, (3) 125 140*, (4) 168*. 

 F. 160:--(1) 38 50 50 60, (2) 80 90 96 98 98, (3) 176*. 

 F. 180:--(1) 21 23, (2) 54 70 84 90, (3) 100 100 108 114 120, (4) 130 145*. 

 F. 200:--(1) -2, (2) 33 37 50, (3) 106 110 to 120 115 120 130 132 138 142. 

The most striking point about these groups is the frequency ofpositions far from the center when F. Also is far out. At F. 120, aposition at which the mechanical choice usually prevails if F. Issmaller, a very marked preference indeed appears for positions of V. Nearer the center--in fact, there is only one opposing (first) choice. Now, if it is not the wide space otherwise left which pulls thevariable in, --and we see from a note that the subjects have no feelingof a large empty space in the center, --it must be that F. Has the sameeffect as if it were really smaller than V. , that is, mechanically'light. ' We see, in fact, that the moment F. Has passed the point, between 80 and 100, at which both lines close together in the centerwould be disagreeable, the preference is marked for inner positions ofV. , and I repeat that this cannot be for space-filling reasons, fromthe testimony of F. 200 (3). 

And this 'lightness' of the line pointed in at 45° is indeed what weshould have expected _a priori_ since we found that objectiveheaviness is balanced by a movement out from the center on themechanical principle. If movement out and objective heaviness are ingeneral alike in effect, then movement in and objective lightnessshould be alike in effect, as we have found to be the case from thepreceding experiments. The inward-pointed line does not actually movein, it is true, but it strongly suggests the completion of themovement. It enters into the 'mechanical' equation--it appears tobalance--as if it had moved. 

The point, however, in which this 'lightness' of the inward-pointedline differs from that of the small or short line is its space-fillingquality. It suggests movement in a certain direction, and, whilegiving the mechanical effect of that movement as completed, seems alsoin a sense to cover that space. We see from F. 180 (3), (4), and 200(3), that the subject does not shrink from large spaces between thelines, and does not, as in Exp. I. (_a_), 4 and 5, bring the variable, which in both cases is evidently 'heavier, ' to the center. This mustbe from the fact that the empty space does not in this experiment feelempty--it is filled with energy of the suggested movement. This viewis confirmed by the dislike which the subjects show to the position F. 40; F. , being 'lighter, ' but the object of attention as close to thecenter, might well balance V. Far out. But as if the whole variablefield would be in that case 'overfilled, ' the records show 50 percent. Of refusals to choose for this position. 

In brief, then, a straight line suggesting movements in a certaindirection has the effect, in the general scheme of mechanical balance, of a static position in which this movement has been carried out, withthe added suggestion of the filling of the space over which suchmovement is suggested. 

A few additional experiments were made with a point on the upper endof V. The groups of III. (_a_) are maintained almost exactly: F. 120is again strikingly 'mechanical'; after F. 120 there are only twomechanical choices out of nineteen; while for F. 40, as in Exp. III. (_a_), out of six choices, four are either refusals or question-marked. 

Exp. IV. Both lines took oblique directions, and, to get a pleasingeffect, were pointed at both ends. They were of the usual size, 80×10mm. , but 1 mm. Broader to allow for the effect of length given by thepoints. F. Was fixed at 45°, as in III. (_a_), on the points 40, 80, 120 and 160; V. Moved also on fixed points, 60, 100, 140, 180, foreach position of F. , but on each point was adjusted at a pleasingangle. Thus, there were four positions of V. To each of F. , each withone or two angular positions; V. Was always in the first quadrant. 

The numbers of the table give the angular degrees of V. 

 F. 40, V. 60:--(1) 10 12 38 44, (2) 50 57* 60, (3) 70. V. 100:--(1) 15 15 30 30, (2) 50 55 50, (3) 69 70*. V. 140:--(1) 12* 14 18 18, (2) 60 60 49, (3) 72. V. 180:--(1) 12 10 38, (2) 60 50, (3) 75. [Many refusals at 140 and 180. ]

 F. 80, V. 60:--(1) 11, (2) 25 35 36*, (3) 45 48 55 58 60, (4) 69. V. 100:--(1) 16 15, (2) 24 27 35 40, (3) 52, (4) 62 74*. V. 140:--(1) 10 15 16, (2) 22 28, (3) 40 40 59 59, (4) 70. V. 180:--(1) 14 8, (2) 28, (3) 41 46, (4) 68 79. 

 F. 120, V. 60: (1) 28, (2) 42 44 35, (3) 52 58 62 65 65. V. 100:--(1) 9, (2) 23 25, (3) 38 40 40 42 58, (4) 68 70. V. 140:--(1) 10, (2) 20 26 21* 24 29, (3) 34 42 42 44 55*, (4) 75. V. 180:--(1) 17 26, (2) 40 42 46, (3) 62 64 70 70*. 

 F. 160, V. 60:--(1) 20 39, (2) 18, (3) 58 60 64 68 70. V. 100:--(1) 23 25 30 38, (2) 44 44 49, (3) 55 58 65. V. 140:--(1) 5, (2) 31 35 40 40 32, (3) 54 55 68. V. 180:--(1) 50 50 58 60, (2) 75. 

The tendency to mechanical balance would, according to our previousanalysis, lead the variable to take a direction which, in itssuggestion of motion inward, should be more or less strong accordingas it were farther from or nearer to the center than the fixed line. Such motion inward would, of course, be more strongly suggested by anangle less than 45° than by an angle greater than 45°, and it seemsthat the angles chosen are in general in harmony with thisexpectation. For the positions where F. Is nearer the center than V. There is a preponderance of the angles less than 45° (cf. F. 40 and F. 80, V. 100 and 140; F. 120, V. 140, 180). When V. Passes over to aposition farther from the center than F. (_e. G. _, from F. 80, V. 60, to F. 80, V. 100 and from F. 120, V. 60, to F. 120, V. 140) the changeis marked. In every case where F. Is farther from the center than V. (_i. E. _, F. 80, V. 60; F. 120, V. 60 and V. 100; F. 160, V. 60, V. 100 and V. 140), there are to be noticed a lack of the very smallangles and a preponderance of the middle and larger angles. F. 160, V. 140 and 180 seem to be the only exceptions, which are easilyexplainable by a dislike of the extremely small angle near the edge;for it appears from the remarks of the subjects that there is always asubconsciousness of the direction suggested by the lower pointed endof the line. For the outer positions of both lines, a large anglewould leave the center empty, and a small one would be disagreeablefor the reason just given; and so we find, indeed, for F. 160, V. 100, 140, 160, the middle position the favorite one. 

The representation of action may be translated into experimental termsby expressing it as a line which changes its direction, thus seemingto be animated by some internal energy. The forms chosen were threecurves 'bulging' from a straight line in differing degrees, and twostraight lines with projections. _C_ and _O_ were the subjects. Theresults are given in outline. 

 Exp. V. Curve I. See Fig. 12, I

 (1) Curve out (turned away from center). 

 (_a_) F. (80×10), V. Curve. 

 About half the positions of V. Are farther from the center than F. _O_ at first refuses to choose, then up to F. 120 puts V. Farther from the center than F. _C_ has a set of positions of V. Nearer the center and several second choices farther than F. 

 (_b_) F. Curve, V. (80×10). 

 No position of V. Nearer center than F. _O_ puts line farther out up to F. 160, then nearer than F. _C_ has a set of nearly symmetrical choices and another where V. Is much farther out than F. 

 (2) Curve in (turned toward center). 

 (_a_) F. (80×10), V. Curve. 

 _C_ is absolutely constant in putting V. Farther from center than F. _O_, after F. 100, brings it slightly nearer. 

 (_b_) F. Curve, V. (80×10). 

 _C_, except for F. 40, invariably puts V. Nearer center than F. _O_ moves between 90 and 135, putting V. Farther to F. 100, nearly symmetrical at F. 100 and 120, and after F. 120, from 100 to 135. 

[Illustration: FIG. 12]

 Exp. V. Curve II. See Fig. 12, II. 

 (1) Curve out. 

 (_a_) F. (80×10), V. Curve. 

 In every case but one V. Is nearer center than F. 

 (_b_) F. Curve, V. (80×10). 

 _C_ puts V. Farther from center than F. _O_ puts V. Farther or symmetrical up to F. 120, then nearer than F. 

 (2) Curve in. 

 (_a_) F. 80×10, V. Curve. 

 _C_ has V. Always farther from center than F. , but a second parallel set, omitting F. 40 (all second choices), of symmetrical positions. _O_ begins with V. Farther from center, but from F. 120 has V. Always nearer, though gradually receding from the center. 

 (_b_) F. Curve. V. (80×10). 

 _C_, refusing for F. 40, continues his parallel sets, one with V. Always nearer than F. , another with symmetrical positions. _O_ begins with V. Nearer, changes at F. 120, and continues with V. Farther. 

Recapitulating these results, grouping together the outward and inwardpositions of the curves, and indicating the distance of the line fromthe center by C. -L. , and of the curve from the center by C. -Cv. , wehave:

_Out_. 

Cv. I. (_a_) Indeterminate. (_b_) C. -Cv. < C. -L. (except where large gap would be left). 

Cv. II. (_a_) C. -Cv. < C. -L. (all cases but one). (_b_) C. -Cv. < C. -L. (except where large gap would be left). 

_In. _

Cv. I. (_a_) C. -Cv. > C. -L. (except a few cases to avoid gap). (_b_) C. -Cv. > C. -L. (more than half of cases). 

Cv. II. (_a_) C. -Cv. > C. -L. (except a few cases to avoid gap). (_b_) C. -Cv. > C. -L. (except a few cases to avoid gap). 

It is evident that in the great majority of cases when the curve turnsout it is placed nearer the center, when it turns in, farther from thecenter, than the straight line. The numerical differences for choicesof the same type for the two curves are slight, but regular, and thegeneral tendencies are more sharply marked for the line of greatercurvature. When Curve II. Is 'out, ' it is usually nearer the centerthan Curve I. For the corresponding positions of the straight line;when 'in' it is always farther from the center than Curve I. Thegreater curvature of II. Has clearly produced this difference, and theeffect of the curvature in general is evidently to make its side'lighter' when turned toward the center, and 'heavier' when turnedaway. Thus, all but the exceptions already noted seem to belong to themechanically balanced arrangement, in which the suggestion of forceworking in the direction of the curve has the same effect as, in Exp. IV. , the direction of the line. The exceptions noted, especiallynumerous choices of _O_, seem governed by some fixed law. The evidencewould seem to be overwhelming that the reversals of the mechanicalbalance occur only where the lines would be crowded together in thecenter or would leave an empty gap there. The remainingexceptions--the symmetrical choices mentioned, made by _C_--areexplained by him as follows. He says there are two ways of regardingthe curve, (1) as a striving in the direction of the 'bulge, ' and (2)as the expression of a power that presses together; and that the usualchoices are the result of the first point of view, the symmetricalchoices of the second. Naturally, a pressure bending down the linewould be conceived as working in a vertical direction, and the linewould be treated as another (80×10)--giving, as is the case, symmetrical positions. Thus, we may consider the principle of thesuggestion of movement by a curve, as giving the same effect as if themovement suggested had actually taken place, to have been established, the positive evidence being strong, and the exceptions accounted for. It is worth noting that the curve-out series are always moreirregular--the subject repeating that it is always harder to choosefor that position. Probably the demands of space-filling come intosharper conflict with the tendency to mechanical balance, which forthe outward curve would always widely separate the two lines. 

Exp. V. Curve III. See Fig. 12, III. 

A series with the upper end turned out from the center was unanimouslypronounced as ugly. The inward position only appears in the results, which are given in full. 

(_a_) F. (80×10), V. CURVE. 

 F. V. O. C. 

 40 106 126 68 73 80 106 128 109 102 120 140 88 156 110* 154 72* 160 104 66 182 80 136* 130* 200 X 52 178 220* 162

(_b_) F. CURVE, V. (80×10)

 F. V. O. C. 

 40 126 122 73 80 80 122 128 66 112* 40 120 90 116 97 156* 55 105 160 65 43 120 182* 87 134 200 70 50 148 66

This curve exemplifies the same principles as the preceding. _O_ takesthe natural mechanical choice from (_a_) F. 40 to F. 120, and from(_b_) F. 120 to F. 200. A mechanical choice, however, for (_a_) F. 120ff. , and for (_b_) F. 40 to F. 120, would have brought the lines toofar apart in (_a_), and too near together in (_b_), hence thereversal. _C_ inclines always to the mechanical choice, but recognizesthe other point of view in his second choices. 

Exp. V. Curve IV. See Fig. 12, IV. 

 Curve in. 

 (_a_) F. (80×10), V. Curve. 

 _C_ puts V. Always further than F. And, even for F. 200, has V. 230, X. _O_ puts V. Farther up to F. 120, then puts it nearer than F. , and always refuses to choose for F. 200. 

 (_b_) F. Curve, V. (80×10). 

 _C_ always puts V. Nearer than F. _O_ puts V. Farther for F. 40 and F. 80, beyond that, nearer than F. ; but refuses to choose once each for F. 40, and F. 200. 

 The same principles of choice appear. _C_ maintains the mechanical choice, and _O_ reverses it only beyond (_a_) F. 120, and up to (_b_) F. 120, to fill space well, showing his preference for the mechanical choice by changing into it at an unusually early point. 

Exp. V. Curve V. See Fig. 12, V. 

 Curve in. 

 (_a_) F. (80×10), V. Curve. 

 _C_ puts V. Farther than F. , except for F. 200, V. 125 and X. _O_ also, changing as usual at F. 120 to V. Nearer than F. 

 (_b_) F. Curve, V. (80×10). 

 _O_ puts V. Always farther than F. _O_ has V. Farther for F. 40 and F. 80, then nearer than F. Refuses to choose for F. 200. Results exactly parallel with those of Curve IV. 

Comparing all the results of this whole series of experiments on thesuggestion of movement, we may conclude that movement, whethersuggested by a whole line or part of a line, produces in terms ofmechanical balance the same effect that the balanced object wouldproduce after the completion of the suggested motion. This tendency tobalance, it appears, lies at the basis of our preference; it oftengives way, however, before considerations of space-filling, when thefigure which on the scheme of mechanical balance is weaker, gainsinterest and so 'heaviness' by being brought nearer the center. 

_D. Experiments on Interest. _

By intrinsic interest is meant the interest which would attach to anobject quite apart from its place in the space composition. In apicture it would be represented by the interest in an importantperson, in an unusual object, or in an especially beautiful object, ifthat beauty were independent of the other forms in the picture--as, for instance, a lovely face, or a jeweled goblet, etc. When thequestion of the influence of interest on composition came to bediscussed, it was found very difficult to abstract the form of theobject from the content presented; still more difficult to obtain aneffect of interest at all without the entrance of an element of forminto the space arrangement. Disembodied intellectual interest was theproblem, and the device finally adopted seemed to present, in asindifferent a form as possible, a content whose low degree of absoluteinterest was compensated for by constant change. Stamps of variouscountries in black and white reproductions and very small outlinepictures on squares of the same size as the stamps were taken asmaterial. The figures were so small in relation to the board that anyinfluence on composition of the lines composing them was impossible;the outline pictures, indeed, gave to the eye which abstracted fromtheir content an impression scarcely stronger than the neighboringblank square. 

The first set of experiments (VI. ) had a small outline picture on theside, and on the other a white paper square of the same size. Thenecessary interest was given in the form of novelty by changing thepicture for every choice. The subjects were _M_, _G_ and _D_. Theresults were of the same type for each subject and could therefore beaveraged. 

Exp. VI. (1). 

 _(a)_ F. Picture, V. Blank. Eight choices for each. _M_, Average: V. 17 mm. Farther from center. _G_, Average: V. 10 mm. Farther from center. (Symmetrical position beyond F. 120. ) _D_, Average: V. 25. 8 mm. Farther from center. 

 _(b)_ F. Blank, V. Picture. _M_, Average: V. 33 mm. Nearer center. _G_, Average: V. 4 mm. Nearer center. (Symmetrical beyond F. 120. ) _D_, Average: V. 30 mm. Nearer center. (But V. Farther at F. 40. )

These results are practically unanimous. They show that an objectwhich possesses intrinsic interest acts like a mechanically heavyobject, being placed nearer the center than a blank. Two markeddeviations from the mechanical choice occur--although they have notaffected the average sufficiently to destroy the general harmony ofresults. _G_, in both _(a)_ and _(b)_, chooses symmetrical positionsfrom F. 120 on. His notes ['_(a)_ F. 140, V. 136, pictureunimportant'; '_(b)_ F. 120 and ff. , loses relation as they separate';'_(b)_ F. 160, picture makes no impression'] show clearly that forpositions wide apart the picture, already a faint outline, becomesonly a white square like the other and is put into geometricalsymmetry. 

Exp. VI. (2), by _G_ and _D_. A stamp on one side unchanged, took theplace of the blank; on the other side the stamp was changed for eachchoice. 

 _(a)_ F. Unchanged stamp; V. Changed stamp. 

 _D_. Two series, (1) V. Always nearer center. (2) Same, except F. 20, V. 52; F. 80, V. 94; F. 140, V. 152; F. 160, V. 175. 

 _G_. Two series. (1) V. Much farther from center up to F. 140, then nearer. (2) V. Farther throughout, except F. 160, V. 121. 

 _(b)_ F. Changed stamp; V. Unchanged stamp. 

 _D_. Two series. (1) V. Farther up to F. 100, then symmetrical. (2) V. Farther up to F. 100, then symmetrical or nearer center. 

 _G_. Two series. (1) V. Farther up to F. 120, then symmetrical, and beyond F. 140, nearer center. F. 140, V. 63. (2) V. Much farther up to F. 120, then nearer center, but more nearly symmetrical than (1). A complete series of second choices beginning at F. 40, V. Slightly nearer center than F. 

Analyzing results, we find the changed stamp, which has the interestof novelty, nearly always nearer the center than the unchanged. Thiswould indicate a balance of the mechanical type, in which the interestmakes an object 'heavier. ' The exceptions are in _(a)_ four choices of_D_, _G_ to F. 140, and in _(b)_, _D_'s choice beyond F. 200, and_G_'s beyond F. 120. The deviations are thus seen to be all of thesame type: for positions of F. Near the center, when a mechanicalchoice would have brought V. Still nearer [(_a_)], it is instead putfarther away; for positions of F. Far from the center, when amechanical choice would have put V. Still farther away [(_b_)], it isinstead brought near. The exceptions are thus fully accounted for bythe demand for space-filling. 

_E. Experiments on Depth. _

The experiments on suggestion of depth in the third dimension were asfollows. It was desired to contrast two objects differing only withrespect to the degree to which they expressed the third dimension. Those objects that do express the third dimension are, in general, views down streets, colonnades, corridors, gates, etc. , or, inlandscape, deep valleys, vistas between trees, distant mountains, etc. It is evident that representations of products of human handiworkwould be less unnatural when isolated for experiment, and two pairs ofpictures were accordingly prepared as follows: There was drawn on asquare of 80 mm. The picture of the mouth of a railway tunnel, closedtightly by an apparently massive door; and another picture ofidentical form and surroundings, but showing the rails entering at aslight curve, the deep blackness within, and the small circle of lightat the farther end. The second pair consisted of the gateway of abaronial castle, with heraldic bearings and closed iron-wrought doors;and the same gateway open, showing a flagged pavement and an opencourt with fountain beyond. The perspective effect was heightened byall possible means for both pictures, and care was taken to have thecontrast of black and white the same for each pair, so that to thehalf-shut eye, opened and closed forms seemed to have the same tone. 

The subjects were directed to try to _feel_ the third dimension asvividly as possible--to project themselves down the vistas, as itwere--and then to arrange the squares in the most pleasing manner. Theexperiments were made by _A_, _M_, _S_, _H_ and _D_. Not all made thesame number of repetitions, but as their notes were unusuallysuggestive, I have made use of all the results, and shall quote thenotes for the most part _verbatim_:

Exp. VIII. F. Closed Tunnel. V. Open Tunnel. 

 F. V. Subject _H_. 40 90 60 57 80 13 100 12 120 39 140 - 1 160 -32 180 -71, +50

 _Notes. _--_H_ finds that he neglects the closed tunnel almost entirely, eye is constantly attracted to open tunnel, F. 180, choice of evils. Position of closed tunnel makes the pictures disagreeable. F. 80, V. 13, closed tunnel grows more uninteresting as it goes out, while the open tunnel seems heavier than ever. F. 140, V. -1, closed tunnel loses force and doesn't gain weight. Open tunnel hangs together with the black field beyond it. 

 F. V. Subject _S_. 40 85 95 60 170 195 80 160 180 100 185 200 120 185 - 35, 200 140 85 20 160 115 115 180 100

 _Notes. _--F. 120, V. 185. After this there is too large a black space between squares, and so a more central position is taken, but there is the necessity of avoiding symmetry, which is displeasing. F. 160, V. 115 is not symmetrical and so is more pleasing. F. 60, V. 195:--the open tunnel holds the eyes, while the other allows them to wander, and so it needs a bigger field on each side. F. 80, V. 180:--a position close together is possible, but it is hard to take them so except as one picture, and that is also difficult. F. 100, V. 200:--there is the same objection to any position which seems to be an acknowledgment of similarity; that is, symmetrical position seems to imply that they are alike, and so is disagreeable. F. 120, V. -35, 200:--now they can be close together because the black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth, while the tunnel 'hangs together' with the black to the left. (Cf. _H_, F. 160, V. --32. ) F. 140, V. 20:--when they are together it is difficult to apperceive the frame as a whole; but this position is not far apart, and not disagreeable because the larger stretch of black to the right again hangs together with the tunnel. F. 160, V. 115:--when the open tunnel was in the middle, the closed one seemed to have no business at all, therefore the open tunnel had to be moved over. The only position which was not disagreeable. 

SUBJECT G. 

 F. V. (1) (2) (3) (4)¹ (5)¹ 40 48 31 36 30 23 60 105 31 40 51 39 80 111 71 60 64 54 100 104 63 78 60 86 120 123 75 91 62 115 140 136 82 111 56 137 160 162 93 148 72 156 180 107 115 181 83 176

 ¹Second pair (Court). 

 _Notes. _--(1) All quite unsatisfactory. The arrangement difficult to apperceive as a whole. Each picture taken by itself. (2) The tunnel closed doesn't amount to much. (3) The significance of the tunnel gives it weight. For F. 160, V. 148, and F. 180, V. 180, relation difficult. (4) Court closed gets weaker as gets farther from center. (5) At F. 100, begins to lose relation between pictures, as if one were in one room, one in another. 

SUBJECT A. 

 F. V. (1) (2) (3) (4)² (5)² 40 70 66 140 59 130 60 80 73 159 62 138 80 103 71 120 77 134 100 113 94 108 93 100 120 119 88 96 96 63 140 108 92 60, 164 82 43 160 92 118 70 109 50 180 130 154 78 101 50

 ²Second pair (Court). 

 _Notes_. --(1) Difficult to apperceive together. From F. 140, V. 108, depth is more strongly imagined. (3) Tunnel closed has not much value. (5) F. 80, V. 134, taken with reference both to frame and to the other picture--must not be symmetrical nor too far out. 

SUBJECT D. 

 F. V. (1) (2) (3) 40 100 47 38 60 75 60 68 80 104 78 80 100 148, -12 104 120 120 159 166 160 140 182 152, 84, 78 168 160 193 184, -75 180 180 200 - 95, 190 190

 _Note_. --F. 100, V. -12; F. 140, V. -52; F. 160, V. -75: they must be close together when on the same side. 

 F. V. (1) (2)¹ Subject M. 40 55 50 60 56 74 80 64 84 100 86 102 120 93 111 140 124 130 160 134 146 180 144 178

 ¹Second pair (Court). 

 _Note_. --(1) Quite impossible to take both together; necessary to keep turning from one to the other to get perception of depth together with both. 

The subjects agree in remarking on the lack of interest of the closedtunnel, and the attractive power of the open tunnel, and notes whichemphasize this accompany choices where the open tunnel is putuniformly nearer. (Cf. _H_, F. 180, V. 50; F. 80, V. 13; _G_, (2), (3), (4), (5); _A_, (3), and F. 140. ) As a glance at the results showsthat the open tunnel is placed on the whole nearer the center, we mayconclude that these choices represent a mechanical balance, in whichthe open tunnel, or depth in the third dimension, is 'heavier. '

But another point of view asserts itself constantly in the results of_S_, and scatteringly in those of the others. Analyzing at first onlythe results of _S_, we find that up to F. 140, with one exception, heplaces the open tunnel much farther out than the other; and from F. 140 on, nearer. He says, F. 120, V. 185, 'After this there is toolarge a black space'; that is, in bringing the open tunnel in, he isevidently filling space. But why does he put the open tunnel so farout? It seems that he is governed by the desire for ease in theapperception of the two objects. In his note for F. 80, V. 180, thispoint of view comes out clearly. He thinks of the objects as beingapperceived side by side with the space about each (which apparentlytakes on the character of its object), and then he seems to balancethese two fields. Cf. F. 60, V. 195: 'The closed tunnel allows theeyes to wander, and so it needs a bigger field on each side. 'Evidently there is an implication here of the idea of balance. Cf. Also F. 120: 'The black tunnel harmonizes with the black to the right, and seems to correspond in distance and depth, ' while the closedtunnel 'hangs together with the black on the left. ' In brief, the viewof F. Seems to be that the closed tunnel is less interesting, andpartly because it 'allows the eyes to wander, ' partly as compensationfor the greater heaviness of the open tunnel, it takes with it alarger space than the open tunnel. It is on the whole better to putthem apart, because it is more difficult to apperceive them when closetogether, and so the open tunnel in the earlier choices must, ofcourse, go farther from the center. When these points conflict withthe necessity of filling space, the open tunnel comes nearer thecenter. In general, the notes which emphasize the difficulty ofapperceiving the two pictures as flat and deep together accompanychoices where the tunnel is put uniformly farther out, orsymmetrically. Cf. _G_, (1), (5); _A_, (1); _M_, F. 40, etc. 

Thus we may continue to separate the two points of view, that ofmechanical balance and that of another kind of balance, which we haveknown heretofore as 'space-filling, ' made possible by the power of thecenter to give 'weight, ' but which seems to be now more explicitlyrecognized as a balancing of 'fields. ' At this point we need repeatonly, however, that the suggestion of depth in the third dimensionseems to confer 'weight, ' 'heaviness, ' 'balancing power' on itsobject. 

Before making a general survey of the results of this chapter, it isnecessary to consider a type of choice which has been up to thispoint consistently neglected--that in which the variable has beenplaced on the same side of the center as the fixed object. On thetheory of balance, either in its simple mechanical form or in itsvarious disguises, this choice would at first seem to be inexplicable. And yet the subjects usually took special pleasure in this choice, when they made it at all. These minus choices are confined to three orfour subjects and to two or three experiments. Exp. I. (a) and (b)show the largest number. We have:

 EXP. I. (_a_) F. (80×10); V. (160×10). F. V. 120 - 44, 160 -150, -105, -88 200 -94, -46, -110

 (_b_) F. (160×10); V. (80×10). F. V. 120 -70, -80 160 -114 200 -155, -146, -148

It will be noticed that, with two exceptions, none of the positionschosen are nearer than 70 mm. To the center, and that most of them aremuch farther away. The two lines seem to be more pleasing when theyare pretty close together on the same side. _S_, in I. (_b_) F. 120, V. -70, notes: 'If V. Is nearer _O_, there is a tendency to imagine afigure by the connection of the ends of the two lines, which isdisagreeable. 'The only other minus choices were in Exp. VII. , by_S, _, _H_, and _D_. _S_, F. 120, V. -35, says: 'Now they can be closetogether, ' and _H_, F. 140, 160 and 180, V. -1, -32, -71, notes thesame. So also _D_, F. 100, V. -12; F. 140, V. -52; F. 160, V. -75; F. 180, V. -95. It is evident from this insistence on the closenesstogether of the objects, and this desire to form no figure, that thetwo are taken as one, and set off against the blackness on the otherside. It seems as if this were not taken as empty space, but acquireda meaning of its own. The association with pictures in which the emptyspace is occupied by a deep vista or an expanse of sky is almostirresistible. The case of Exp. VII. Seems a little different. _S_, atleast, separates the two fields as usual, but for him also the blackspace is living, 'corresponds in distance and depth. ' It is at leastcertain that there is no subjective feeling of emptiness or ofunoccupied energies on the empty side. And it would seem that someinfluence from the objects sweeps across the central field andvitalizes it. The most natural view would seem to be that the ease ofapperception of the two objects together, and the tendency of the eyemovement to begin on the occupied side, and to sweep across to theunoccupied, which we think of as deep, combine to give a feeling ofpleasure and of balance. 

 * * * * *

We have now reached a point from which a backward glance can be castupon the territory traversed. Experiment with the isolated elements inpictorial composition has shown that pleasing arrangements of theseelements can be interpreted by the formula of mechanical balance. Thisprinciple was obtained by opposing two lines whose relative value(corresponding to 'weight' in balance) was known; and it was foundthat their relative positions corresponded to the relation of the armsof a balance. Further opposition of lines, of which one was alreadydetermined in 'weight, ' showed the same variations and suggestedcertain valuations of the undetermined lines on the basis of thiscommon term of weight. Thus, the line suggesting movement out from thecenter fitted the formula if taken as 'heavy' and _vice versa_, theline suggesting movement in, if taken as 'light. ' Similarly, objectsof interest and objects suggesting movement in the third dimensionwere 'heavy' in the same interpretation. But this interpretation, inits baldest form, fitted only a majority of the pleasing arrangements;the minority, in which the consistent carrying out of the leverprinciple would have left a large unoccupied space in the center, exactly reversed it, bringing the 'light' element to the center andthe 'heavy' to the outer edge. Later experiments showed that thischoice implied a power in the 'lighter' objects, owing to theircentral position, to cover or infuse with vitality the empty spaceabout them, so that the principle of balance seemed to maintain itselfin one form or another. 

All this does not go beyond the proof that all pleasing spacearrangements can be described in terms of mechanical balance. Butwhat is this mechanical balance? A metaphor, no matter howconsistently carried out, explains nothing. The fact that a smallobject far from the center is usually opposed by a large object nearthe center tells us nothing of the real forces involved. Physicalbalance can be explained by principles of mechanics, but no one willmaintain that the visual representation of a long line weighs morethan that of a short one. Moreover, the elements in the balance seemutterly heterogeneous. The movement suggested by an idea--the pictureof a man running--has been treated as if equivalent to the movementactually made by the eye in following a long line; the intrinsicinterest--that is, the ideal interest--of an object insignificant inform has been equated to the attractive power of a perspective whichhas, presumably, a merely physiological effect on the visualmechanism. What justification can be given either of thisheterogeneous collection of elements or of the more or less arbitraryand external metaphor by which they have been interpreted?

I believe that the required justification of both points of view isgiven in the reduction of all elements to their lowest term--asobjects for the expenditure of attention. A large object and aninteresting object are 'heavy' for the same reason, because they callout the attention; a deep perspective, because the eye rests init;--why, is another question. And expenditure of effort isexpenditure of attention; thus, if an object on the outskirts of thefield of vision requires a wide sweep of the eye to take it in, itdemands the expenditure of attention, and so is felt as 'heavy. ' Itmay be said that involuntary attention is given to the object ofintrinsic interest, while the uninteresting object far on theoutskirts needs a voluntary effort to perceive it, and that the twoattitudes cannot be treated as identical. To this it may be answeredthat an object on the outskirts of a field of view so definitelylimited calls out of itself a reflex movement of the eye toward it, astruly spontaneous as the impulse toward the object of intrinsicinterest. But what is 'the expenditure of attention' in physiologicalterms? It is nothing more than the measure of the motor impulsesdirected to the object of attention. And whether the motor impulseappears as the tendency to fixate an object or as the tendency tofollow out the suggestions of motion in the object, they reduce tothe same physiological basis. It may here be objected that our motorimpulses are, nevertheless, still heterogeneous, inasmuch as some are_toward_ the object of interest, and some _along_ the line ofmovement. But it must be said, first, that these are not felt in thebody, but transferred as values of weight to points in the picture--itis the amount and not the direction of excitement that is counted; andsecondly, that even if it were not so, the suggested movement along aline is felt as 'weight' at a particular point. 

From this point of view the justification of the metaphor ofmechanical balance is quite clear. Given two lines, the most pleasingarrangement makes the larger near the center, and the smaller far fromit. This is balanced because the spontaneous impulse of attention tothe near, large line, equals in amount the involuntary expenditure ofattention to apprehend the small farther one. And this expenditure ofmotor impulses is pleasing, because it is the type of motor impulsesmost in harmony with our own physical organism. 

We may thus think of a space to be composed as a kind of target, inwhich certain spots or territories count more or less, both accordingto their distance from the center and according to what fills them. Every element of a picture, in whatever way it gains power to excitemotor impulses, is felt as expressing that power in the flat pattern. A noble vista is understood and enjoyed as a vista, but it is_counted_ in the motor equation, our 'balance, ' as a spot of so muchintrinsic value at such and such a distance from the center. Theskilful artist will fill his target in the way to give the maximum ofmotor impulses with the perfection of balance between them. 

IV. SYMMETRY IN PICTURES. 

_A. The Balancing Factors. _

The experimental treatment of suggestions as to the elements inpictorial composition has furnished an hypothesis for the basis of ourpleasure in a well-composed picture, and for the particular functionof each of the several elements. This hypothesis may be expressed asfollows: (1) The basis of ęsthetic pleasure in composition is a_balance of motor impulses_ on the part of the spectator; (2) thisbalance of motor impulses is brought about by means of the elements, through the power which they possess of drawing the attention withmore or less strength towards a certain field. But to the experimentalworking out of an hypothesis must succeed a verification, in itsapplication to the masterpieces of civilized art. We have, then, toask whether there is in all great pictures a balance, _i. E. _, an equaldistribution of attention on the two sides of the central linesuggested by the frame of the picture. It might be, for instance, thata picture of pleasing composition would show, when analyzed, all theattractions for attention on one side; which would go far to impugneither our hypothesis of balance as the basis of pleasure, or ourattribution of particular functions to the elements. But as thissecond matter may be considered to have been sufficiently determinedby the results of the preceding section, the first question onlyremains: Is there a balance of attention in a good picture--or rather, in the particular good pictures known to the student of art?

This question could only be answered by the examination of a largenumber of pictures of accepted merit, and it was also desirable thatthey should be studied in a form which lent itself to the easycomparison of one picture with another. These conditions seemed to bebest fulfilled by the collection of reproductions in black and whiteknown as the _Classischer Bilderschatz_, published by F. Bruckmann, atMunich, which contains over a thousand pictures arranged in schools. Of these a thousand were taken--substantially the first thousandissued, after the frescoes, triptych doors, panels, etc. , which areevidently parts of a larger whole, had been laid aside. In thefollowing discussion the pictures will be designated, when they arenot further described, by the numbers which they bear in thiscollection. 

The equations in the following discussion are based on a system ofexact measurement, corresponding to that followed in the experimentalsection. This numerical treatment is pre-supposed in all the generalattributions of balance in the analysis of single pictures. The methodof measurement was given by the conditions of viewing pictures, whichare framed and thus isolated from surrounding influences, andreferred, as compositions, to the middle line suggested by thisemphasized frame. An adjustable frame of millimeter paper, divided inhalf vertically by a white silk thread, was fitted over the picture tobe measured, and measurements were made to left and to right of thisthread-line and, as required, vertically, by reference to themillimeter frame divisions. 

The main question, of course, to be answered by a statisticalexamination of these thousand pictures refers to the existence ofbalance, but many other problems of symmetry are also seen to beclosely involved; the relative frequency of the elements in picturesof different types, and the result of their employment in producingcertain emotional effects, also the general types of space arrangementas a whole, the feeling-tone belonging to them, and the relationbetween content and shape. The first question will not be treated inthis paper in the statistical fulness which was necessary to establishmy conclusions in the investigation itself, inasmuch as the tableswere very extensive. But examples of the tables, together with thefull results, will be given, and a sufficient amount of detaileddiscussion to show my methods. The two other subjects, the use of theelements and the types of composition, will be briefly treated. Iexpect in other publications to go more closely into statisticaldetail on these matters than is possible in a merely experimentalthesis. 

In the beginning of the proposed statistical analysis a naturalobjection must first be forestalled: it will be said, and truly, thatcolor also has its effect in bringing about balance, and that a set ofblack and white reproductions, therefore, ignores an importantelement. To this it may be answered, first, that as a matter of factthe color scheme is, as it were, superimposed upon the space-shape, and with a balance of its own, all the elements being interdependent;and secondly, that the black and white does render the intensitycontrasts of the colors very well, giving as light and dark, and thusas interesting (= attractive) and the reverse, those factors in thescheme which are most closely related to the complex of motorimpulses. After having compared, in European galleries, the originalsof very many of these reproductions with the equation of balanceworked out from the black and white, the writer has seldom found anessential correction needed. 

The pictures were first classified by subjects. This may seem lesslogical than a division by types of arrangement. But it really, for amajority, amounted to the same thing, as the historical masterpiecesof art mostly follow conventional arrangements; thus the altarpieces, portraits, genre pictures, etc. , were mostly after two or threemodels, and this classification was of great convenience from everyother point of view. The preliminary classification was as follows:(1) Religious, Allegorical and Mythical Pictures; (2) Portraits; (3)Genre; (4) Landscape. The historical pictures were so extremely fewthat they were included in the religious, as were also all theallegorical pictures containing Biblical persons. Some pictures, ofwhich Watteau's are representative, which hovered between genre andlandscape, were finally classified according as they seemed to owetheir interest to the figures or to the scenery. A preliminaryclassification of space arrangements, still with reference to content, showed three large general types: (1) A single subject or group in themiddle; (2) the same somewhat on one side, with subordinate elementsoccupying the rest of the space; (3) two objects or groups eachoccupying a well-defined center. These were designated as SingleCenter, Single and Subordinate Center, and Double Center pictures, orS. C. , S. & S. , and D. C. They are in proportions of S. C. 79 per cent. , S. & S. 5 percent. , D. C. 16 per cent. The D. C. Type is evidentlyalready explicitly balanced as regards shape and intrinsic interest, and is hence of comparative unimportance to our problem. The S. C. Willshow a balance, if at all, in more or less accessory factors; S. & S. , broadly, between interest and other factors. As logically moreimportant, this last group will be treated more fully. The fullclassification of the thousand pictures by subjects is as follows:

 S. C. D. C. S. S. Altarpieces 78 70 7 1 Madonna & Child 47 47 0 0 Holy Family 67 40 14 13 Adorations 19 19 0 0 Crucifixions 23 21 0 2 Descents f. Cross 27 26 0 1 Annunciations 21 0 21 0 Misc. Religious 162 93 55 14 Allegorical 46 36 6 4 Genre 93 63 19 11 Landscape 88 65 22 1 Portrait Groups 64 42 17 5 Relig. Single Fig. 28 28 0 0 Alleg. Single Fig. 12 12 0 0 Portrait Single Fig. 207 207 0 0 Genre Single Fig. 18 18 0 0

Altarpieces. 

The pictures of the first group, consisting of the _Madonna_ and_Infant Christ_ surrounded by worshippers, and briefly designated asAltarpieces, are good for detailed study because they present a simpletype, and it will be easy to show whether the variations from symmetryare in the direction of balance or not. A few examples will make thisclear. The Madonna in the S. C. Pictures is invariably seated holdingthe Christ. 

In the following descriptions M. Will denote Madonna, C. Child, Cn. Central line. The elements, Size or Mass, Direction of Motion orAttention, Direction of Line, Vista, and Interest, will be set down asMs. , D. , L. , V. , and I. A couple of examples will show the method ofdescribing and of drawing a conclusion as to balance. 

1. 969. Lorenzo Lotto, _Madonna with St. Bernard and St. Onofrius. _ C. Is on one side turning to the same; M. Leans far to the other; henceinterest in C. , and direction of C. 's attention are over against Massof M. And direction of M. 's attention; _i. E. _, I. + D. = Ms. + D. , andso far, balance. The surrounding saints are insignificant, and we maymake the equation I. = Ms. 

2. 368. Raffaelino di Francesco, _Madonna Enthroned. _ The C. Is onRight facing front, M. Turns away Left, hence interest in C. Is overagainst direction of M. 's attention. Moreover, all the saints but oneturn Left, and of two small vistas behind the throne, the one on theLeft is deeper. The superior interest we feel in C. Is thus balancedby the tendency of attention to the opposite side, and we have I. = D. + V. 

It is clear that the broad characteristics of the composition can besymmetrically expressed, so that a classification of the 70 S. C. Altarpieces can be made on a basis of these constant elements, in theorder of decreasing balance. Thus: Class 1, below, in which the C. Isone side of the central line, turned away from the center, the M. Turned to the other, balances in these broad lines, or I. + D. = D. ;while in (9), I. + D. + D. = (x), the constant elements work all onone side. 

CLASSIFICATION OF ALTARPIECES. 

 1 C. One side turned to same, M. To other 11 2 " " " other, " " 8 3 " " " front, " " 2 4 " " " other, M. Front. 9 5 " " " facing M. 6 6 " " " front, M. Front. 7 7 " " " " M. Turned to same. 6 8 " " " to same M. Turned front. 7 9 " " " " M. " to same, 14 10 " in middle, turned front. 0

Thus the constant elements, understanding always that C. Has moreinterest than M. , are as follows: For (1) I. + D. = D. ; (2) I. = D. +D. ; (3) I. = D. ; (4) I. = D. ; (5) I. + D. = D. ; etc. These are inorder of complete balance, but it will be seen that from (7) on, whilethe factors are constant, the framework is not balanced; _e. G. _ in (9)both I. And D. Work on the same side. For these groups, therefore, thevariations, if there is balance, will be more striking. Eliminatingthe balancing elements in the framework, the tables for the ten groupsare:

 (1) I. + D. = D. (2) I. = D. + D(M). (3) I. = D. 969. I. = Ms. 680. I. = D. 1094. Ms. + I. = I. + D. 601. I. = Ms. 735. I. = D. 33. I. = I. + D 49. I. = Ms. + I. 1121. I. = D. 634. I. = Ms. + I. 1035. I. = D. (4) I. = D. 584. I. = I. 333. I. = I. + D. 775. I. = D. 686. I. = I. 80. I. = I. + D. 746. I. = D. 794. I. = D. 753. I. = I. + D. 1106. I. = Ms. + D. 164. I. = D. 1114. I. = D. + L. 781. I. = Ms. + D. 368. I. = D. + V. 1131. I. = I. + D. 927. I. = V. 517. I. = I. + D. 273. I. = V. 327. I. + Ms. = D. + V. 951. I. + L. = D. + V. 715. Unbalanced. 

 (5) I. + D. = D. (6) I. = (7) I. + D. = 43. I. = I. 854. I. = Ms. 725. I. + D. = I. + L. 711. I. = I. 1148. I. = I. 206. I. + D. = I. + L. 447. I. = Ms. 709. I. = D. 155. I. + D. = D. + L. 643. I. = Ms. 907. I. = D. 739. I. + D. = L. 777. I. = Ms. + I. 586. I. = Ms. + I. 331. I. + D. = V. 637. I. = Ms. + I. 137. I. = Ms. + I. 980. Unbalanced. 187. Unbalanced. 

 (8) I. + D. = (9) I. + (D. + D. ) = (10) 0. 57. I. + D. = Ms. 835. I. + D. = Ms + I. 979. I. + D. = I. + L. 724. I. + D. = Ms + L. 134. I. + D. = D. 495. I. + D. = Ms + L. 106. I. + D. = D. + V. 182. I. + D. = Ms + V. 220. I. + D. = L. 817. I. + D. = I. 118. I. + D. = V. + L. 662. I. + D. = I. 157. Unbalanced. 806. I. + D. = I. 1136. I. + D. = I. + L. 865. I. + D. = I. + V. 1023. I. + D. = V. 531. I. + D. = L. 553. I. + D. = L. 

The most used element is I. , in 100 per cent. Of cases; the leastused, V. , 13 per cent. D. , in 91 per cent. Of cases; Ms. , 26 percent. ; L. , 19 per cent. 175, 433, unbalanced. 

As seen in the table, a balance of elements is kept, except in fourcases which will be hereafter considered. In all cases the balance isbetween the interest in C. , sometimes plus D. , (in the attention ofthe figures to C. ), on the one side, and other elements on the other. Very seldom are other salient points found on the C. Side. When the C. Side is especially 'heavy, ' the number of opposing elements increases, and especially takes the form of V. And L. [cf. (7), (8), (9)], whichwere observed in the experimental chapter to be powerful in attractingattention. For the fairly well-balancing framework--(i), (2), (3) and(4)--Ms. , I. , and D. Are much more often the opposing elements. 

The pictures listed as unbalanced are, with one exception, among theoldest examples given; conceived in the most slavish geometricalsymmetry in which, indeed, the geometrical outline almost hides thefact that the slight variations are all toward a lack of balance. 

There is but one S. & S. Case (1054), Titian, _The Madonna of theHouse of Pesaro_. In this, M. And C. Are on a high throne on theRight, other figures lower down on the Left bearing a flag that leansback to the Left. All the lines of the figures and of the massivearchitecture and the general direction of attention bear down sostrongly to Left that the importance of the Right figures is balanced. We should have, then, I. = I. + L. + D. The D. C. Cases, seven innumber, are remarkably alike. Six have a vista separating the twogroups, in five remarkably deep and beautiful, as if to fix theoscillating attention there. In all, M. And C. , either in position orby the direction of their lines, are nearer the Cn. Than the opposingfigures, which are naturally less interesting, thus giving an instanceof the mechanical balance. Their general equation, then, would be I. =M. Or M. + L. Having shown that the small variations from the generalsymmetrical type of altar-pieces are invariably, except in primitiveexamples, in the direction of substitutional symmetry, or balance, wemay next study the Madonna pictures, using the same classificationsfor purposes of comparison. 

MADONNA WITH INFANT CHRIST. 

 (1) I. + D. = D. (2) I. = D. + D. (4) I. = D. 56. I. = L. 271. I. = D. + L. 668. I. = D. + Ms. 332. I. = L. 867. I. = D. + V. + D. 14. I. = D. + I. 633. I. = D. 91. I. = D. + V. (3) I. = D. 1111. I. = D. + V. 144. I. = D. 1011. I. = D. = L. 521. I. = D. 915. I. = D. = L. 356. I. = L. + D. + D. 296. I. + Ms. = V. + L. 

 (5) I. + D. = D. (6) I. = 51. I. = D. 596. I. = Ms. 581. I. = D. 892. I. = Ms. 829. I. = D. + I. 224. I. = I. + D. 159. I. = I. + D. 908. I. = D. + L. 683. I. = D. + L. 1045. I. = I. + L. (7) I. + D. = 745. I. = I. + L. 344. I. + D. = Ms. 734. I. = D. + L. 949. I. + D. = Ms. + V. + L. 404. I. = D. + L. 608. I. + D. = L. 248. I. = L. 524. I. + D. = L. 37. I. = L. 97. I. = L. (8) 0. 363. I. = V. + L. 674. I. = V. + L. (9) I. + D. + D. = 62. I. = V. + L. 361. I. + D. = L. 1142. I. = V. + L. 1018. I. = V. + L. (10) 110. I. + V. = Ms. + L. 538. I. = D. 411. I. + V. = Ms. + L. 614. I. + Ms. = V. 771. I. + Ms. = V. + L. 34. D. = Ms. + L. 

Most used element, I. , 100 per cent. ; least used, Ms. , 21 per cent. D. , 96 per cent. ; L. , 64 per cent. ; V. , 27 per cent. 

The first thing to be noted, on comparing this table with thepreceding, is the remarkable frequency of the use of the vista and theline. Among the altarpieces, the direction of attention was theelement most often opposed to the interesting object; and next tothat, another object of interest. These two elements, however, heresink into comparative insignificance. In general, balance is broughtabout through the disposition of form rather than of interests. Thisappears in comparing the numbers; against the use of L. In 19 percent. Of the cases among the altarpieces, we have 64 per cent. Amongthe Madonna pictures; V. Is used in the former cases 13 per cent. Ofthe times, in the latter 27 per cent. The reason for this would appearto be that the lack of accessories in the person of saints, worshippers, etc. , and the consequent increase in the size of M. AndC. In the picture heightens the effect of any given outline, and somakes the variations from symmetry greater. This being the case, thecompensations would be stronger--and as we have learned that V. And L. Are of this character, we see why they are needed. None of the M. AndC. , S. C. Pictures fails to give a complete balance of elementsaccording to hypothesis. There are no well-defined cases of S. & S. OrD. C. 

Portraits. 

A study of the Madonna pictures of all types, then, results in anoverwhelming confirmation of the hypothesis of substitutionalsymmetry. It may be objected that the generally symmetrical frameworkof these pictures suggests a complete balance, and the next step inour analysis would, therefore, be a type of picture which is lessbound by tradition to the same form. The portrait would seem tocombine this desideratum with generally large and simple outlines, sothat the whole surface can be statistically reported with comparativeease. A detailed analysis of a couple of portraits may justify theclassification adopted. 

900. Anton Raphael Mengs, _Self-Portrait_. The head of the painter isexactly in Cn. , but is turned sharply to Right, while his shouldersturn Left. His arm and hand are stretched out down to Right, while hisother hand, holding pencil, rests on his portfolio to Left. Hence, theD. Of attention plus that of L. On Right, balances I. In implements, plus D. Of body on Left, or D. + L. = D. + I. 

438. B. Van der Helst, _Portrait of Paul Potter_. The head of thesubject is entirely to Left of Cn. , his easel on Right. His body isturned sharply to Right, and both hands, one holding palette andbrushes, are stretched down to Right. His full face and frontwardglance are on Left. Hence, Ms. + I. In person balances I. Inimplements + D. Of L. , or Ms. + I. = I. + L. 

It is seen that the larger elements in these pictures are thedirections of the head and body, and the position of the head, withreference to Cn. The following classification is based on thisframework. 

CLASSIFICATION OF PORTRAITS. 

 A. Head in Cn. I. Body front, head front, 6 II. Body turned, head turned other way, 7 D. = D. III. Body turned, head front, 31 D. = IV. Body front, head turned, 1 D. = V. Body turned, head turned same way, 106 D. + D. =

 B. Head not in Cn. I. Body turned to empty side, head to same, 18 Ms. =D. II. Body turned to empty side, head front, 23 Ms. = D. III. Body turned to empty side, head to other, 3 Ms. + D. = D. IV. Body front, head front, 2 Ms. = V. Body turned from empty side, head same way, 10 Ms. + D. =

This is also in order of less complete balancing of the originalelements. The principal characteristics of the different divisions areas follows:--

A. I. (Symmetrical. ) Most used element, L. ; least used, V. 

 II. (Balanced, D. = D. ) Most used element, L. ; least used, V. 

 III. (D. = . ) Most used element, Ms. , in 74 per cent, of cases opposed to D. ; in 30 per cent, of cases, D. Of glance opposed to D. Of body; least used, V. (1 per cent. ). 

 IV. One case only. 

 V. (D. = . ) Most used element, Ms. , in 73 per cent. Of cases opposed to D. ; in 40 per cent. Of cases, D. Of glance opposed to D. ; in 28 per cent. Ms. + D. Of glance opposed to D. ; least used element, V. (15 per cent. ). I. 39 per cent. ; L. 38 per cent. 

B. I. (Balanced, Ms. + I. = D. ) Most used element (not counting those already included in equation), I. , 55 per cent. ; least used, V. , 2 per cent. ; L. , 50 per cent. In 44 per cent. , D. Of glance opposed to D. 

 II. (Ms. + I. = D. ) Most used element (not in equation), I. , 52 per cent. Least used, V. , 26 per cent. L. , 43 per cent. In 21 per cent. , D. Of glance opposed to D. 

 III. (Ms. + I. + D. = D. ) Three cases. Two cases V. On empty side. 

 IV. (Ms. + I. = . ) Two cases. One case V. On empty side. 

 V. (Ms. + I. + D. = . ) Most used element, L. , 60 per cent. ; least used, V. , 10 per cent. ; 33-1/3 per cent. , D. Of glance to empty side. 

The portrait class is an especially interesting object for study, inasmuch as while its general type is very simple and constant, forthis very reason the slightest variations are sharply felt, and havetheir very strongest characteristic effect. We shall, therefore, findthat the five principal factors in composition express themselves veryclearly. The general type of the portrait composition is, of course, the triangle with the head at the apex, and this point is alsogenerally in the central line--in 73 per cent. Of the whole number ofcases, as is seen from the table. All cases but one are longer thanthey are wide, most are half-length or more. Nevertheless, greatrichness of effect is brought about by emphasizing variations. Forinstance, the body and head are, in the great majority of cases, turned in the same way, giving the strongest possible emphasis to thedirection of attention--especially powerful, of course, where all theinterest is in the personality. But it is to be observed that the verystrongest suggestion of direction is given by the direction of theglance; and in no case, when most of the other elements are directedin one way, does the glance fail to come backward. (Cf. A. II. , V. , and B. I. , II. , V. )

A. It is of especial value for our conclusions that that division inwhich the constant elements are least balanced (V. ) is far the mostnumerous. Comparison of this with III. Shows that the principalelement, direction of movement of head or body, is balanced by thelarger mass of the body or accessories. Very significant, also, is thegreat increase in the use of V. In this most irregular class (15 percent. As against 1 per cent. In III. ). Three cases (214, 1087, 154, all A. V. , ) fail to show substitutional symmetry. 

B. With the head on one side of Cn. , of course the greatest interestis removed to one side, and the element of direction is brought in tobalance. Again, with this decrease in symmetry, we see the significantincrease in the use of the especially effective elements, V. And L. (Cf. B. I. , II. , III. , IV. , and especially V. ) In fact, the use of thesmall deep vista is almost confined to the class with heads not in themiddle. The direction of the glance also plays an important part. Itis to be noted that in B. I. And II. , I. Appears as the mostfrequently used element, exclusive of the general equation, which is, of course, between the mass of the body and interest of the face, onone side, and the direction of suggested movement on the other. Thismeans that very often the direction of movement alone is notsufficient to balance the powerful Ms. + I. Of the other side, andthat the eye has to be attracted by a definite object of interest. This is usually the hand, with or without an implement--like thepalette, etc. , of our first examples--or a jewel, vase, or bit ofembroidery. This is very characteristic of the portraits of Rembrandtand Van Dyck. 

In general, it may be said that (1) portraits with the head in thecenter of the frame show a balance between the direction of suggestedmovement on one side, and mass or direction of attention, or bothtogether, on the other; while (2) portraits with the head not in thecenter show a balance between mass and interest on one side, anddirection of attention, or of line, or vista, or combinations ofthese, on the other. The hypothesis of substitutional symmetry is thuscompletely confirmed. 

Genre. 

Still more unsymmetrical in their framework than portraits, in factthe most unfettered type of all, are the genre pictures. Being soirregular, they admit of no complete classification based on constantelements in the framework, such as was possible for the types alreadydealt with. A grouping, based on types of composition, is indeedpossible, as of triangles, diagonals, etc. , but as this begs thequestion of the relative importance of line and direction ofattention, and assumes that the shape is all-important, it will not bemade use of here. The broad divisions and the relative use of theelements are given as follows:

 S. C. 63. Most frequent form (I. = or I. + D. =). Most used element, I. , 89 per cent. ; least used, L. , 44 per cent. ; D. , 57 per cent. ; Ms. , 57 per cent. ; V. , 46 per cent. 

 D. C. 19. Most frequent form (I. + D. = I. + D. ) Most used element, I. (all cases); least used, L. , 31 per cent. ; V. , 47 per cent. ; Ms. , 63 per cent. ; D. , 42 per cent. 

 S. &S. 11. Most frequent form (I. Or I. + Ms. = V. Or V. +). Most used element, I. , 100 per cent. ; least used, L. , 20 per cent. ; V. , 82 per cent. ; Ms. , 72 per cent. ; D. , 27 per cent. 

As these are pictures with a human interest, and, therefore full ofaction and particular points of interest, it was to be expected thatI. Would be in all forms the element most frequently appearing. Incompositions showing great variations from geometrical symmetry, itwas also to be expected that V. And L. , elements which have beenlittle used up to this point, should suddenly appear in very highpercentages; for, as being the most strikingly 'heavy' of theelements, they serve to compensate for other variations combined. Ingeneral, however, the balance is between the interesting side, whichis also often the most occupied (I. + Ms. ), and the direction ofsuggestion to the other side. 

For the first time in this investigation the S. & S. And D. C. Typesappear in appreciable numbers. It is of some significance that themost irregular type of all, S. & S. , in which the weight of interestand of mass is overwhelmingly on one side, should be invariablybalanced by the third dimension (V. ). As these somewhat infrequentcases are especially enlightening for the theory of substitutionalsymmetry, it is worth while to analyze one in detail. 

286. Pieter de Hooch, _The Card-players_, in Buckingham Palace, portrays a group completely on the Right of Cn. , all facing in to thetable between them. Directly behind them is a high light window, screened, and high on the wall to the extreme Right are a picture andhanging cloaks. All goes to emphasize the height, mass and interest ofthe Right side. On the Left, which is otherwise empty, is a door halfthe height of the window, giving on a brightly lighted courtyard, fromwhich is entering a woman, also in light clothing. The light streamsin diagonally across the floor. Thus, with all the 'weight' on theRight, the effect of this deep vista on the Left and of its brightnessis to give a complete balance, while the suggestion of line fromdoorway and light makes, together with the central figure, a roughlyoutlined V, which serves to bind together all the elements. Thismatter of binding together of elements is reserved for furtherdiscussion--the purpose of this detailed description is only to showthe extraordinary power of a single element, vista, to balance a wholecomposition of others, and its significance in the tables as anincreasing accompaniment of increasing variations from symmetry. 

The D. C. Cases, inasmuch as they always present a balance of interestat least, are less valuable for our theory; among the variations thelarger side, Ms. , is often balanced by a vista, or, combining with theusual equation for genre pictures, Ms. + I. + D. = V. + I. + D. Thereis only one picture which cannot be schematized (263). 

Landscape. 

The landscape is another type of unfettered composition. As itrepresents no action or single object or group of objects, its partsare naturally more or less unconnected. It should, therefore, be saidthat no picture was taken as D. C. Unless there was a distinctseparation of the two sides. The typical examples are analyzed indetail. 

S. C. 912. J. Van Ruysdael, _Forest Landscape_, in the London NationalGallery. In the Cn. Is a stagnant pool, backed on the Right by thickwoods. A dead tree, white, very prominent in the Right foreground, another at its foot sloping down to Cn. On the Left a bank slopingdown to Cn. , a tree at its foot; behind both, and seen also betweenthe two central trees, bright sky and clouds. Thus, there is on theRight, Mass and Direction to Cn. ; on the Left, Vista and Direction toCn. ; Ms. + D. = V. + D. 

D. C. 642. Hobbema, _The Watermill_, in Buckingham Palace. On theRight, a bank sloping upward, a large cluster of trees, a path leadingdown to Right lower corner. On the Left, somewhat lower, the mill, andwater in front of it, flowing down to Left; clearest sky between milland trees. Thus Mass and Direction out are placed over againstInterest (in mill) and Direction out, plus possibly a hint of Vista, or Ms. + D. = I. + D + V. 

S. C. 65. Most frequent form, Ms. + I. = V. + L. Most used element, V. , 98 per cent. ; least used, D. , 22 per cent. I. 73 per cent. ; Ms. 66 percent. ; L. 31 per cent. 

S. & S. One case. Ms. + I. + V. = V. 

D. C. 22. Most frequent form, Ms. + I. Or Ms. = V. Or V. + (almostinvariable). Most used element, V. , 100 per cent. ; least used, D. , percent. Ms. 82 per cent. ; I. 73 per cent. ; L. 23 per cent. 

It was, of course, to be expected that in pictures without actionthere should be little suggestion of attention or of direction ofmovement. What is less evident is the reason for the high percentageof I. Of course, figures do appear in many examples, and in mostpictures some inanimate object is emphasized--as, for instance, themill in our second example. But the most remarkable point ofdifference in these tables from the preceding is the presence of V. Inpractically every example. It is, of course, natural that somewhere inalmost every picture there should be a break to show the horizon line, for the sake of variety, if for nothing else--but what is significantis the part played by this break in the balancing of the picture. Inabout two thirds of the examples the vista is enclosed by lines, ormasses, and when near the center, as being at the same time the'heaviest' part of the picture, serves as a fulcrum or center to bindthe parts--always harder to bring together than in the other types ofpictures--into a close unity. The most frequent form of thisarrangement, as seen by the table, is a diagonal, which just savesitself by turning up at its far end. Thus the mass, and hence usuallythe special interest of the picture, is on the one side, on the otherthe vista and the sloping line of the diagonal. In very few cases isthe vista behind an attractive or noticeable part of the picture, thefact showing that it acts in opposition to the latter, leading the eyeaway from it, and thus serving at once the variety and richness of thepicture, and its unity. A pure diagonal would have line and vista bothworking at the extreme outer edge of the picture, and thus toostrongly--unless, indeed, balanced by very striking elements near theother edge. 

This function of the vista as a unifying element is of interest inconnection with the theory of Hildebrand, [16] that the landscapeshould have a narrow foreground and wide background, since that ismost in conformity with our experience. He adduces Titian's _Sacredand Profane Love_ as an example. But of the general principle it maybe said that not the reproduction of nature, but the production of aunified complex of motor impulses, is the aim of composition, and thatthis aim is best reached by focusing the eye by a narrowbackground--_i. E. _, vista. No matter how much it wanders, it returnsto that central spot and is held there, keeping hold on all the otherelements. Of Hildebrand's example it may be said that the pyramidalcomposition with the dark and tall tree in the center effectuallyaccomplishes the binding together of the two figures, so that a vistais not needed. A wide background without that tree would leave themrather disjointed. 

 [16] A. Hildebrand, 'Das Problem der Form in der Bildenden Kunst, ' Strassburg, 1897. 

Another interesting observation concerns the use of water inlandscapes. In nearly all appears an expanse of water, and in fourfifths of the cases it is either on the same side as the vista, or inthe same line with it. This is no doubt partly due to thelight-effects which can be got on the water, but it also greatlyreinforces the peculiar effect of the vista. That effect, as has beenrepeatedly said, is to concentrate, to hold, to fixate vision. Thesame thing is true of the horizontal line, as was shown by somepreliminary experiments not here reported. The contrast to theordinary trend of lines--particularly in a landscape--together withthe strong suggestion of quiet and repose, serve to give the sameconcentrating effect to the horizontal lines as to the vista. 

In general, it may be said that balance in landscape is effectedbetween Mass and Interest on one side and Vista and Line on the other;and that unity is given especially by the use of Vista and thehorizontal lines of water. 

A survey of the subject-types remaining on the list of page 514 showsthat they may quite well be grouped together with those alreadyexamined; that is, the Holy Families, Adorations, Crucifixions, andAnnunciations are very symmetrical in type, and present the samecharacteristics as the Altarpieces. The Miscellaneous (mostlyreligious) pictures, the Descents, and the Allegorical are, for themost part, freely composed, irregular, full of action, and resemblethe genre pictures. The Single Figure pictures, Religious, Allegoricaland Genre, and the Portrait Groups, resemble the portraits. Therefore, it may be considered that the existence of a perfect substitutionalsymmetry has been established, inasmuch as it has been shown to bealmost invariably present in the types examined. 

The experimental treatment of the isolated elements determined theparticular function of each in distributing attention in the field ofview. The object of large size claims attention, but does not rivet itnor draw it out powerfully; the intrinsically interesting object doesexcite it, but limits it to a comparatively small field; thesuggestion of movement or of attention on the part of pictured objectscarries the attention through the field of its operation; the vistarivets the attention without powerfully exciting it, and the lineextending in a certain direction carries the attention in the same wayas does the suggestion of movement. But the preceding statisticalanalysis has shown that while all are possibly operative in a givenpicture, some are given much more importance than others, and that inpictures of different types different elements predominate. 

The following table gives the distribution of the elements in thesingle-center pictures already examined. The numbers represent the percent. Of the whole number of balanced pictures in which the givenelement appears once or more. 

 S. C. Ms. I. D. V. L. 

 Alt. P. 26 100 91 13 31 Mad. 21 100 96 27 64 Port. 80 63 98 17 61 Genre 57 89 57 46 44 Lands. 66 73 22 98 31

It is seen that in those classes with a general symmetrical framework, the altar and Madonna pictures, the elements of interest and directionof attention are overwhelmingly predominant--which is the more to beexpected as they appear, of course, as variations in a symmetry whichhas already, so to speak, disposed of mass and line. They give whataction there is, and when they are very strongly operative, we see bypage 516, (8) and (9) and note, that they are opposed by salient linesand deep vistas, which act more strongly on the attention than mass;compare further Mad. , V. 27 per cent. , L. 64 per cent. , as againstAlt. , V. 13 per cent. , L. 19 per cent. , as confirming the view thatthey are used in the more irregular and active pictures. But I. Keepsits predominance throughout the types, except in the portraits, where, indeed, we should not expect it to be so powerful, since the principalobject of interest must always be the portrait head, and that is inmost cases in the Cn. , and therefore not counted. Yet I. Has arespectable representation even in the portrait table, showing thatsuch objects as jewels, embroideries, beautiful hands, etc. , countlargely too in composition. Its greatest is in the genre table, where, of course, human interests constitute the subject matter. 

It is among the portraits that the direction of suggestion is mostoperative. Since these pictures represent no action, it must be givenby those elements which move and distribute the attention; inaccordance with which we see that line also is unusually influential. As remarked above, the altarpieces and Madonna pictures, also largelywithout action, depend largely for it on D. , in the form of directionof attention (D. 91 per cent. ). 

The vista, as said above, rivets and confines the attention. We can, therefore, understand how it is that in the genre table it suddenlyappears very numerous. The active character of these picturesnaturally requires to be modified, and the vista introduces a powerfulbalancing element, which is yet quiet; or, it might be said, inasmuchas energy is certainly expended in plunging down the third dimension, the vista introduces an element of action of counterbalancingcharacter. In the landscape it introduces the principal element ofvariety. It is always to be found in those parts of the picture whichare opposed to other powerful elements, and the 'heavier' the otherside, the deeper the vista. This is especially to be noted in allpictures of the S. & S. Type, where the one side is very 'heavy' andthe deep vista practically invariable on the other. Also in D. C. Pictures it serves as a kind of fulcrum, or unifying element, inasmuchas it rivets the attention between the two detached sides. (Cf. D. C. Among Alt. And Mad. )

The direction of suggestion by means of the indication of a line (L. ), quite naturally is more frequent in the Madonna-picture and Portraitclasses. Both these types are of large simple outline, so that L. Would be expected to tell, but more or less irregular, so that itwould not appear on both sides, thus neutralizing its action, as oftenin the symmetrical altarpieces. This neutralizing explains why it hasa comparatively small per cent. In the landscape table, it havingappeared in minor form all over the field, but less often in largesalient outline. It is worth noticing that for the D. C. Of both genreand landscape, the per cent. Drops appreciably. As it is, in a decidedmajority of cases, combined with V. --the shape being more or less adiagonal slope--it is clear that it acts as a kind of bond between thetwo sides, carrying the attention without a break from one to theother. 

The element of mass requires less comment. It appears in greatestnumber in those pictures which have little action, portraits andlandscapes, and which are yet not symmetrical--in which last case massis, of course, already balanced. In fact, it must of necessity exerta certain influence in every unsymmetrical picture, and so itspercentage, even for genre pictures, is large. 

Thus we may regard the elements as both attracting attention to acertain spot and dispersing it over a field. Those types which are ofa static character abound in elements which disperse the attention;those which are of a dynamic character, in those which make it stable. The ideal composition seems to combine the dynamic and staticelements--to animate, in short, the whole field of view, but in agenerally bilateral fashion. The elements, in substitutional symmetry, are then simply means of introducing variety and action. As a dance inwhich there are complicated steps gives the actor and beholder avaried and thus vivified 'balance, ' and is thus more beautiful thanthe simple walk, so a picture composed in substitutional symmetry ismore rich in its suggestions of motor impulse, and thus morebeautiful, than an example of geometrical symmetry. 

_B. Principles of Composition. _

The particular function of the elements which are substituted forgeometrical symmetry has been made clear; their presence lends varietyand richness to the balance of motor impulses. But the natural motorresponse to stimulation has another characteristic which belongs to usas individuals. The motor response must be balanced, but also unified. In a picture, therefore, there must be a large outline in which allthe elements are held together, corresponding to this requirement ofunity. Now this way of holding together, this manner of combination, may vary; and I hope to show that it not only varies with the subjectand purpose of the picture, but bears a very close relationthereto--that, in short, it is what determines the whole character ofthe picture. Just what this relation is will appear in the study ofour material. 

Examples of these types of composition may best be found by analyzinga few very well-known pictures. We may begin with the class firststudied, the Altarpiece, choosing a picture by Botticelli, in theFlorence Academy (746). Under an arch is draped a canopy held up byangels; under this, again, sits the M. With the C. On her lap, on athrone, at the foot of which, on each side, stand three saints. Theoutline of the whole is markedly pyramidal--in fact, there are, broadly speaking, three pyramids; of the arch, the canopy, and thegrouping. A second, much less symmetrical example of this type, isgiven by another Botticelli in the Academy--_Spring_ (140). Here thecentral female figure, topped by the floating Cupid, is slightlyraised above the others, which, however, bend slightly inward, so thata triangle, or pyramid with very obtuse angle at the apex, issuggested; and the whole, which at first glance seems a littlescattered, is at once felt, when this is grasped, as closely boundtogether. 

Closely allied to this is the type of the _Madonna of BurgomasterMeyer_, Holbein (725), in the Grand-Ducal Castle, Darmstadt. It istrue that the same pyramid is given by the head of the M. Against theshell-like background, and her spreading cloak which envelops thekneeling donors. But still more salient is the diamond form given bythe descending rows of these worshipping figures, especially againstthe dark background of the M. 's dress. A second example, without thepyramid backing, is found in Rubens' _Rape of the Daughters ofLeucippus_ (88), in the Alte Pinakothek at Munich. Here the diamondshape formed by the horses and struggling figures is mostremarkable--an effect of lightness which will be discussed later ininterpreting the types. 

The famous _Bull_ of Paul Potter (149), in the Royal Museum at theHague, furnishes a third type, the diagonal. High on one side aregrouped the herdsman, leaning on a tree which fills up the sky on thatside, and his three sheep and cow. The head of the bull is turnedtoward this side, and his back and hind leg slope down to the otherside, as the ground slopes away to a low distant meadow. The pictureis thus divided by an irregular diagonal. Somewhat more regular is thediagonal of the _Evening Landscape_, by Cuyp (348), in the BuckinghamPalace, London. High trees and cliffs, horsemen and others, occupy oneside, and the mountains in the background, the ground and the clouds, all slope gradually down to the other side. 

It is a natural transition from this type to the V-shape of thelandscapes by Aart van der Neer, _Dutch Villages_, 245 and 420, in theLondon National Gallery and in the Rudolphinum at Prague, respectively. Here are trees and houses on each side, graduallysloping to the center to show an open sky and deep vista. Otherexamples, of course, show the opening not exactly in the center. 

In the _Concert_ by Giorgione (758), in the Pitti Gallery, Florence, is seen the less frequent type of the square. The three figures turnedtoward each other with heads on the same level make almost a squarespace-shape, although it might be said that the central player gives apyramidal foundation. This last may also be said of Verrocchio's_Tobias and the Archangels_ in the Florence Academy, for the square, or rather rectangle, is again lengthened by the pyramidal shape of thetwo central figures. The unrelieved square, it may here beinterpolated, is not often found except in somewhat primitiveexamples. Still less often observed is the oval type of _Samson'sWedding feast_, Rembrandt (295), in the Royal Gallery, Dresden. Hereone might, by pressing the interpretation, see an obtuse-angleddouble-pyramid with the figure of Delilah for an apex, but a few veryirregular pictures seem to fall best under the given classification. 

Last of all it must be remarked that the great majority of picturesshow a combination of two or even three types; but these are usuallysubordinated to one dominant type. Such, for instance, is the casewith many portraits, which are markedly pyramidal, with thedouble-pyramid suggested by the position of the arms, and the invertedpyramid, or V, in the landscape background. The diagonal sometimesjust passes over into the V, or into the pyramid; or the square iscombined with both. 

It is, of course, not necessary at this point to show how it is thatsuch an apparently unsymmetrical shape as the diagonal, alone or incombination with other forms, nevertheless produces an effect ofbalance. In all these cases of the diagonal type the mass or interestof the one side, or the direction of subordinate lines backward to it, balances the impulse of the line descending to the other side. Thepresence of balance or substitutional symmetry is taken for grantedin this treatment, having been previously established, and only themodifications of this symmetry are under consideration. 

Now, in order to deal properly with the question of the relation ofthe type of composition to the subject of the picture, completestatistical information will be necessary. A table of the pictures, classified by subjects and distributed under the heads of the sixmajor types, is accordingly subjoined. 

 Pyramid. Double-Pyr. Diagonal. S. C. D. C. S. S. S. C. D. C. S. S. S. C. D. C. S. S. Altarpieces, 49 0 1 10 4 0 1 0 0 Mad. W. C. , 40 0 0 7 0 0 0 0 0 Holy Family, 25 0 4 0 0 1 2 2 2 Adorations, 19 0 0 0 0 0 0 0 0 Crucifixions, 11 0 0 7 0 1 0 0 1 Desc. Fr. Cross, 12 0 0 3 0 0 1 0 0 Annunciations, 0 8 0 0 4 0 0 0 0 Misc. Religious, 55 16 3 4 4 0 10 7 5 Allegorical, 20 2 1 4 0 0 4 0 2 Genre, 25 4 4 5 0 0 18 2 1 Landscape, 8 2 1 3 0 0 25 6 0 Port. Group, 20 4 2 9 0 0 3 3 2 Rel. Single Fig. , 20 0 0 2 0 0 2 0 0 Alleg. S. F. , 7 0 0 2 0 0 3 0 0 Portrait S. F. , 179 0 0 28 0 0 0 0 0 Genre S. F. , 15 0 0 1 0 0 1 0 0

 V-shaped. Square. Oval. S. C. D. C. S. S. S. C. D. C. S. S. S. C. D. C. S. S. Altarpieces, 6 1 0 4 1 0 0 1 0 Mad. W. C. , 0 0 0 0 0 0 0 0 0 Holy Family, 13 3 6 0 0 0 0 0 0 Adorations, 0 0 0 0 0 0 0 0 0 Crucifixions, 0 0 0 3 0 0 0 0 0 Desc. Fr. Cross, 5 0 1 3 0 0 2 0 0 Annunciations, 0 1 0 0 8 0 0 0 0 Misc. Religious, 20 14 2 9 12 1 2 2 3 Allegorical, 3 2 1 3 1 0 3 1 0 Genre, 10 7 6 4 4 0 1 3 0 Landscape, 20 12 0 4 0 0 5 2 0 Port. Group, 10 7 1 0 3 0 0 0 0 Rel. Single Fig. , 3 0 0 1 0 0 0 0 0 Alleg. S. F. , 0 0 0 0 0 0 0 0 0 Portrait S. F. , 0 0 0 0 0 0 0 0 0 Genre S. F. , 1 0 0 0 0 0 0 0 0

What types are characteristic of the different kinds of pictures? Inorder to answer this question we must ask first, What are thedifferent kinds of pictures? One answer, at least, is at oncesuggested to the student on a comparison of the pictures with theirgroupings according to subjects. All those which represent the Madonnaenthroned, with all variations, with or without saints, shepherds orHoly Family, are very quiet in their action; that is, it is not reallyan action at all which they represent, but an attitude--the attitudeof contemplation. This is no less true of the pictures I have called'Adorations, ' in which, indeed, the contemplative attitude is stillmore marked. On the other hand, such pictures as the 'Descents, ' the'Annunciations, ' and very many of the 'miscellaneous religious, 'allegorical and genre pictures, portray a definite action or event. Taking together, for instance, in two groups of five each, the firstten classes in the table, we find that they fall to the six types inthe following proportion:

 P. D. P. Dg. V. Sq. Ov. I. 66 13 05 13 03 0 II. 43 07 14 20 12 04

Inasmuch as II. Contains also many 'contemplative' pictures, while I. Contains no 'active' ones, the contrast between the proportions of thegroups would really be sharper than the figures indicate. But as itis, we see that the pyramid type is characteristic of the'contemplative' pictures in a much higher degree. If the closelyallied double-pyramid type is taken with it, we have 79 per cent ofthe 'contemplative' to 50 per cent, of the 'active' ones. This view isconfirmed by contrasting the 'Adoration, ' the most complete example ofone group, with the genre pictures, the most complete example of theother--and here we see that in the first all are pyramidal, and in thesecond only 26 per cent. A class which might be supposed to suggestthe same treatment in composition is that of the portraits--absolutelack of action being the rule. And we find, indeed, that no singletype is represented within it except the pyramid and double-pyramid, with 86 per cent. Of the former. Thus it is evident that for the typeof picture which expresses the highest degree of quietude, contemplation, concentration, the pyramid is the characteristic typeof composition. 

But is it not also characteristic of the 'active' pictures, since, aswe see, it has the largest representation in that class too? Perhapsit might be said that, inasmuch as all pictures are really more'quiet' than they are 'active, ' so the type _par excellence_ is thepyramidal--a suggestion which is certainly borne out by the table as awhole. But setting aside for the moment the pyramid and itssub-variety, we see that the diagonal V-shaped and square types aremuch more numerous in the roughly outlined 'active' class. Taking, again, the genre class as especially representative, we find 23 percent. Of the diagonal type, and 25 per cent. Of the V-shaped. We haveseen how closely allied are these two types, and how gradually onepasses over into the other, so that we may for the nonce take themtogether as making up 47 per cent. Of the whole. The type of picturewhich expresses the highest degree of activity, which aims to tell astory, has, then, for its characteristic type the V and its varieties. 

The landscape picture presents a somewhat different problem. It cannotbe described as either 'active' or 'passive, ' inasmuch as it does notexpress either an attitude or an event. There is no definite idea tobe set forth, no point of concentration, as with the altarpieces andthe portraits, for instance; and yet a unity is demanded. Anexamination of the proportions of the types shows at once thecharacteristic type. 

 P. D. P. Dg. V. Sq. Or. Landscapes, 13 03 35 36 05 08

It is now necessary to ask what must be the interpretation of the useof these types of composition. Must we consider the pyramid theexpression of passivity, the diagonal or V, of activity? But thegreatly predominating use of the second for landscapes would remainunexplained, for at least nothing can be more reposeful than thelatter. It may aid the solution of the problem to remember that thecomposition taken as a whole has to meet the demand for unity, at thesame time that it allows free play to the natural expression of thesubject. The altarpiece has to bring about a concentration ofattention to express or induce a feeling of reverence. This isevidently brought about by the suggestion of the converging lines tothe fixation of the high point in the picture--the small area occupiedby the Madonna and Child--and by the subordination of the free play ofother elements. The contrast between the broad base and the apex givesa feeling of solidity, of repose; and it seems not unreasonable tosuppose that the tendency to rest the eyes above the center of thepicture directly induces the associated mood of reverence or worship. Thus the pyramidal form serves two ends; primarily that of givingunity; and secondarily, by the peculiarity of its mass, that ofinducing the feeling-tone appropriate to the subject of the picture. 

Applying this principle to the so-called 'active' pictures, we seethat the natural movement of attention between the different 'actors'in the picture must be allowed for, while yet unity is secured. And itis clear that the diagonal type is just fitted for this. The attentionsweeps down from the high side to the low, from which it returnsthrough some backward suggestion of lines or interest in the objectsof the high side. Action and reaction--movement and return ofattention--is inevitable under the conditions of this type; and thisit is which allows the free play--which, indeed, _constitutes_ andexpresses the activity belonging to the subject, just as the fixationof the pyramid constitutes the quietude of the religious picture. Thusit is that the diagonal composition is particularly suited to portrayscenes of grandeur, and to induce a feeling of awe in the spectator, because only here can the eye rove in one large sweep from side toside of the picture, recalled by the mass and interest of the sidefrom which it moves. The swing of the pendulum is here widest, so tospeak, and all the feeling-tones which belong to wide, free movementare called into play. If, at the same time, the element of the deepvista is introduced, we have the extreme of concentration combinedwith the extreme of movement; and the result is a picture in the'grand style'--comparable to high tragedy--in which all thefeeling-tones which wait on motor impulses are, as it were, while yetin the same reciprocal relation, tuned to the highest pitch. Such apicture is the _Finding of the Ring_, Paris Bordone (1048), in theVenice Academy. All the mass and the interest and the suggestion ofattention is toward the right--the sweep of the downward lines and ofthe magnificent perspective toward the left--and the effect of thewhole space-composition is of superb largeness of life and feeling. With it may be compared Titian's _Presentation of the Virgin_ (107), also in the Academy, Venice. The composition, from the figure movingupward to one high on the right, to the downward lines, waiting groupsand deep vista on the left, is almost identical with that of theBordone. Neither is pure diagonal--that is, it saves itself at last byan upward movement. Compare also the two great compositions byVeronese, _Martyrdom of St. Mark_, etc. (1091), in the Doge's Palace, Venice, and _Esther before Ahasuerus_ (566), in the Uffizi, Florence. In both, the mass, direction of interest, movement and attention aretoward the left, while all the lines tend diagonally to the right, where a vista is also suggested--the diagonal making a V just at theend. Here, too, the effect is of magnificence and vigor. 

If, then, the pyramid belongs to contemplation, the diagonal toaction, what can be said of the type of landscape? It is withoutaction, it is true, and yet does not express that positive quality, that _will_ not to act, of the rapt contemplation. The landscapeuncomposed is negative; and it demands unity. Its type of composition, then, must give it something positive besides unity. It lacks bothconcentration and action; but it can gain them both from a spacecomposition which shall combine unity with a tendency to movement. Andthis is given by the diagonal and V-shaped type. This type merelyallows free play to the natural tendency of the 'active' picture; butit constrains the neutral, inanimate landscape. The shape itselfimparts motion to the picture: the sweep of line, the concentration ofthe vista, the unifying power of the inverted triangle between twomasses, act, as it were, externally to the suggestion of the objectitself. There is always enough quiet in a landscape--the overwhelmingsuggestion of the horizontal suffices for that; it is movement that isneeded for richness of effect; and, as I have shown, no type impartsthe feeling of movement so strongly as the diagonal and V-shaped typeof composition. It is worth remarking that the perfect V, which is ofcourse more regular, concentrated, quiet, than the diagonal, is morefrequent than the diagonal among the 'Miscellaneous Religious'pictures (that is, it is more _needed_), since after all, as has beensaid, the final aim of all space composition is just the attainment ofrepose. But the landscapes need energy, not repression; and so thediagonal type is proportionately more numerous. 

The square and oval types, as is seen from the table, are far lessoften used. The oval, most infrequent of all, appears only among the'active' pictures, with the exception of landscape. It usually servesto unite a group of people among whom there is no one especiallystriking--or the object of whose attention is in the center of thepicture, as in the case of the Descent from the Cross. It imparts acertain amount of movement, but an equable and regular one, as the eyereturns in an even sweep from one side to the other. 

The square type, although only three per cent. Of the whole number ofpictures, suggests a point of view which has already been touched onin the section on Primitive Art. The examples fall into two classes:in the first, the straight lines across the picture are unrelieved bythe suggestion of any other type; in the second, the pyramid or V issuggested in the background with more or less clearness by means ofarchitecture or landscape. In the first class are found, almostexclusively, early examples of Italian, Dutch and German art; in thesecond, pictures of a later period. The rigid square, in short, isfound only at an early stage in the development of composition. Moreover, all the examples are 'story' pictures, for the most partscenes from the lives of the saints, etc. Many of them aredouble-center--square, that is, with a slight break in the middle, thegrouping purely logical, to bring out the relations of the characters. Thus, in the _Dream of Saint Martin_, Simone Martini (325), a frescoat Assisi, the saint lies straight across the picture with his head inone corner. Behind him on one side, stand the Christ and angels, grouped closely together, their heads on the same level. Compare alsothe _Finding of the Cross_, Piero della Francesca (1088), a serialpicture in two parts, with their respective backgrounds all on thesame level; and most of the frescoes by Giotto at Assisi--inparticular _St. Francis before the Sultan_ (1057), in which the actorsare divided into parties, so to speak. 

These are all, of course, in one sense symmetrical--in the weight ofinterest, at least--but they are completely amorphous from an ęstheticpoint of view. The _forms_, that is, do not count at all--only themeanings. The story is told by a clear separation of the parts, andas, in most stories, there are two principal actors, it merely happensthat they fall into the two sides of the picture. Interesting inconnection with this is the observation that, although the moreanecdotal the picture the more likely it is to be 'double-centered, 'the later the picture the less likely it is to be double-centered. Thus the square and the double-center composition seem often to befound in the same picture and to be, both, characteristic of earlycomposition. On the other hand, a rigid geometrical symmetry is alsocharacteristic, and these two facts seem to contradict each other. Butit is to be noted, first, that the rigid geometrical symmetry belongsonly to the Madonna Enthroned, and general Adoration pieces; andsecondly, that this very rigidity of symmetry in details can coexistwith variations which destroy balance. Thus, in the _MadonnaEnthroned_, Giotto (715), where absolute symmetry in detail is kept, the Child sits far out on the right knee of the Madonna. Compare also_Madonna_, Vitale di Bologna (157), in which the C. Is almost fallingoff M. 's arms to the right, her head is bent to the right, and a monkis kneeling at the right lower corner; also _Madonna_, Ottaviano Nelli(175)--all very early pictures. Hence, it would seem that the symmetryof these early pictures was not dictated by a conscious demand forsymmetrical arrangement, or rather for real balance, else suchfailures would hardly occur. The presence of geometrical symmetry ismore easily explained as the product, in large part, of technicalconditions: of the fact that these pictures were painted asaltarpieces to fill a space definitely symmetrical in character--often, indeed, with architectural elements intruding into it. We may evenventure to connect the Madonna pictures with the temple images of theclassic period, to explain why it was natural to paint the object ofworship seated exactly facing the worshipper. Thus we may separate thetwo classes of pictures, the one giving an object of worship, and thustaking naturally, as has been said, the pyramidal, symmetrical shape, and being moulded to symmetry by all other suggestions of technique;the other aiming at nothing except logical clearness. This antithesisof the symbol and the story has a most interesting parallel in the twogreat classes of primitive art--the one symbolic, merely suggestive, shaped by the space it had to fill, and so degenerating into theslavishly symmetrical, the other descriptive, 'story-telling' andwithout a trace of space composition. On neither side is thereevidence of direct ęsthetic feeling. Only in the course of artisticdevelopment do we find the rigid, yet often unbalanced, symmetryrelaxing into a free substitutional symmetry, and the formlessnarrative crystallizing into a really unified and balanced space form. The two antitheses approach each other in the 'balance' of themasterpieces of civilized art--in which, for the first time, a realfeeling for space composition makes itself felt. 

 * * * * *

THE ĘSTHETICS OF UNEQUAL DIVISION. 

BY ROSWELL PARKER ANGIER. 

PART I. 

The present paper reports the beginnings of an investigation designedto throw light on the psychological basis of our ęsthetic pleasure inunequal division. It is confined to horizontal division. Owing to theprestige of the golden section, that is, of that division of thesimple line which gives a short part bearing the same ratio to thelong part that the latter bears to the whole line, experimentation ofthis sort has been fettered. Investigators have confined their effortsto statistical records of approximations to, or deviations from, thegolden section. This exalts it into a possible ęsthetic norm. But sucha gratuitous supposition, by limiting the inquiry to the verificationof this norm, distorts the results, tempting one to forget theprovisional nature of the assumption, and to consider divergence fromthe golden section as an error, instead of another example, merely, ofunequal division. We have, as a matter of fact, on one hand, investigations that do not verify the golden section, and, on theother hand, a series of attempts to account for our pleasure in it, asif it were, beyond dispute, the norm. In this way the statisticalinquiries have been narrowed in scope, and interpretation retarded andmisdirected. Statistically our aim should be to ascertain within howwide limits ęsthetically pleasing unequal divisions fall; and aninterpretative principle must be flexible enough to include persistentvariations from any hypothetical norm, unless they can be otherwiseaccounted for. If it is not forced on us, we have, in either case, nothing to do with the golden section. 

Since Fechner, the chief investigation in the ęsthetics of simpleforms is that of Witmer, in 1893. [1] Only a small part of his workrelates to horizontal division, but enough to show what seems to me aradical defect in statistical method, namely, that of accepting ageneral average of the average judgments of the several subjects, as'the most pleasing relation' or 'the most pleasing proportion. '[2]Such a total average may fall wholly without the range of judgments ofevery subject concerned, and tells us nothing certain about thespecific judgments of any one. Even in the case of the individualsubject, if he shows in the course of long experimentation that he hastwo distinct sets of judgments, it is not valid to say that his realnorm lies between the two; much less when several subjects areconcerned. If averages are data to be psychophysically explained, theymust fall well within actual individual ranges of judgment, else theycorrespond to no empirically determinable psychophysical processes. Each individual is a locus of possible ęsthetic satisfactions. Sincesuch a locus is our ultimate basis for interpretation, it is inept tochoose, as 'the most pleasing proportion, ' one that may have nocorrespondent empirical reference. The normal or ideal individual, which such a norm implies, is not a psychophysical entity which mayserve as a basis of explanation, but a mathematical construction. 

 [1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher räumlicher Formverhältnisse, ' _Phil. Studien_, 1893, IX. , S. 96-144, 209-263. 

This criticism would apply to judgments of unequal division on eitherside the center of a horizontal line. It would apply all the more toany general average of judgments including both sides, for, as weshall soon see, the judgments of individuals differ materially on thetwo sides, and this difference itself may demand its explanation. Andif we should include within this average, judgments above and belowthe center of a vertical line, we should have under one heading fourdistinct sets of averages, each of which, in the individual cases, might show important variations from the others, and therefore requiresome variation of explanation. And yet that great leveller, thegeneral average, has obliterated these vital differences, and isrecorded as indicating the 'most pleasing proportion. '[3] That such anaverage falls near the golden section is immaterial. Witmer himself, as we shall see, [4] does not set much store by this coincidence as astarting point for explanation, since he is averse to any mathematicalinterpretation, but he does consider the average in questionrepresentative of the most pleasing division. 

 [2] _op. Cit. _, 212-215. 

 [3] Witmer: _op. Cit. _, S. 212-215. 

 [4] _op. Cit. _, S. 262. 

I shall now, before proceeding to the details of the experiment to berecorded, review, very briefly, former interpretative tendencies. Zeising found that the golden section satisfied his demand for unityand infinity in the same beautiful object. [5] In the golden section, says Wundt, [6] there is a unity involving the whole; it is thereforemore beautiful than symmetry, according to the ęsthetic principle thatthat unification of spatial forms which occurs without marked effort, which, however, embraces the greater manifold, is the more pleasing. But to me this manifold, to be ęsthetic, must be a sensible manifold, and it is still a question whether the golden section set of relationshas an actual correlate in sensations. Witmer, [7] however, wrote, atthe conclusion of his careful researches, that scientific ęstheticsallows no more exact statement, in interpretation of the goldensection, than that it forms 'die rechte Mitte' between a too great anda too small variety. Nine years later, in 1902, he says[8] that thepreference for proportion over symmetry is not a demand for anequality of ratios, but merely for greater variety, and that 'theamount of unlikeness or variety that is pleasing will depend upon thegeneral character of the object, and upon the individual's grade ofintelligence and ęsthetic taste. ' Külpe[9] sees in the golden section'a special case of the constancy of the relative sensiblediscrimination, or of Weber's law. ' The division of a line at thegolden section produces 'apparently equal differences' between minorand major, and major and whole. It is 'the pleasingness of apparentlyequal differences. '

 [5] Zelsing, A. : 'Aesthetische Forschungen, ' 1855, S. 172; 'Neue Lehre von den Proportionen des menschlichen Körpera, ' 1854, S. 133-174. 

 [6] Wundt, W. : 'Physiologische Psychologie, ' 4te Aufl. , Leipzig, 1893, Bd. II. , S. 240 ff. 

 [7] _op. Cit. _, S. 262. 

 [8] Witmer, L. : 'Analytical Psychology, ' Boston, 1902, p. 74. 

 [9] Külpe, O. : 'Outlines of Psychology, ' Eng. Trans. , London, 1895, pp. 253-255. 

These citations show, in brief form, the history of the interpretationof our pleasure in unequal division. Zeising and Wundt were alike inerror in taking the golden section as the norm. Zeising used it tosupport a philosophical theory of the beautiful. Wundt and others toohastily conclude that the mathematical ratios, intellectuallydiscriminated, are also sensibly discriminated, and form thus thebasis of our ęsthetic pleasure. An extension of this principle wouldmake our pleasure in any arrangement of forms depend on themathematical relations of their parts. We should, of course, have nospecial reason for choosing one set of relationships rather thananother, nor for halting at any intricacy of formulę. But we cannotmake experimental ęsthetics a branch of applied mathematics. A theory, if we are to have psychological explanation at all, must be pertinentto actual psychic experience. Witmer, while avoiding and condemningmathematical explanation, does not attempt to push interpretationbeyond the honored category of unity in variety, which is applicableto anything, and, in principle, is akin to Zeising's unity andinfinity. We wish to know what actual psychophysical functioningscorrespond to this unity in variety. Külpe's interpretation is such anattempt, but it seems clear that Weber's law cannot be applied to thedivision at the golden section. It would require of us to estimate thedifference between the long side and the short side to be equal tothat of the long side and the whole. A glance at the division showsthat such complex estimation would compare incomparable facts, sincethe short and the long parts are separated, while the long part isinclosed in the whole. Besides, such an interpretation could not applyto divisions widely variant from the golden section. 

This paper, as I said, reports but the beginnings of an investigationinto unequal division, confined as it is to results obtained from thedivision of a simple horizontal line, and to variations introduced ashints towards interpretation. The tests were made in a partiallydarkened room. The apparatus rested on a table of ordinary height, thepart exposed to the subject consisting of an upright screen, 45 cm. High by 61 cm. Broad, covered with black cardboard, approximately inthe center of which was a horizontal opening of considerable size, backed by opal glass. Between the glass and the cardboard, flush withthe edges of the opening so that no stray light could get through, acardboard slide was inserted from behind, into which was cut theexposed figure. A covered electric light illuminated the figure with ayellowish-white light, so that all the subject saw, besides a dimoutline of the apparatus and the walls of the room, was theilluminated figure. An upright strip of steel, 1½ mm. Wide, movable ineither direction horizontally by means of strings, and controlled bythe subject, who sat about four feet in front of the table, dividedthe horizontal line at any point. On the line, of course, thisappeared as a movable dot. The line itself was arbitrarily made 160mm. Long, and 1½ mm. Wide. The subject was asked to divide the lineunequally at the most pleasing place, moving the divider from one endslowly to the other, far enough to pass outside any pleasing range, or, perhaps, quite off the line; then, having seen the divider at allpoints of the line, he moved it back to that position which appealedto him as most pleasing. Record having been made of this, by means ofa millimeter scale, the subject, without again going off the line, moved to the pleasing position on the other side of the center. Hethen moved the divider wholly off the line, and made two morejudgments, beginning his movement from the other end of the line. These four judgments usually sufficed for the simple line for oneexperiment. In the course of the experimentation each of nine subjectsgave thirty-six such judgments on either side the center, orseventy-two in all. 

In Fig. 1, I have represented graphically the results of thesejudgments. The letters at the left, with the exception of _X_, markthe subjects. Beginning with the most extreme judgments on either sidethe center, I have erected modes to represent the number of judgmentsmade within each ensuing five millimeters, the number in each casebeing denoted by the figure at the top of the mode. The two verticaldot-and-dash lines represent the means of the several averages of allthe subjects, or the total averages. The short lines, dropped fromeach of the horizontals, mark the individual averages of the divisionseither side the center, and at _X_ these have been concentrated intoone line. Subject _E_ obviously shows two pretty distinct fields ofchoice, so that it would have been inaccurate to condense them allinto one average. I have therefore given two on each side the center, in each case subsuming the judgments represented by the four end modesunder one average. In all, sixty judgments were made by _E_ on eachhalf the line. Letter _E¹_ represents the first thirty-six; _E²_ thefull number. A comparison of the two shows how easily averages shift;how suddenly judgments may concentrate in one region after having beenfor months fairly uniformly distributed. The introduction of one moresubject might have varied the total averages by several points. TableI. Shows the various averages and mean variations in tabular form. 

TABLE I. Left. Right. Div. M. V. Div. M. V. _A_ 54 2. 6 50 3. 4 _B_ 46 4. 5 49 5. 7 _C_ 75 1. 8 71 1. 6 _D_ 62 4. 4 56 4. 1 _E¹_ 57 10. 7 60 8. 7 _F_ 69 2. 6 69 1. 6 _G_ 65 3. 7 64 2. 7 _H_ 72 3. 8 67 2. 1 _J_ 46 1. 9 48 1. 3 -- --- -- ---Total 60 3. 9 59 3. 5

Golden Section = 61. 1. 

 ¹These are _E_'s general averages on 36 judgments. Fig. 1, however, represents two averages on each side the center, for which the figures are, on the left, 43 with M. V. 3. 6; and 66 with M. V. 5. 3. On the right, 49, M. V. 3. 1; and 67, M. V. 2. 7. For the full sixty judgments, his total average was 63 on the left, and 65 on the right, with mean variations of 9. 8 and 7. 1 respectively. The four that _E²_ in Fig. 1 shows graphically were, for the left, 43 with M. V. 3. 6; and 68, M. V. 5. 1. On the right, 49, M. V. 3. 1; and 69, M. V. 3. 4. 

[Illustration: FIG. 1. ]

Results such as are given in Fig. 1, appear to warrant the criticismof former experimentation. Starting with the golden section, we findthe two lines representing the total averages running surprisinglyclose to it. This line, however, out of a possible eighteen chances, only twice (subjects _D_ and _G_) falls wholly within the moderepresenting the maximum number of judgments of any single subject. Insix cases (_C_ twice, _F_, _H_, _J_ twice) it falls wholly without anymode whatever; and in seven (_A_, _B_ twice, _E_, _F_, _G_, _H_)within modes very near the minimum. Glancing for a moment at theindividual averages, we see that none coincides with the total(although _D_ is very near), and that out of eighteen, only four (_D_twice, _G_ twice) come within five millimeters of the general average, while eight (_B_, _C_, _J_ twice each, _F_, _H_) lie between ten andfifteen millimeters away. The two total averages (although near thegolden section), are thus chiefly conspicuous in showing those regionsof the line that were avoided as not beautiful. Within a range ofninety millimeters, divided into eighteen sections of five millimeterseach, there are ten such sections (50 mm. ) each of which representsthe maximum of some one subject. The range of maximum judgments isthus about one third the whole line. From such wide limits it is, Ithink, a methodological error to pick out some single point, andmaintain that any explanation whatever of the divisions there madeinterprets adequately our pleasure in unequal division. Can, aboveall, the golden section, which in only two cases (_D_, _G_) fallswithin the maximum mode; in five (_A_, _C_, _F_, _J_ twice) entirelyoutside all modes, and in no single instance within the maximum onboth sides the center--can this seriously play the role of ęstheticnorm?

I may state here, briefly, the results of several sets of judgments onlines of the same length as the first but wider, and on other lines ofthe same width but shorter. There were not enough judgments in eithercase to make an exact comparison of averages valuable, but in threesuccessively shorter lines, only one subject out of eight varied in aconstant direction, making his divisions, as the line grew shorter, absolutely nearer the ends. He himself felt, in fact, that he keptabout the same absolute position on the line, regardless of thesuccessive shortenings, made by covering up the ends. This I found tobe practically true, and it accounts for the increasing variationtoward the ends. Further, with all the subjects but one, two out ofthree pairs of averages (one pair for each length of line) bore thesame relative positions to the center as in the normal line. That is, if the average was nearer the center on the left than on the right, then the same held true for the smaller lines. Not only this. With oneexception, the positions of the averages of the various subjects, whenconsidered relatively to one another, stood the same in the shorterlines, in two cases out of three. In short, not only did the pair ofaverages of each subject on each of the shorter lines retain the samerelative positions as in the normal line, but the zone of preferenceof any subject bore the same relation to that of any other. Suchapproximations are near enough, perhaps, to warrant the statement thatthe absolute length of line makes no appreciable difference in theęsthetic judgment. In the wider lines the agreement of the judgmentswith those of the normal line was, as might be expected, still closer. In these tests only six subjects were used. As in the former case, however, _E_ was here the exception, his averages being appreciablynearer the center than in the original line. But his judgments of thisline, taken during the same period, were so much on the central tackthat a comparison of them with those of the wider lines shows veryclose similarity. The following table will show how _E_'s judgmentsvaried constantly towards the center:

 AVERAGE. L. R. 1. Twenty-one judgments (11 on L. And 10 on R. ) during experimentation on _I¹, I²_, etc. , but not on same days. 64 65

 2. Twenty at different times, but immediately before judging on _I¹, I²_, etc. 69 71

 3. Eighteen similar judgments, but immediately after judging on _I¹, I²_, etc. 72 71

 4. Twelve taken after all experimentation with _I¹_, _I²_, etc. , had ceased. 71 69

The measurements are always from the ends of the line. It looks as ifthe judgments in (3) were pushed further to the center by beingimmediately preceded by those on the shorter and the wider lines, butthose in (1) and (2) differ markedly, and yet were under no suchinfluences. 

From the work on the simple line, with its variations in width andlength, these conclusions seem to me of interest. (1) The recordsoffer no one division that can be validly taken to represent 'the mostpleasing proportion' and from which interpretation may issue. (2) Withone exception (_E_) the subjects, while differing widely from oneanother in elasticity of judgment, confined themselves severally topretty constant regions of choice, which hold, relatively, fordifferent lengths and widths of line. (3) Towards the extremitiesjudgments seldom stray beyond a point that would divide the line intofourths, but they approach the center very closely. Most of thesubjects, however, found a _slight_ remove from the centerdisagreeable. (4) Introspectively the subjects were ordinarily awareof a range within which judgments might give equal pleasure, althougha slight disturbance of any particular judgment would usually berecognized as a departure from the point of maximum pleasingness. Thisfeeling of potential elasticity of judgment, combined with that ofcertainty in regard to any particular instance, demands--when theother results are also kept in mind--an interpretative theory to takeaccount of every judgment, and forbids it to seize on an average asthe basis of explanation for judgments that persist in maintainingtheir ęsthetic autonomy. 

I shall now proceed to the interpretative part of the paper. Bilateralsymmetry has long been recognized as a primary principle in ęstheticcomposition. We inveterately seek to arrange the elements of a figureso as to secure, horizontally, on either side of a central point ofreference, an objective equivalence of lines and masses. At oneextreme this may be the rigid mathematical symmetry of geometricallysimilar halves; at the other, an intricate system of compensations inwhich size on one side is balanced by distance on the other, elaboration of design by mass, and so on. Physiologically speaking, there is here a corresponding equality of muscular innervations, asetting free of bilaterally equal organic energies. Introspection willlocalize the basis of these in seemingly equal eye movements, in astrain of the head from side to side, as one half the field isregarded, or the other, and in the tendency of one half the bodytowards a massed horizontal movement, which is nevertheless held incheck by a similar impulse, on the part of the other half, in theopposite direction, so that equilibrium results. The psychicaccompaniment is a feeling of balance; the mind is ęstheticallysatisfied, at rest. And through whatever bewildering variety ofelements in the figure, it is this simple bilateral equivalence thatbrings us to ęsthetic rest. If, however, the symmetry is not good, ifwe find a gap in design where we expected a filling, the accustomedequilibrium of the organism does not result; psychically there is lackof balance, and the object is ęsthetically painful. We seem to have, then, in symmetry, three aspects. First, the objective quantitativeequality of sides; second, a corresponding equivalence of bilaterallydisposed organic energies, brought into equilibrium because acting inopposite directions; third, a feeling of balance, which is, insymmetry, our ęsthetic satisfaction. 

It would be possible, as I have intimated, to arrange a series ofsymmetrical figures in which the first would show simple geometricalreduplication of one side by the other, obvious at a glance; and thelast, such a qualitative variety of compensating elements that onlypainstaking experimentation could make apparent what elements balancedothers. The second, through its more subtle exemplification of therule of quantitative equivalence, might be called a higher order ofsymmetry. Suppose now that we find given, objects which, ęstheticallypleasing, nevertheless present, on one side of a point of reference, or center of division, elements that actually have none correspondingto them on the other; where there is not, in short, _objective_bilateral equivalence, however subtly manifested, but, rather, acomplete lack of compensation, a striking asymmetry. The simplest, most convincing case of this is the horizontal straight line, unequally divided. Must we, because of the lack of objective equalityof sides, also say that the bilaterally equivalent muscularinnervations are likewise lacking, and that our pleasure consequentlydoes not arise from the feeling of balance? A new aspect ofpsychophysical ęsthetics thus presents itself. Must we invoke a newprinciple for horizontal unequal division, or is it but a subtlydisguised variation of the more familiar symmetry? And in verticalunequal division, what principle governs? A further paper will dealwith vertical division. The present paper, as I have said, offers atheory for the horizontal. 

To this end, there were introduced, along with the simple line figuresalready described, more varied ones, designed to suggestinterpretation. One whole class of figures was tried and discardedbecause the variations, being introduced at the ends of the simpleline, suggested at once the up-and-down balance of the lever about thedivision point as a fulcrum, and became, therefore, instances ofsimple symmetry. The parallel between such figures and the simple linefailed, also, in the lack of homogeneity on either side the divisionpoint in the former, so that the figure did not appear to center at, or issue from the point of division, but rather to terminate orconcentrate in the end variations. A class of figures that obviatedboth these difficulties was finally adopted and adhered to throughoutthe work. As exposed, the figures were as long as the simple line, butof varying widths. On one side, by means of horizontal parallels, thehorizontality of the original line was emphasized, while on the otherthere were introduced various patterns (fillings). Each figure wasmovable to the right or the left, behind a stationary opening 160 mm. In length, so that one side might be shortened to any desired degreeand the other at the same time lengthened, the total length remainingconstant. In this way the division point (the junction of the twosides) could be made to occupy any position on the figure. The figureswere also reversible, in order to present the variety-filling on theright or the left. 

If it were found that such a filling in one figure varied from one inanother so that it obviously presented more than the other of someclearly distinguishable element, and yielded divisions in which itoccupied constantly a shorter space than the other, then we could, theoretically, shorten the divisions at will by adding to the fillingin the one respect. If this were true it would be evident that what wedemand is an equivalence of fillings--a shorter length being madeequivalent to the longer horizontal parallels by the addition of moreof the element in which the two short fillings essentially differ. Itwould then be a fair inference that the different lengths allotted bythe various subjects to the short division of the simple line resultfrom varying degrees of substitution of the element, reduced to itssimplest terms, in which our filling varied. Unequal division wouldthus be an instance of bilateral symmetry. 

The thought is plausible. For, in regarding the short part of the linewith the long still in vision, one would be likely, from the ęsthetictendency to introduce symmetry into the arrangement of objects, to beirritated by the discrepant inequality of the two lengths, and, inorder to obtain the equality, would attribute an added significance tothe short length. If the assumption of bilateral equivalenceunderlying this is correct, then the repetition, in quantitativeterms, on one side, of what we have on the other, constitutes theunity in the horizontal disposition of ęsthetic elements; a unityreceptive to an almost infinite variety of actual visualforms--quantitative identity in qualitative diversity. If presentedmaterial resists objective symmetrical arrangement (which gives, withthe minimum expenditure of energy, the corresponding bilateralequivalence of organic energies) we obtain our organic equivalence insupplementing the weaker part by a contribution of energies for whichit presents no obvious visual, or objective, basis. From this thereresults, by reaction, an objective equivalence, for the psychiccorrelate of the additional energies freed is an attribution to theweaker part, in order to secure this feeling of balance, of some addedqualities, which at first it did not appear to have. In the case ofthe simple line the lack of objective symmetry that everywhere meetsus is represented by an unequal division. The enhanced significanceacquired by the shorter part, and its psychophysical basis, willengage us further in the introspection of the subjects, and in thefinal paragraph of the paper. In general, however, the phenomenon thatwe found in the division of the line--the variety of divisions givenby any one object, and the variations among the several subjects--iseasily accounted for by the suggested theory, for the differentsubjects merely exemplify more fixedly the shifting psychophysicalstates of any one subject. 

In all, five sets of the corrected figures were used. Only the second, however, and the fifth (chronologically speaking) appeared indubitablyto isolate one element above others, and gave uniform results. Buttime lacked to develop the fifth sufficiently to warrant positivestatement. Certain uniformities appeared, nevertheless, in all thesets, and find due mention in the ensuing discussion. The two figuresof the second set are shown in Fig. 2. Variation No. III. Shows adesign similar to that of No. II. , but with its parts set more closelytogether and offering, therefore, a greater complexity. In Table II. Are given the average divisions of the nine subjects. The total lengthof the figure was, as usual, 160 mm. Varying numbers of judgments weremade on the different subjects. 

[Illustration: FIG. 2. ]

TABLE II. 

 No. I. No. II. No. I. (reversed). No. II. (reversed). L. R. L. R. R. L. R. L. 

 A 55 0 48 0 59 0 50 0 B 59 0 44 0 63 0 52 0 C 58 0 56 0 52 0 50 0 D 60 0 56 0 60 0 55 0 E 74 59 73 65 74 60 75 67 F 61 67 60 66 65 64 62 65 G 64 64 62 68 63 64 53 67 H 76 68 75 64 66 73 67 71 J 49 0 41 0 50 0 42 0 -- -- -- -- -- -- -- -- Total. 61 64 57 65 61 65 54 67

With the complex fillings at the left, it will be seen, firstly, thatin every case the left judgment on No. III. Is less than that on No. II. With the figures reversed, the right judgments on No. III. Areless than on No. II. , with the exception of subjects _E_ and _H_. Secondly, four of the subjects only (_E_, _F_, _G_ and _H_) hadjudgments also on the side which gave the complex filling the largerspace; to _E_, _F_ and _G_, these were secondary preferences; to _H_they were always primary. Thirdly, the judgments on No. III. Are less, in spite of the fact that the larger component parts of No. II. , mightbe taken as additional weight to that side of the line, and given, therefore, the shorter space, according to the principle of the lever. 

The subjects, then, that appear not to substantiate our suggestedtheory are _E_ and _H_, who in the reversed figures give the shorterspace to the less complex filling, and _F_ and _G_, who, together with_E_ and _H_, have always secondary judgments that allot to eithercomplex filling a larger space than to the simple horizontal. Consider, first, subjects _E_ and _H_. For each, the difference indivision of II. And III. Is in any case very slight. Further, subject_E_, in judgments where the complex filling _exceeds_ the horizontalparallels in length, still gives the more complex of the two fillingsmarkedly the shorter space, showing, apparently, that its additionalcomplexity works there in accord with the theory. There was, accordingto his introspection, another principle at work. As a figure, heemphatically preferred II. To III. The filling of II. Made up, hefound, by its greater interest, for lack of length. He here secured abalance, in which the interest of the complex material compensated forthe greater _extent_ of the simpler horizontals. This accounts for itssmall variation from III. , and even for its occupying the smallerspace. But in judgments giving the two complex fillings the largerspace, the more interesting material _exceeded_ in extent the lessinteresting. In such divisions the balance was no longer uppermost inmind, but the desire to get as much as possible of the interestingfilling. To this end the horizontal parallels were shortened as far asthey could be without becoming insignificant. But unless some elementof balance were there (although not present to introspection) eachcomplex filling, when up for judgment, would have been pushed to thesame limit. It, therefore, does seem, in cases where the complexfillings occupied a larger space than the horizontals, that thesubject, not trying consciously to secure a balance of _interests_, was influenced more purely by the factor of complexity, and that hisjudgments lend support to our theory. 

Subject H was the only subject who consistently _preferred_ to haveall complex fillings occupy the larger space. Introspection invariablyrevealed the same principle of procedure--he strove to get as much ofthe interesting material as he could. He thought, therefore, that inevery case he moved the complex filling to that limit of the pleasingrange that he found on the simple line, which would yield him most ofthe filling. Balance did not appear prominent in his introspection. Aglance, however, at the results shows that his introspection iscontradicted. For he maintains approximately the same division on theright in all the figures, whether reversed or not, and similarly onthe left. The average on the right for all four is 67; on the left itis 74. Comparing these with the averages on the simple line, we seethat the right averages coincide exactly, while the left but slightlydiffer. I suspect, indeed, that the fillings did not mean much to _H_, except that they were 'interesting' or 'uninteresting'; that asidefrom this he was really abstracting from the filling and making thesame judgments that he would make on the simple line. Since he wascontinually aware that they fell within the 'pleasing range' on thesimple line, this conclusion is the more plausible. 

Perhaps these remarks account for the respective uniformities of thejudgments of _E_ and _H_, and their departure from the tendency of theother subjects to give the more complex filling constantly the shorterspace. But subjects _F_ and _G_ also had judgments (secondary withboth of them) giving to the complex filling a larger extent than tothe parallels. With them one of two principles, I think, applies: Thejudgments are either instances of abstraction from the filling, aswith _H_, or one of simpler gravity or vertical balance, asdistinguished from the horizontal equivalence which I conceive to beat the basis of the other divisions. With _F_ it is likely to be thelatter, since the divisions of the figures under discussion do notapproach very closely those of the simple line, and becauseintrospectively he found that the divisions giving the complex thelarger space were 'balance' divisions, while the others weredetermined with 'reference to the character of the fillings. ' From _G_I had no introspection, and the approximation of his judgments tothose he gave for the simple line make it probable that with him thechanges in the character of the filling had little significance. Theaverage of his judgments in which the complex filling held the greaterspace is 66, while the averages on the simple line were 65 on theleft, and 64 on the right. And, in general, abstraction from fillingwas easy, and to be guarded against. Subject _C_, in the course of thework, confessed to it, quite unsolicited, and corrected himself bygiving thenceforth _all_ complex fillings much smaller space thanbefore. Two others noticed that it was particularly hard not toabstract. Further, none of the four subjects mentioned (with thatpossible exception of _E_) showed a sensitiveness similar to that ofthe other five. 

With the exception of _H_, and in accord with the constant practice ofthe other five, these subjects, too, occasionally found no pleasingdivision in which the complex filling preponderated in length over thehorizontals. It was uniformly true, furthermore, in every variationintroduced in the course of the investigation, involving a complex anda simple filling, that all the nine subjects but _H_ _preferred_ thecomplex in the shorter space; that five refused any divisions offeringit in the larger space; that these five showed more sensitiveness todifferences in the character of fillings; and that with one exception(_C_) the divisions of the simple line which these subjects gave werenearer the ends than those of the others. It surely seems plausiblethat those most endowed with ęsthetic sensitiveness would find adivision near the center more unequal than one nearer the end; for oneside only slightly shorter than the other would at once seem to meanthe same thing to them, and yet, because of the obvious difference inlength, be something markedly different, and they would thereforedemand a part short enough to give them sharp qualitative difference, with, however, in some way, quantitative equivalence. When the shortpart is too long, it is overcharged with significance, it strives tobe two things at once and yet neither in its fulness. 

We thus return to the simple line. I have considered a series ofjudgments on it, and a series on two different figures, varying in thedegree of complexity presented, in one of their fillings. It remainsvery briefly to see if the introspection on the simple line furnishesfurther warrant for carrying the complexities over into the simpleline and so giving additional validity to the outlined theory ofsubstitution. The following phrases are from introspective notes. 

_A_. Sweep wanted over long part. More attention to short. Significance of whole in short. Certainly a concentration of interestin the short. Short is efficacious. Long means rest; short is thecenter of things. Long, an effortless activity; short, a morestrenuous activity. When complex fillings are introduced, subject ishelped out; does not have to put so much into the short division. Insimple line, subject _introduces_ the concentration. In complexfigures the concentration is objectified. In _equal_ division subjecthas little to do with it; the _unequal_ depends on the subject--itcalls for appreciation. Center of references is the division point, and the eye movements to right and left begin here, and here return. The line centers there. The balance is a horizontal affair. 

_B_. Center a more reposing division. Chief attention to divisionpoint, with side excursions to right and left, when refreshment ofperception is needed. The balance is horizontal and not vertical. 

_C_. A balance with variety, or without symmetry. Centers at divisionpoint and wants sweep over long part. More concentration on shortpart. Subjective activity there--an introduction of energy. Acontraction of the muscles used in active attention. Long side easier, takes care of itself, self-poised. Line centers at division point. Active with short division. Introduces activity, which is equivalentto the filling that the complex figures have; in these the introducedactivity is objectified--made graphic. 

_D_. Focal point at division point: wants the interesting things in apicture to occupy the left (when short division is also on left). Short division the more interesting and means greater complication. When the pleasing division is made, eyes move first over long and thenover short. Division point the center of real reference from whichmovements are made. 

_E_. No reference to center in making judgments; hurries over center. All portions of simple line of equal interest; but in unequal divisionthe short gets a non-apparent importance, for the line is then ascheme for the representation of materials of different interestvalues. When the division is too short, the imagination refuses togive it the proportionally greater importance that it would demand. When too long it is too near equality. In enjoying line, the divisionpoint is fixed, with shifts of attention from side to side. Anunderlying intellectual assignment of more value to short side, andthen the sense-pleasure comes; the two sides have then an equality. 

_F_. Middle vulgar, common, prosaic; unequal lively. Prefers thelively. Eyes rest on division point, moving to the end of long andthen of short. Ease, simplicity and restfulness are proper to the longpart of complex figures. Short part of simple line looks wider, brighter and more important than long. 

_G_. Unequal better than equal. Eye likes movement over long and thenover short. Subject interested only in division point. Short partgives the ęsthetic quality to the line. 

_H_. Center not wanted. Division point the center of interest. (Nofurther noteworthy introspection from _H_, but concerning complexfigures he said that he wanted simple or the compact on the short, andthe interesting on the long. )

These introspective notes were given at different times, and anyrepetitions serve only to show constancy. The subjects were usuallyvery certain of their introspection. In general it appears to me towarrant these three statements: (1) That the center of interest is thedivision point, whence eye-movements, or innervations involving, perhaps, the whole motor system, are made to either side. (2) Thatthere is some sort of balance or equivalence obtained (a bilateralsymmetry), which is not, however, a vertical balance--that is, one ofweights pulling downwards, according to the principle of the lever. All the subjects repudiated the suggestion of vertical balance. (3)That the long side means ease and simplicity, and representsgraphically exactly what it means; that the short side means greaterintensity, concentration, or complexity, and that this is substitutedby the subject; the short division, unlike the long, means somethingthat it does not graphically represent. 

So much for the relation between what is objectively given and thesignificance subjectively attributed to it. There remains still thetranslation into psychophysical terms. The results on the complexfigures (showing that a division may be shortened by making theinnervations on that side increasingly more involved) lendplausibility to the interpretation that the additional significanceis, in visual terms, a greater intricacy or difficulty ofeye-movement, actual or reproduced; or, in more general terms, agreater tension of the entire motor system. In such figures thepsychophysical conditions for our pleasure in the unequal division ofthe simple horizontal line are merely graphically symbolized, notnecessarily duplicated. On page 553 I roughly suggested what occurs inregarding the unequally divided line. More exactly, this: the longsection of the line gives a free sweep of the eyes from the divisionpoint, the center, to the end; or again, a free innervation of themotor system. The sweep the subject makes sure of. Then, with that asstandard, the ęsthetic impulse is to secure an equal and similarmovement, from the center, in the opposite direction. It is checked, however, by the end point of the short side. The result is theinnervation of antagonistic muscles, by which the impression isintensified. For any given subject, then, the pleasing unequaldivision is at that point which causes quantitatively equalphysiological discharges, consisting of the simple movement, on onehand, and, on the other, the same kind of movement, compounded withthe additional innervation of the antagonists resulting from theresistance of the end point. Since, when the characteristic movementsare being made for one side, the other is always in simultaneousvision, the sweep receives, by contrast, further accentuation, and theinnervation of antagonists doubtless begins as soon as movement on theshort side is begun. The whole of the short movement is, therefore, really a resultant of the tendency to sweep and this necessaryinnervation of antagonists. The correlate of the equivalentinnervations is equal sensations of energy of movement coming from thetwo sides. Hence the feeling of balance. Hence (from the lack ofunimpeded movement on the short side) the feeling there of'intensity, ' or 'concentration, ' or 'greater significance. ' Hence, too, the 'ease, ' the 'simplicity, ' the 'placidity' of the long side. 

As in traditional symmetry, the element of unity or identity, inunequal division, is a repetition, in quantitative terms, on one side, of what is given on the other. In the simple line the _equal_ divisiongives us obviously exact objective repetition, so that thepsychophysical correlates are more easily inferred, while the_unequal_ offers apparently no compensation. But the psychophysicalcontribution of energies is not gratuitous. The function of theincrement of length on one side, which in the centrally divided linemakes the divisions equal, is assumed in unequal division by the endpoint of the short side; the uniform motor innervations in the formerbecome, in the latter, the additional innervation of antagonists, which gives the equality. The two are separated only in degree. Thelatter may truly be called, however, a symmetry of a higher order, because objectively the disposition of its elements is not graphicallyobvious, and psychophysically, the quantitative unity is attainedthrough a greater variety of processes. Thus, in complex works of art, what at first appears to be an unsymmetrical composition, is, ifbeautiful, only a subtle symmetry. There is present, of course, anarithmetically unequal division of horizontal extent, aside from thefilling. But our pleasure in this, _without_ filling, has been seen tobe also a pleasure in symmetry. We have, then, the symmetry of equallydivided extents and of unequally divided extents. They have in commonbilateral equivalence of psychophysical processes; the nature of thesediffers. In both the principle of unity is the same. The varietythrough which it works is different. 

 * * * * *

 STUDIES IN ANIMAL PSYCHOLOGY. 

 * * * * *

HABIT FORMATION IN THE CRAWFISH CAMBARUS AFFINIS. [1]

BY ROBERT M. YERKES AND GURRY E. HUGGINS. 

 [1] See also Yerkes, Robert: 'Habit-Formation in the Green Crab, _Carcinus Granulalus_, ' _Biological Bulletin_, Vol. III. , 1902, pp. 241-244. 

This paper is an account of some experiments made for the purpose oftesting the ability of the crawfish to profit by experience. It iswell known that most vertebrates are able to learn, but of theinvertebrates there are several classes which have not as yet beentested. 

The only experimental study of habit formation in a crustacean whichwe have found is that of Albrecht Bethe[2] on the crab, _Carcinusmaenas_. In his excellent paper on the structure of the nervous systemof _Carcinus_ Bethe calls attention to a few experiments which he madeto determine, as he puts it, whether the crab possesses psychicprocesses. The following are the observations made by him. ExperimentI. A crab was placed in a basin which contained in its darkest corneran _Eledone_ (a Cephalopod). The crab at once moved into the darkregion because of its instinct to hide, and was seized by the_Eledone_ and drawn under its mantle. The experimenter then quicklyfreed the crab from its enemy and returned it to the other end of thebasin. But again the crab returned to the dark and was seized. Thiswas repeated with one animal five times and with another six timeswithout the least evidence that the crabs profited by theirexperiences with the _Eledone_. Experiment 2. Crabs in an aquariumwere baited with meat. The experimenter held his hand above the foodand each time the hungry crab seized it he caught the animal andmaltreated it, thus trying to teach the crabs that meat meant danger. But as in the previous experiment several repetitions of theexperience failed to teach the crabs that the hand should be avoided. From these observations Bethe concludes that _Carcinus_ has no'psychic qualities' (_i. E. _, is unable to profit by experience), butis a reflex machine. 

 [2] Bethe, Albrecht: 'Das Centralnervensystem von _Carcinus maenas_, ' II. Theil. , _Arch. F. Mikr. Anat. _, Bd. 51, 1898, S. 447. 

Bethe's first test is unsatisfactory because the crabs have a strongtendency to hide from the experimenter in the darkest corner. Hence, if an association was formed, there would necessarily be a conflict ofimpulses, and the region in which the animal would remain would dependupon the relative strengths of its fear of the experimenter and of the_Eledone_. This objection is not so weighty, however, as is that whichmust obviously be made to the number of observations upon which theconclusions are based. Five or even twenty-five repetitions of such anexperiment would be an inadequate basis for the statements made byBethe. At least a hundred trials should have been made. The sameobjection holds in case of the second experiment. In all probabilityBethe's statements were made in the light of long and closeobservation of the life habits of _Carcinus_; we do not wish, therefore, to deny the value of his observations, but before acceptinghis conclusions it is our purpose to make a more thorough test of theability of crustaceans to learn. 

[Illustration: FIG. 1. Ground Plan of Labyrinth. _T_, triangularcompartment from which animal was started; _P_, partition at exit;_G_, glass plate closing one exit passage. Scale 1/6. ]

For determining whether the crawfish is able to learn a simple form ofthe labyrinth method was employed. A wooden box (Fig. 1) 35 cm. Long, 24 cm. Wide and 15 cm. Deep, with one end open, and at the other enda triangular compartment which communicated with the main portion ofthe box by an opening 5 cm. Wide, served as an experiment box. At theopen end of this box a partition (_P_) 6 cm. Long divided the openinginto two passages of equal width. Either of these passages could beclosed with a glass plate (_G_), and the subject thus forced to escapefrom the box by the choice of a certain passage. This box, during theexperiments, was placed in the aquarium in which the animals lived. Inorder to facilitate the movement of the crawfish toward the water, theopen end was placed on a level with the water in the aquarium, and theother end was raised so that the box made an angle of 6° with thehorizontal. 

Experiments were made under uniform conditions, as follows. A subjectwas taken from the aquarium and placed in a dry jar for about fiveminutes, in order to increase the desire to return to the water; itwas then put into the triangular space of the experiment box andallowed to find its way to the aquarium. Only one choice of directionwas necessary in this, namely, at the opening where one of thepassages was closed. That the animal should not be disturbed duringthe experiment the observer stood motionless immediately behind thebox. 

Before the glass plate was introduced a preliminary series of testswas made to see whether the animals had any tendency to go to one sideon account of inequality of illumination, of the action of gravity, orany other stimulus which might not be apparent to the experimenter. Three subjects were used, with the results tabulated. 

 Exit by Exit by Right Passage Left Passage. No. 1 6 4 No. 2 7 3 No. 3 3 7 16 14

Since there were more cases of exit by the right-hand passage, it wasclosed with the glass plate, and a series of experiments made todetermine whether the crawfish would learn to avoid the blockedpassage and escape to the aquarium by the most direct path. BetweenMarch 13 and April 14 each of the three animals was given sixtytrials, an average of two a day. In Table I. The results of thesetrials are arranged in groups of ten, according to the choice ofpassages at the exit. Whenever an animal moved beyond the level of thepartition (_P_) on the side of the closed passage the trial wascounted in favor of the closed passage, even though the animal turnedback before touching the glass plate and escaped by the open passage. 

TABLE I. 

HABIT FORMATION IN THE CRAWFISH. ¹

 Experiments. No. 1 No. 2 No. 3 Totals Per cent Open Closed Open Closed Open Closed Open Closed Open 1-10 8 2 5 5 2 8 15 15 50. 0 11-20 4 6 8 2 6 4 18 12 60. 0 21-30 6 3² 8 2 8 2 22 7 75. 8 31-40 9 1 8 2 8 2 25 5 83. 3 41-50 8 2 8 2 7 3 23 7 76. 6 51-60 10 0 8 2 9 1 27 3 90. 0

 TEST OF PERMANENCY OF HABIT AFTER 14 DAYS' REST. 

 61-70 6 4 8 2 8 2 22 8 73. 3 (1-10) 71-80 6 4 8 2 7 3 21 9 70. 0 (11-20)

 ¹The experiments of this table were made by F. D. Bosworth. 

 ²One trial in which the subject failed to return to the water within thirty minutes. 

In these experiments there is a gradual increase in the number ofcorrect choices (_i. E. _, choice of the 'open' passage) from 50 percent. For the first ten trials to 90 per cent. For the last ten(trials 51-60). The test of permanency, made after two weeks, showsthat the habit persisted. 

Although the observations just recorded indicate the ability of thecrawfish to learn a simple habit, it seems desirable to test thematter more carefully under somewhat different conditions. For in theexperiments described the animals were allowed to go through the boxday after day without any change in the floor over which they passed, and as it was noted that they frequently applied their antennae to thebottom of the box as they moved along, it is possible that they weremerely following a path marked by an odor or by moistness due to theprevious trips. To discover whether this was really the caseexperiments were made in which the box was thoroughly washed out aftereach trip. 

The nature of the test in the experiments now to be recorded is thesame as the preceding, but a new box was used. Fig. 2 is the floorplan and side view of this apparatus. It was 44. 5 cm. Long, 23. 5 cm. Wide and 20 cm. Deep. The partition at the exit was 8. 5 cm. In length. Instead of placing this apparatus in the aquarium, as was done in theprevious experiments, a tray containing sand and water was used toreceive the animals as they escaped from the box. The angle ofinclination was also changed to 7°. For the triangular space in whichthe animals were started in the preceding tests a rectangular box wassubstituted, and from this an opening 8 cm. Wide by 5 cm. Deep gaveaccess to the main compartment of the box. 

[Illustration: FIG. 2. Floor Plan and Side View of Labyrinth Number 2. _E_, entrance chamber from which animal was started; _C_, clothcovering _E_; _M_, mirror; _T_, tray containing sand and water; _G_, glass plate; _P_, partition; _R_, right exit passage; _L_, left exitpassage. Scale 1/8. ]

A large healthy crawfish was selected and subjected to tests in thisapparatus in series of ten experiments given in quick succession. Oneseries a day was given. After each test the floor was washed; as aresult the experiments were separated from one another by athree-minute interval, and each series occupied from thirty minutes toan hour. Table II. Gives in groups of five these series of tenobservations each. The groups, indicated by Roman numerals, run fromI. To IX. , there being, therefore, 450 experiments in all. Groups I. And II. , or the first 100 experiments, were made without having eitherof the exit passages closed, in order to see whether the animal woulddevelop a habit of going out by one side or the other. It did veryquickly, as a matter of fact, get into the habit of using the leftpassage (L. ). The last sixty experiments (Groups I. And II. ) show nota single case of escape by the right passage. The left passage was nowclosed. Group III. Gives the result. The time column (_i. E. _, thethird column of the table) gives for each series of observations theaverage time in seconds occupied by the animal in escaping from thebox. It is to be noted that the closing of the Left passage caused anincrease in the time from 30. 9 seconds for the last series of thesecond group to 90 seconds for the first series of the third group. Inthis there is unmistakable evidence of the influence of the change inconditions. The animal after a very few experiences under the newconditions began going to the Right in most cases; and after 250experiences it had ceased to make mistakes. Group VII. Indicates onlyone mistake in fifty choices. 

TABLE II. 

 HABIT FORMATION AND THE MODIFICATION OF HABITS IN THE CRAWFISH. 

 Results in Series of Ten. Avs. In Groups of 50. Series L. R. Time. L. R. L. R. Time. Group I. 1 9 1 45 Per Cent. 2 3 7 69 3 9 1 20 4 4 6 72 5 10 31 -- -- 35 15 70 30 47. 4

 II. 1 10 29 2 10 30 3 10 30 4 10 28. 8 5 10 30. 9 -- ---- 50 100 30 . . . . . . . . III. 1 4 6 90 2 2 2 8 89. 2 1 3 1 9 36. 7 1 4 2 8 51 2 5 1 9 43 2 -- -- -- 10 40 7 20 80 62 . . . . . . . . IV. 1 3 7 124 1 2 2 8 44 5 3 2 8 37 4 4 10 34 5 2 8 1 -- -- -- 9 41 11 18 82 60 . . . . . . . . V. 1 10 44 2 2 10 35 4 3 3 7 76 3 4 2 8 50 7 5 1 9 50 4 -- -- -- 6 44 20 12 88 51 . . . . . . . . VI. 1 2 8 45 2 2 10 41 5 3 1 9 41. 8 7 4 10 32. 7 7 5 10 8 -- -- -- 3 47 29 6 94 40 . . . . . . . . VII. 1 1 9 39 4 2 10 38 7 3 10 30. 7 3 4 10 42 6 5 10 48 4 -- -- -- 1 49 24 2 98 39. 5

 R. L. . . . . . . . . VIII. 1 8 2 147 1 2 9 1 26 3 8 2 49 2 4 9 1 38 2 5 9 1 41 -- -- -- 43 7 5 86 14 60. 2 . . . . . . . . IX. 1 1 9 41 2 2 8 39 1 3 10 29 4 1 9 47 5 1 9 32 1 10 90 38 -- -- -- 5 45 2

The dotted lines at the beginning of groups indicate the closed passage. 

At the beginning of Group VIII. The Right instead of the Left passagewas closed in order to test the ability of the animal to change itsnewly formed habit. As a result of this change in the conditions theanimal almost immediately began going to the Left. What is mostsignificant, however, is the fact that in the first trial after thechange it was completely confused and spent over fifteen minuteswandering about, and trying to escape by the old way (Fig. 4represents the path taken). At the end of the preceding group the timeof a trip was about 48 seconds, while for the first ten trips of GroupVIII. The time increased to 147 seconds. This remarkable increase isdue almost entirely to the great length of time of the first trip, inwhich the animal thoroughly explored the whole of the box and madepersistent efforts to get out by the Right passage as it had beenaccustomed to do. It is at the same time noteworthy that the averagetime for the second series of Group VIII. Is only 26 seconds. 

For Group IX. The conditions were again reversed, this time the Leftpassage being closed. Here the first trial was one of long and carefulexploration, but thereafter no more mistakes were made in the firstseries, and in the group of fifty tests there were only five wrongchoices. 

The fifth column, R. L. And L. R. , of Table II. Contains cases inwhich the subject started toward one side and then changed its coursebefore reaching the partition. In Group III. , for instance, when theLeft passage was closed, the subject started toward the Left seventimes, but in each case changed to the Right before reaching thepartition. This is the best evidence of the importance of vision thatthese experiments furnish. 

The first experiments on habit formation proved conclusively that thecrawfish is able to learn. The observations which have just beendescribed prove that the labyrinth habit is not merely the followingof a path by the senses of smell, taste or touch, but that othersensory data, in the absence of those mentioned, direct the animals. So far as these experiments go there appear to be at least foursensory factors of importance in the formation of a simple labyrinthhabit: the chemical sense, touch, vision and the muscle sense. Thatthe chemical sense and touch are valuable guiding senses is evidentfrom even superficial observation, and of the importance of vision andthe muscle sense we are certain from the experimental evidence athand. 

[Illustration: FIG. 3. Path taken by crawfish while being trained toavoid the left passage. Marks along the glass plate and partitionindicate contact by the antennae and chelę. ]

Of the significance of the sensations due to the 'direction ofturning' in these habits the best evidence that is furnished by thiswork is that of the following observations. In case of the tests ofTable II. The subject was, after 100 preliminary tests, trained by 250experiences to escape by the Right-hand passage. Now, in Groups III. To VII. , the subject's usual manner of getting out of the closedpassage, when by a wrong choice it happened to get into it, was todraw back on the curled abdomen, after the antennae and chelę hadtouched the glass plate, and then move the chelę slowly along theRight wall of the partition until it came to the upper end; it wouldthen walk around the partition and out by the open passage. Fig. 3represents such a course. In Group VIII. The Right passage was closed, instead of the Left as previously. The first time the animal tried toget out of the box after this change in the conditions it walkeddirectly into the Right passage. Finding this closed it at once turnedto the Right, _as it had been accustomed to do when it came in contactwith the glass plate_, and moved along the side of the box just as itdid in trying to get around the end of the partition. The path takenby the crawfish in this experiment is represented in Fig. 4. It isvery complex, for the animal wandered about more than fifteen minutesbefore escaping. 

The experiment just described to show the importance of the tendencyto turn in a certain direction was the first one of the first seriesafter the change in conditions. When given its second chance in thisseries the subject escaped directly by the Left passage in 33 seconds, and for the three following trips the time was respectively 25, 25 and30 seconds. 

Upon the experimental evidence presented we base the conclusion thatcrawfish are able to profit by experience in much the same way thatinsects do, but far more slowly. 

[Illustration: FIG. 4. Path taken by crawfish which had been trainedto avoid the Left passage, when the Right passage was closed. Showingturning to the right as in Fig. 3. ]

It was thought that a study of the way in which crawfish rightthemselves when placed upon their backs on a smooth surface mightfurnish further evidence concerning the ability of the animals toprofit by experience. 

Dearborn[3] from some observations of his concludes that there is noone method by which an individual usually rights itself, and, furthermore, that the animals cannot be trained to any one method. Hisexperiments, like Bethe's, are too few to warrant any conclusions asto the possibility of habit formation. 

 [3] Dearborn, G. V. N. : 'Notes on the Individual Psychophysiology of the Crayfish, ' _Amer. Jour. Physiol. _, Vol. 3, 1900, pp. 404-433. 

For the following experiments the subject was placed on its back on asmooth surface in the air and permitted to turn over in any way itcould. Our purpose was to determine (1) whether there was any markedtendency to turn in a certain way, (2) whether if such was not thecase a tendency could be developed by changing the conditions, and (3)how alteration in the conditions of the test would affect the turning. 

A great many records were taken, but we shall give in detail only arepresentative series. In Table III. , 557 tests made upon foursubjects have been arranged in four groups for convenience ofcomparison of the conditions at different periods of the trainingprocess. Each of these groups, if perfect, would contain 40 tests foreach of the four subjects, but as a result of accidents II. , III. , andIV. Are incomplete. 

TABLE III. 

 RE-TURNING OF CRAWFISH. 

 Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. I. 2 22. 5 77. 5 14. 6 40 3 42. 5 57. 5 2. 6 40 4 52. 8 47. 2 4. 3 38 16 44. 5 55. 5 22. 5 45 -- ---- ---- ---- --- 40. 6 59. 4 10. 8 163

 Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. II 2 28 72 50 43 3 32 68 6. 2 50 4 -- 100 6. 8 40 16 31. 3 68. 7 39. 3 42 -- ---- ---- ---- --- 22. 8 77. 2 25. 6 175

 Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. III 2 2. 5 97. 5 46. 5 40 -- -- -- -- -- 4 20 80 5. 5 40 16 41 59 15 49 -- ---- ---- ---- --- 21. 2 78. 8 22 129

 Group. Number of L. R. Time in Tests. Animal. Per cent. Seconds. IV. 2 2 98 41 50 -- -- -- -- -- 4 32. 5 67. 5 7. 3 40 -- ---- ---- ---- --- 17 83 24 90

Group I. , representing 163 tests, shows 59 per cent. To the right, with a time interval of 10. 8 seconds (_i. E. _, the time occupied inturning). Group II. Shows 77 per cent. To the right; and so throughoutthe table there is an increase in the number of returnings to theright. These figures at first sight seem to indicate the formation ofa habit, but in such case we would expect, also, a shortening of thetime of turning. It may be, however, that the animals were graduallydeveloping a tendency to turn in the easiest manner, and that at thesame time they were becoming more accustomed to the unusual positionand were no longer so strongly stimulated, when placed on their backs, to attempt to right themselves. 

All the subjects were measured and weighed in order to discoverwhether there were inequalities of the two sides of the body whichwould make it easier to turn to the one side than to the other. Thechelę were measured from the inner angle of the joint of theprotopodite to the angle of articulation with the dactylopodite. Thecarapace was measured on each side, from the anterior margin of thecephalic groove to the posterior extremity of the lateral edge. Themedian length of the carapace was taken, from the tip of the rostrumto the posterior edge, and the length of the abdomen was taken fromthis point to the edge of the telson. These measurements, togetherwith the weights of three of the subjects, are given in theaccompanying table. 

TABLE IV. 

MEASUREMENTS OF CRAWFISH. 

 Chelę. Carapace. Abdomen. Weight. Left. Right. Left. Right. Median. 

 No. 2, 9. 8 10. 0 38. 2 38. 7 47. 3 48. 1 29. 7 No. 4, 7. 7 7. 7 33. 6 33. 8 39. 4 42. 3 17. 7 No. 16, 12. 5 12. 4 37. 6 37. 6 46. 4 53. 2 36. 2

Since these measurements indicate slightly greater size on the rightit is very probable that we have in this fact an explanation of thetendency to turn to that side. 

To test the effect of a change in the conditions, No. 16 was tried ona surface slanted at an angle of 1° 12'. Upon this surface the subjectwas each time so placed that the slant would favor turning to theright. Under these conditions No. 16 gave the following results in twoseries of tests. In the first series, consisting of 46 turns, 82. 6 percent. Were to the right, and the average time for turning was 17. 4seconds; in the second series, of 41 tests, there were 97. 5 per cent, to the right, with an average time of 2. 5 seconds. We have here animmediate change in the animal's method of re-turning caused by aslight change in the conditions. The subject was now tested again ona level surface, with the result that in 49 tests only 59 per cent. Were toward the right, and the time was 15 seconds. 

SUMMARY. 

1. Experiments with crawfish prove that they are able to learn simplelabyrinth habits. They profit by experience rather slowly, from fiftyto one hundred experiences being necessary to cause a perfectassociation. 

2. In the crawfish the chief factors in the formation of such habitsare the chemical sense (probably both smell and taste), touch, sightand the muscular sensations resulting from the direction of turning. The animals are able to learn a path when the possibility of followinga scent is excluded. 

3. The ease with which a simple labyrinth habit may be modifieddepends upon the number of experiences the animal has had; the morefamiliar the animal is with the situation, the more quickly it changesits habits. If the habit is one involving the choice of one of twopassages, reversal of the conditions confuses the subject much morethe first time than in subsequent cases. 

4. Crawfish right themselves, when placed on their backs, by theeasiest method; and this is found to depend usually upon the relativeweight of the two sides of the body. When placed upon a surface whichis not level they take advantage, after a few experiences, of theinclination by turning toward the lower side. 

 * * * * *

THE INSTINCTS, HABITS, AND REACTIONS OF THE FROG. 

BY ROBERT MEARNS YERKES. 

PART I. THE ASSOCIATIVE PROCESSES OF THE GREEN FROG. 

I. SOME CHARACTERISTICS OF THE GREEN FROG. 

The common green frog, _Rana clamitans_, is greenish or brownish incolor, usually mottled with darker spots. It is much smaller than thebull frog, being from two to four inches in length ordinarily, and mayreadily be distinguished from it by the presence of prominentglandular folds on the sides of the back. In the bull frog, _Ranacatesbeana_, these folds are very small and indistinct. The green frogis found in large numbers in many of the ponds and streams of theeastern United States, and its peculiar rattling croak may be heardfrom early spring until fall. It is more active, and apparentlyquicker in its reactions, than the bull frog, but they are in manyrespects similar in their habits. Like the other water frogs it feedson small water animals, insects which chance to come within reach and, in times of famine, on its own and other species of frogs. The prey iscaptured by a sudden spring and the thrusting out of the tongue, whichis covered with a viscid secretion. Only moving objects are noticedand seized; the frog may starve to death in the presence of anabundance of food if there is no movement to attract its attention. Most green frogs can be fed in captivity by swinging pieces of meat infront of them, and those that will not take food in this way can bekept in good condition by placing meat in their mouths, for as soon asthe substance has been tasted swallowing follows. 

The animals used for these experiments were kept in the laboratoryduring the whole year in a small wooden tank. The bottom of this tankwas covered with sand and small stones, and a few plants helped topurify the water. An inch or two of water sufficed; as it was notconvenient to have a constant stream, it was changed at least everyother day. There was no difficulty whatever in keeping the animals inexcellent condition. 

Of the protective instincts of the green frog which have come to mynotice during these studies two are of special interest: Theinstinctive inhibition of movement under certain circumstances, andthe guarding against attack or attempt to escape by 'crouching' and'puffing. ' In nature the frog ordinarily jumps as soon as a strange orstartling object comes within its field of vision, but under certainconditions of excitement induced by strong stimuli it remainsperfectly quiet, as do many animals which feign death, until forced tomove. Whether this is a genuine instinctive reaction, or the result ofa sort of hypnotic condition produced by strong stimuli, I am notprepared to say. The fact that the inhibition of movement is mostfrequently noticed after strong stimulation, would seem to indicatethat it is due to the action of stimuli upon the nervous system. 

What appears to be an instinctive mode of guarding against attack andescaping an enemy, is shown whenever the frog is touched about thehead suddenly, and sometimes when strong stimuli are applied to otherparts of the body. The animal presses its head to the ground as iftrying to dive or dodge something, and inflates its body. This kind ofaction is supposed to be a method of guarding against the attack ofsnakes and other enemies which most frequently seize their prey fromthe front. It is obvious that by pressing its head to the ground thefrog tends to prevent any animal from getting it into its mouth, andin the few instants' delay thus gained it is able to jump. This isjust the movement necessary for diving, and it is probable that theaction should be interpreted in the light of that instinctive reflex. The 'puffing' also would seem to make seizure more difficult. Anotherfact which favors this interpretation is that the response is mostcommonly given to stimuli which seem to come from the front and whichfor this reason could not easily be escaped by a forward jump, whileif the stimulus is so given that it appears to be from the rear theanimal usually jumps away immediately. We have here a complexprotective reaction which may be called a forced movement. It is, sofar as one can see, very much like many reflexes, although it does notoccur quite so regularly. 

The machine-like accuracy of many of the frog's actions gives a basisfor the belief that the animal is merely an automaton. Certain it isthat one is safe in calling almost all the frog's actions reflex orinstinctive. During months of study of the reaction-time of the frog Iwas constantly impressed with the uniformity of action and surprisedat the absence of evidences of profiting by experience. In order tosupplement the casual observations on the associations of the greenfrog made in the course of reaction-time experiments, the testsdescribed in this paper were made. They do not give a complete view ofthe associative processes, but rather such a glimpse as will enable usto form some conception of the relation of the mental life of the frogto that of other animals. This paper presents the outlines of work thedetails of which I hope to give later. 

II. EXPERIMENTAL STUDY OF HABITS. 

A. The Chief Problems for which solutions were sought in the followingexperimental study were: (1) Those of associability in general, itscharacteristics, and the rapidity of learning; (2) of discrimination, including the parts played in associative processes by the differentsenses, and the delicacy of discrimination in each; (3) of themodifiability of associational reactions and general adaptation in thefrog, and (4) of the permanency of associations. 

B. Simple Associations, as studied in connection with reaction-timework, show that the green frog profits by experience very slowly ascompared with most vertebrates. The animals have individualpeculiarities in reaction which enable one in a short time torecognize any individual. To these characteristic peculiarities theystick tenaciously. One, for instance, always jumps upward whenstrongly stimulated; another has a certain corner of the tank in whichit prefers to sit. Their habits are remarkably strong and invariable, and new ones are slowly formed. While using a large reaction box Inoticed that the frogs, after having once escaped from an openingwhich could be made by pushing aside a curtain at a certain point inthe box, tended to return to that place as soon as they were again putinto the box. This appeared to be evidence of an association; but thefact that such stimuli as light and the relation of the opening to theplace at which the animals were put into the box might in themselvesbe sufficient to direct the animals to this point without the help ofany associations which had resulted from previous experience, makes itunsatisfactory. In addition to the possibility of the action being dueto specific sensory stimuli of inherent directive value, there is thechance of its being nothing more than the well-known phenomenon ofrepetition. Frogs, for some reason, tend to repeat any action whichhas not proved harmful or unpleasant. 

For the purpose of more carefully testing this kind of association, asmall box with an opening 15 cm. By 10 cm. Was arranged so that theanimal could escape from confinement in it through the upper part ofthe opening, the lower portion being closed by a plate of glass 10 cm. By 10 cm. , leaving a space 5 cm. By 10 cm. At the top. One subjectplaced in this box escaped in 5 minutes 42 seconds. After 5 minutes'rest it was given another trial, and this time got out in 2 minutes 40seconds. The times for a few subsequent trials were: Third, 1 minute22 seconds; fourth, 4 minutes 35 seconds; fifth, 2 minutes 38 seconds;sixth, 3 minutes 16 seconds. Although this seems to indicate someimprovement, later experiments served to prove that the frogs did notreadily form any associations which helped them to escape. They tendedto jump toward the opening because it was light, but they did notlearn with twenty or thirty experiences that there was a glass at thebottom to be avoided. Thinking that there might be an insufficientmotive for escape to effect the formation of an association, I triedstimulating the subject with a stick as soon as it was placed in thebox. This frightened it and caused violent struggles to escape, butinstead of shortening the time required for escape it greatlylengthened it. Here was a case in which the formation of anassociation between the appearance of the upper part of the clearspace and the satisfaction of escape from danger would have been ofvalue to the frog, yet there was no evidence of adaptation to the newconditions within a reasonably short time. There can be little doubtthat continuation of the training would have served to establish thehabit. This very clearly shows the slowness of adaptation in the frog, in contrast with the rapidity of habit formation in the cat or chick;and at the same time it lends additional weight to the statement thatinstinctive actions are all-important in the frog's life. A few thingsit is able to do with extreme accuracy and rapidity, but to this listnew reactions are not readily added. When put within the boxdescribed, an animal after having once escaped would sometimes makefor the opening as if it knew perfectly the meaning of the wholesituation, and yet the very next trial it would wander about for halfan hour vainly struggling to escape. 

A considerable number of simple experiments of this kind were triedwith results similar to those just given. The frog apparently examinesits surroundings carefully, and just when the observer thinks it hasmade itself familiar with the situation it reacts in such a way as toprove beyond doubt the absence of all adaptation. In all theseexperiments it should be said, for the benefit of any who may betrying similar work, that only animals of exceptional activity wereused. Most green frogs when placed in the experiment box either sitstill a great part of the time or jump about for only a short time. Itis very important for studies of this kind, both on account of timesaving and the obtaining of satisfactory records, to have animalswhich are full of energy and eager to escape when in confinement. Bychoosing such subjects one may pretty certainly avoid all unhealthyindividuals, and this, it seems to me, counterbalances thedisadvantage of taking animals which may be unusually quick inlearning. 

C. Complex Associations. 

1. _Labyrinth Habits_. --A more thorough investigation of theassociative processes, sensory discrimination and the permanency ofimpressions has been made by the labyrinth method. A wooden box, 72cm. Long, 28 cm. Wide and 28 cm. Deep, whose ground plan isrepresented by Fig. 1, served as the framework for a simple labyrinth. At one end was a small covered box, _A_, from which the frog wasallowed to enter the labyrinth. This entrance passage was used inorder that the animal might not be directed to either side by thedisturbance caused by placing it in the box. _E_, the entrance, marksa point at which a choice of directions was necessary. _P_ is amovable partition which could be used to close either the right or theleft passage. In the figure the right is closed, and in this case ifthe animal went to the right it had to turn back and take the leftpassage in order to get out of the box. A series of interruptedelectrical circuits, _IC_, covered the bottom of a portion of thelabyrinth; by closing the key, _K_, the circuit could be made whenevera frog rested upon any two wires of the series. When the frog happenedto get into the wrong passage the key was closed and the animalstimulated. This facilitated the experiment by forcing the animal toseek some other way of escape, and it also furnished material for anassociation. Having passed through the first open passage, which forconvenience we may know as the entrance passage, the animal had tochoose again at the exit. Here one of the passages was closed by aplate of glass (in the figure the left) and the other opened into atank containing water. The box was symmetrical and the two sides werein all respects the same except for the following variable conditions. At the entrance the partition on one side changed the appearance, asit was a piece of board which cut off the light. On either side of theentrance there were grooves for holding card-boards of any desiredcolor. The letters _R, R_ mark sides which in this case were coveredwith red; _W, W_ mark white spaces. These pieces of cardboard couldeasily be removed or shifted at any time. At the exit the glass platealone distinguished the sides, and it is not likely that the animalswere able to see it clearly. We have thus at the entrance widelydiffering appearances on the two sides, and at the exit similarity. The opening from _A_ into the large box was provided with a slide doorso that the animal could be prevented from returning to _A_ afterentering the labyrinth. The partitions and the triangular division atthe entrance extended to the top of the box, 28 cm. , so that theanimals could not readily jump over them. 

[Illustration: FIG. 1. Ground Plan of Labyrinth. _A_, small boxopening into labyrinth; _E_, entrance of labyrinth; _T_, tankcontaining water; _G_, glass plate closing one passage of exit; _P_, partition closing one passage at entrance; _IC_, interruptedelectrical circuit; _C_, cells; _K_, key in circuit; _RR_, redcardboard; _WW_, white cardboard. Scale 1/12. ]

The experiments were made in series of ten, with ten-minute intervalsbetween trials. In no case was more than one series a day taken, andwherever a day was missed the fact has been indicated in the tables. The only motive of escape from the box depended upon was the animal'sdesire to return to the water of the tank and to escape fromconfinement in the bright light of the room. The tank was one in whichthe frogs had been kept for several months so that they were familiarwith it, and it was as comfortable a habitat as could conveniently bearranged. Usually the animals moved about almost constantly until theysucceeded in getting out, but now and then one would remain inactivefor long intervals; for this reason no record of the time taken forescape was kept. On account of the great amount of time required byexperiments of this kind I have been unable to repeat this series ofexperiments _in toto_ on several animals in order to get averages, butwhat is described for a representative individual has been provednormal by test observations on other animals. There are very largeindividual differences, and it may well be that the subject of theseries of experiments herein described was above the average inability to profit by experience. But, however that may be, what isdemonstrated for one normal frog is thereby proved a racialcharacteristic, although it may be far from the mean condition. 

Before beginning training in the labyrinth, preliminary observationswere made to discover whether the animals had any tendencies to goeither to the right or to the left. When the colored cardboards wereremoved it was found that there was usually no preference for right orleft. In Table I. The results of a few preliminary trials with No. 2are presented. For these the colors were used, but a tendency to theright shows clearly. Trials 1 to 10 show choice of either the right orthe red throughout; that it was partly both is shown by trials 11 to30, for which the colors were reversed. This individual has therefore, to begin with, a tendency to the right at the entrance. At the exit itwent to the right the first time and continued so to do for severaltrials, but later it learned by failure that there was a blockedpassage as well as an open one. In the tables the records refer tochoices. It was useless to record time or to lay much stress upon thecourse taken, as it was sometimes very complicated; all that is given, therefore, is the action in reference to the passages. _Right_ inevery case refers to the choice of the open way, and _wrong_ to thechoice of the blocked passage. The paths taken improved steadily inthat they became straighter. A few representative courses are given inthis report. Usually if the animal was not disturbed a few jumpsserved to get it out of the labyrinth. 

TABLE I. 

 PRELIMINARY TRIALS WITH FROG NO. 2. 

 Trials. Red on Right. White on Left. 1 to 10 10 times to red 0

 Red on Left. White on Right. 11 to 20 4 times to red 6

 Red on Left. White on Right. 21 to 30 3 times to red 7

 To Red. To White. To Right. To Left. Totals. 17 13 23 7

This table indicates in trials 1 to 10 a strong tendency to the redcardboard. Trials 21 to 30 prove that there was also a tendency to theright. 

Training was begun with the labyrinth arranged as shown in Fig. 1, that is, with the left entrance passage and the right exit passageopen, and with red cardboard on the right (red was always on the sideto be avoided) and white on the left. Table II. Contains the resultsof 110 trials with No. 2, arranged according to right and wrong choiceat the entrance and exit. Examination of this table shows a gradualand fairly regular increase in the number of right choices from thefirst series to the last; after 100 experiences there were practicallyno mistakes. 

With another subject, No. _6a_, the results of Table III. Wereobtained. In this instance the habit formed more slowly and to allappearances less perfectly. Toward the end of the second week of work_6a_ showed signs of sickness, and it died within a few weeks, so I donot feel that the experiments with it are entirely trustworthy. Duringthe experiments it looked as if the animal would get a perfectlyformed habit very quickly, but when it came to the summing up ofresults it was obvious that there had been little improvement. 

[Illustration: FIG. 2. Labyrinth as arranged for experiments. _E_, entrance; _R, R_, regions covered with red; _W, W_, regions coveredwith white. The tracing represents the path taken by No. 2 on thesixth trial. Dots mark jumps. ]

TABLE II. 

 LABYRINTH HABIT. FROG NO. 2. 

 Entrance. Exit. Remarks. Trials. Right. Wrong. Right. Wrong. 1- 10 1 9 4 6 One day rest. 11- 20 2 8 5 5 21- 30 4 6 7 3 31- 40 5 5 6 4 41- 50 5 5 6 2 (17) (33) (30) (20) 51- 60 9 1 8 2 61- 70 6 4 10 0 71- 80 7 3 9 1 81- 90 9 1 8 2 91-100 10(50) 0(10) 10(52) 0( 8) --- --- --- --- 67 43 82 28

Other animals which were used gave results so similar to those forfrog No. 2 that I feel justified in presenting the latter asrepresentative of the rapidity with which the green frog profits byexperience. 

TABLE III. 

 LABYRINTH HABIT. FROG NO. _6a_. 

 Entrance. Exit. Remarks. Trials Right. Wrong. Right. Wrong. 1- 10 6 4 5 5 One day rest. 11- 20 7 3 4 6 21- 30 2 8 1 9 31- 40 6 4 1 9 41- 50 7 3 8 2 (28) (22) (19) (31) 51- 60 5 5 7 3 61- 70 6 4 4 6 71- 80 4 6 3 7 One day rest. 81- 90 5 5 7 3 91-100 10(30) 0(20) 8(29) 2(21) ---- ---- ---- ---- (58) (44) (48) (52)

 Preliminary Trials. 

 Red on Left Partition at Exit on Right 1- 5 5 times to Red 4 times to Partition. 

 Red on Right Partition at Exit on Left 6-10 3 times to Red 5 times to Partition. 

2. _Rapidity of Habit Formation_. --As compared with other vertebrateswhose rapidity of habit formation is known, the frog learns slowly. Experimental studies on the dog, cat, mouse, chick and monkey furnishexcellent evidence of the ability of these animals to profit quicklyby experience through the adapting of their actions to new conditions. They all show marked improvement after a few trials, and after fromten to thirty most of them have acquired perfect habits. But thecomparison of the frog with animals which are structurally moresimilar to it is of greater interest and value, and we have to inquireconcerning the relation of habit formation in the frog to that offishes and reptiles. Few experimental studies with these animals havebeen made, and the material for comparison is therefore veryunsatisfactory. E. L. Thorndike[1] has demonstrated the ability offishes to learn a labyrinth path. In his report no statement of thetime required for the formation of habit is made, but from personalobservation I feel safe in saying that they did not learn more quicklythan did the frogs of these experiments. Norman Triplett[2] statesthat the perch learns to avoid a glass partition in its aquarium afterrepeatedly bumping against it. Triplett repeated Moebius' famousexperiment, and found that after a half hour's training three times aweek for about a month, the perch would not attempt to capture minnowswhich during the training periods had been placed in the aquarium withthe perch, but separated from them by a glass partition. Triplett'sobservations disprove the often repeated statement that fishes do nothave any associative processes, and at the same time they show thatthe perch, at least, learns rapidly--not so rapidly, it is true, asmost animals, but more so in all probability than the amphibia. 

 [1] Thorndike, Edward: 'A Note on the Psychology of Fishes, ' _American Naturalist_. 1899, Vol. XXXIII. , pp. 923-925. 

 [2] Triplett, Norman: 'The Educability of the Perch, ' _Amer. Jour. Psy. _, 1901, Vol. XII. , pp. 354-360. 

The only quantitative study of the associative processes of reptilesavailable is some work of mine on the formation of habits in theturtle. [3] In the light of that study I can say that the turtle learnsmuch more rapidly than do fishes or frogs. Further observations onother species of turtles, as yet unpublished, confirm this conclusion. 

 [3] Yerkes, Robert Mearns: 'The Formation of Habits in the Turtle, ' _Popular Science Monthly_, 1901, Vol. LVIII. , pp. 519-535. 

For the frog it is necessary to measure and calculate the improvementin order to detect it at first, while with the turtle or chick themost casual observer cannot fail to note the change after a fewtrials. In connection with the quickness of the formation ofassociations it is of interest to inquire concerning their permanency. Do animals which learn slowly retain associations longer? is aquestion to which no answer can as yet be given, but experiments mayreadily be made to settle the matter. I have tested the frog forpermanency, and also the turtle, but have insufficient data forcomparison. 

3. _Sensory Data Contributing to the Associations_. --Among the mostimportant of the sensory data concerned in the labyrinth habit are thevisual impressions received from the different colored walls, theslight differences in brightness of illumination due to shadows fromthe partitions and the contrast in form of the two sides of thelabyrinth resulting from the use of the partitions, and the muscularsensations dependent upon the direction of turning. The experimentsproved beyond question that vision and the direction of turning werethe all-important factors in the establishment of the habit. At firstit seemed as if the direction of turning was the chief determinant, and only by experimenting with colors under other conditions was Iable to satisfy myself that the animals did notice differences in theappearance of their surroundings and act accordingly. In Table IV. Some results bearing on this point have been arranged. To begin with, the habit of going to the left when the red was on the right at theentrance had been established; then, in order to see whether thecolors influenced the choice, I reversed the conditions, placing thered on the left, that is, on the open-passage side. The results astabulated in the upper part of Table IV. Show that the animals werevery much confused by the reversal; at the entrance where there wereseveral guiding factors besides the colors there were 50 per cent. Ofmistakes, while at the exit where there were fewer differences bywhich the animal could be directed it failed every time. This work wasnot continued long enough to break up the old habit and replace it bya new one, because I wished to make use of the habit already formedfor further experiments, and also because the animals remained so longin the labyrinth trying to find their way out that there was constantdanger of losing them from too prolonged exposure to the dry air. 

TABLE IV. 

 INFLUENCE OF CHANCES OF CONDITIONS. FROG NO. 2. 

 Habit perfectly formed of going to Left (avoiding Red) at entrance and to Right at exit. Conditions now reversed. Red on Left. Partition at Exit on Right. 

 Trials. Entrance. Exit. Remarks. Right. Wrong. Right. Wrong. 1- 5 3 2 0 5 6-10 2 3 0 5

 Discontinued because animal remained so long in labyrinth that there was danger of injuring it for further work. This shows that the habit once formed is hard to change. 

 Given 20 trials with conditions as at first in order to establish habit again. 

 1-10 9 1 8 2 11-20 10 0 9 1

 Colors reversed, no other change. To test influence of colors. 

 1-10 6 4 10 0

 INFLUENCE OF DISTURBANCE WHEN ANIMAL IS ENTERING BOX. 

 No Disturbance. Animal Touched. 

 To Red (Right). To White (Left). To Red. To White. 2 8 5 5

 This was after the tendency to go to the Left at the entrance had been established. 

These experiments to test the effect of changing colors are also ofinterest in that they show in a remarkable way the influence of thedirection of turning. The animal after succeeding in getting aroundthe first part of the labyrinth failed entirely to escape at the exit. Here it should have turned to the left, instead of the right as it wasaccustomed to, but it persisted in turning to the right. Fig. 3represents approximately the path taken in the first trial; it showsthe way in which the animal persisted in trying to get out on theright. From this it is clear that both vision and the complexsensations of turning are important. 

[Illustration: FIG. 3. Labyrinth with Conditions the Reverse of theUsual. (Compare with FIG. 2. ) The colors as well as the partitionshave been shifted. The path is, approximately, that taken by No. 2 inthe first trial after the reversal of conditions. ]

The latter part of Table IV. Presents further evidence in favor ofvision. For these tests the colors alone were reversed. Previous tothe change the animal had been making no mistakes whatever, thereafterthere were four mistakes at the entrance and none at the exit. Later, another experiment under the same conditions was made with the sameanimal, No. 2, with still more pronounced results. In this case theanimal went to the white, that is, in this instance, into the blindalley, and failed to get out; several times it jumped over to the leftside (the open-passage side) of the box but each time it seemed to beattracted back to the white or repelled by the red, more probably thelatter, as the animal had been trained for weeks to avoid the red. Concerning the delicacy of visual discrimination I hope to havesomething to present in a later paper. 

The tactual stimuli given by contact with the series of wires used forthe electrical stimulus also served to guide the frogs. They wereaccustomed to receive an electrical shock whenever they touched thewires on the blocked side of the entrance, hence on this side thetactual stimulus was the signal for a painful electrical stimulus. When the animal chose the open passage it received the tactualstimulus just the same, but no shock followed. After a few days'experimentation it was noted that No. 2 frequently stopped as soon asit touched the wires, whether on the open or the closed side. If onthe closed side, it would usually turn almost immediately and byretracing its path escape by the open passage; if on the open side, itwould sometimes turn about, but instead of going back over the courseit had just taken, as on the other side, it would sit still for a fewseconds, as if taking in the surroundings, then turn again and go onits way to the exit. This whole reaction pointed to the formation ofan association between the peculiar tactual sensation and the painfulshock which frequently followed it. Whenever the tactual stimulus cameit was sufficient to check the animal in its course until othersensory data determined the next move. When the wrong passage had beenchosen the visual data gotten from the appearance of the partitionwhich blocked the path and other characteristics of this side of thelabyrinth determined that the organism should respond by turning back. When, on the other hand, the open passage had been selected, amoment's halt sufficed to give sensory data which determined thecontinuation of the forward movement. Although this reaction did notoccur in more than one tenth of the trials, it was so definite in itsphases as to warrant the statements here made. Fig. 4 gives the pathtaken by No. 2 in its 123d trial. In this experiment both choices werecorrectly made, but when the frog touched the wires on the open sideit stopped short and wheeled around; after a moment it turned towardthe exit again, but only to reverse its position a second time. Soonit turned to the exit again, and this time started forward, taking adirect course to the tank. The usual course for animals which hadthoroughly learned the way to the tank is that chosen in Fig. 5. 

[Illustration: FIG. 4. Path of No. 2 for 123d Trial. Showing theresponse to the tactual stimulus from wires. ]

An interesting instance of the repetition of a reaction occurred inthese experiments. A frog would sometimes, when it was first placed inthe box, by a strong jump get up to the edge; it seldom jumped over, but instead caught hold of the edge and balanced itself there untilexhaustion caused it to fall or until it was taken away. Why an animalshould repeat an action of the nature of this is not clear, but almostinvariably the second trial resulted in the same kind of reaction. Theanimal would stop at the same point in the box at which it hadpreviously jumped, and if it did not jump, it would look up as ifpreparing to do so. Even after a frog had learned the way to the tanksuch an action as this would now and then occur, and almost alwaysthere would follow repetition in the manner described. 

[Illustration: FIG. 5. Path Usually Taken by Animal HavingPerfectly-formed Habit. ]

4. _The Effect of Fear upon Habit Formation. _--A certain amount ofexcitement undoubtedly promotes the formation of associations, butwhen the animal is frightened the opposite is true. I have nohesitation in stating that, in case of the green frog, any strongdisturbing stimulus retards the formation of associations. Althoughthe frogs gave little evidence of fear by movements after being keptin the laboratory for a few weeks, they were really very timid, andthe presence of any strange object influenced all their reactions. Quiescence, it is to be remembered, is as frequently a sign of fear asis movement, and one is never safe in saying that the frog is notdisturbed just because it does not jump. The influence of theexperimenter's presence in the room with the frogs which were beingtried in the labyrinth became apparent when the animals were tried ina room by themselves. They escaped much more quickly when alone. Inorder to keep records of the experiments it was necessary for me to bein the room, but by keeping perfectly quiet it was possible to do thiswithout in any objectionable way influencing the results. It may be, however, that for this reason the learning is somewhat slower than itwould have been under perfectly natural conditions. Early in thispaper reference was made to the fact that the frog did not learn toescape from a box with a small opening at some distance from the floorif it was prodded with a stick. I do not mean to say that the animalwould never learn under such conditions, but that they are unfavorablefor the association of stimuli and retard the process. This conclusionis supported by some experiments whose results are tabulated at thebottom of Table IV. In these trials the animal had been trained to goto the left and to avoid red. At first ten trials were given in whichthe frog was in no way disturbed. The result was eight right choicesand two wrong ones. For the next ten trials the frog was touched witha stick and thus made to enter the labyrinth from the box, _A_. Thisgave five right and five wrong choices, apparently indicating that thestimulus interfered with the choice of direction. Several otherobservations of this nature point to the same conclusion, and it maytherefore be said that fright serves to confuse the frog and toprevent it from responding to the stimuli which would ordinarilydetermine its reaction. 

5. _The Permanency of Associations. _--After the labyrinth habit hadbeen perfectly formed by No. 2, tests for permanency were made, (1)after six days' rest and (2) after thirty days. Table V. Contains theresults of these tests. They show that for at least a month theassociations persist. And although there are several mistakes in thefirst trials after the intervals of rest, the habit is soon perfectedagain. After the thirty-day interval there were forty per cent. Ofmistakes at the exit for the first series, and only 20 per cent. Atthe entrance. This in all probability is explicable by the fact thatthe colors acted as aids at the entrance, whereas at the exit therewas no such important associational material. 

TABLE V. 

 PERMANENCY OF ASSOCIATIONS. FROG NO. 2. 

 Tests after six days' rest (following the results tabulated in Table III. ). 

 Trial. Entrance. Exit. Right. Wrong. Right. Wrong 1-10 7 3 8 2 (110-120) 11-20 10 0 10 0

 Tests after THIRTY days' rest. 1-10 8 2 6 4 10-20 10 0 10 0

D. Association of Stimuli. --In connection with reaction-time work anattempt was made to form an association between a strong visualstimulus and a painful electrical shock, with negative results. Areaction box, having a series of interrupted circuits in the bottomlike those already described for other experiments, and an opening onone side through which a light could be flashed upon the animal, served for the experiments. The tests consisted in the placing of afrog on the wires and then flashing an electric light upon it: if itdid not respond to the light by jumping off the wires, an electricalstimulus was immediately given. I have arranged in Table VI. Theresults of several weeks' work by this method. In no case is thereclear evidence of an association; one or two of the frogs reacted tothe light occasionally, but not often enough to indicate anything morethan chance responses. At one time it looked as if the reactionsbecame shorter with the continuation of the experiment, and it wasthought that this might be an indication of the beginning of anassociation. Careful attention to this aspect of the results failed tofurnish any satisfactory proof of such a change, however, and althoughin the table statements are given concerning the relative numbers ofshort and long reactions I do not think they are significant. 

TABLE VI. 

 ASSOCIATION OF ELECTRICAL AND VISUAL STIMULI. FROG No. 1a, 2a, 3a, 4a, 5a, A and Z. 

 Frog. Total No. Days. Result. Trials. 

 No. 1a 180 18 Increase in number of long reaction toward end. No evidence of association. 

 No. 2a 180 17 Increase in number of short reactions toward end. No evidence of association. 

 No. 3a 180 17 Marked increase in the number of short reactions toward end. No other evidence of association. 

 No. 4a 200 19 Slight increase in the short reactions. There were a few responses to the light on the third day. 

 No. 5a 200 20 No increase in the number of short reactions. Few possible responses to light on second and third days. 

 Frog A 250 20 No evidence of association. 

 Frog Z 450 28 No evidence of association. 

To all appearances this is the same kind of an association that wasformed, in the case of the labyrinth experiments, between the tactualand the electrical stimuli. Why it should not have been formed in thiscase is uncertain, but it seems not improbable that the light was toostrong an excitement and thus inhibited action. There is also theprobability that the frog was constrained by being placed in a smallbox and having the experimenter near. 

III. SUMMARY. 

1. The green frog is very timid and does not respond normally to moststimuli when in the presence of any strange object. Fright tends toinhibit movement. 

2. That it is able to profit by experience has been proved by testingit in simple labyrinths. A few experiences suffice for the formationof simple associations; but in case of a series of associations fromfifty to a hundred experiences are needed for the formation of aperfect habit. 

3. Experiment shows that the frog is able to associate two kinds ofstimuli, _e. G. _, the peculiar tactual stimulus given by a wire and apainful electric stimulus which in the experiments followed thetactual. In this case the animal learns to jump away, upon receivingthe tactual stimulus, before the experimenter gives the electricstimulus. 

4. Vision, touch and the organic sensations (dependent upon directionof turning) are the chief sensory factors in the associations. Theanimals discriminate colors to some extent. 

5. Perfectly formed habits are hard to change. 

6. Fear interferes with the formation of associations. 

7. Associations persist for at least a month. 

PART II. REACTION TIME OF THE GREEN FROG TO ELECTRICAL AND TACTUALSTIMULI. 

IV. THE PROBLEMS AND POSSIBILITIES OF COMPARATIVE REACTION-TIMESTUDIES. 

Animal reaction time is at present a new field of research of evidentimportance and full of promise. A great deal of time and energy hasbeen devoted to the investigation of various aspects of the timerelations of human neural processes; a multitude of interesting factshave been discovered and a few laws established, but the results seemdisproportionate to the amount of patient labor expended. Physiologists have determined the rate of transmission of the neuralimpulse for a few animals, and rough estimates of the time requiredfor certain changes in the nervous system have been made, but this isall we have to represent comparative study. Just the path of approachwhich would seem most direct, in case of the time of neural changes, has been avoided. Something is known of the ontogenetic aspect of thesubject, practically nothing of the phylogenetic; yet, in the study offunction the comparative point of view is certainly as important as itis in the study of structure. In calling attention to the importanceof the study of animal reaction time I would not detract from orminimize the significance of human investigations. They are all ofvalue, but they need to be supplemented by comparative studies. 

It is almost impossible to take up a discussion of the time relationsof neural processes without having to read of physiological andpsychological time. The time of nerve transmission, we are told, ispure physiological time and has nothing whatever to do with psychicprocesses; the time occupied by the changes in brain centers is, onthe contrary, psychological time. At the very beginning of mydiscussion of this subject I wish to have it clearly understood that Imake no such distinction. If one phase of the neural process be calledphysiological time, with as good reason may all be so named. I prefer, therefore, to speak of the time relations of the neural process. 

Of the value of reaction-time studies, one may well believe that itlies chiefly in the way of approach which they open to theunderstanding of the biological significance of the nervous system. Certainly they are not important as giving us knowledge of the time ofperception, cognition, or association, except in so far as we discoverthe relations of these various processes and the conditions underwhich they occur most satisfactorily. To determine how this or thatfactor in the environment influences the activities of the nervoussystem, and in what way system may be adjusted to system orpart-process to whole, is the task of the reaction-time investigator. 

The problems of reaction time naturally fall within three classes:Those which deal with (1) nerve transmission rates; (2) the timerelations of the spinal center activities, and (3) brain processes. Within each of these groups there are innumerable special problems forthe comparative physiologist or psychologist. Under class 1, forinstance, there is the determining of the rates of impulsetransmission in the sensory and the motor nerves, (_a_) for a varietyof stimuli, (_b_) for different strengths of each stimulus, (_c_) fordifferent conditions of temperature, moisture, nourishment, fatigue, etc. , in case of each stimulus, (_d_) and all this for hundreds ofrepresentative animals. From this it is clear that lines of work arenot lacking. 

Closely related to these problems of rate of transmission are certainfundamental problems concerning the nature of the nerve impulse orwave. Whether there is a nerve wave, the reaction-time worker has asfavorable an opportunity to determine as anyone, and we have a rightto expect him to do something along this line. The relations of theform of the nerve impulse to the rhythm of vital action, to fatigueand to inhibition are awaiting investigation. Some of the mostimportant unsettled points of psychology depend upon those aspects ofneural activities which we ordinarily refer to as phenomena ofinhibition, and which the psychologist is helpless to explain so longas the physiological basis and conditions are not known. 

Then, too, in the study of animals the relation of reaction time toinstincts, habits, and the surroundings of the subject are to benoted. Variability and adaptability offer chances for extendedbiological inquiries; and it is from just such investigations asthese that biology has reason to expect much. The development ofactivity, the relation of reflex action to instinctive, of impulsiveto volitional, and the value of all to the organism, should be madeclear by reaction-time study. Such are a few of the broad lines ofinquiry which are before the comparative student of animal reactiontime. It is useless to dwell upon the possibilities and difficultiesof the work, they will be recognized by all who are familiar with theresults of human studies. 

In the study of the time relations of neural processes Helmholtz wasthe pioneer. By him, in 1850, the rate of transmission of the nerveimpulse in the sciatic nerve of the frog was found to be about 27meters per second[4]. Later Exner[5] studied the time occupied byvarious processes in the nervous system of the frog by stimulating theexposed brain in different regions and noting the time whichintervened before a contraction of the gastrocnemius in each case. Further investigation of the frog's reflex reaction time has been madeby Wundt[6], Krawzoff and Langendorff[7], Wilson[8] and others, but inno case has the method of study been that of the psychologist. Most ofthe work has been done by physiologists who relied upon vivisectionalmethods. The general physiology of the nervous system of the frog hasbeen very thoroughly worked up and the papers of Sanders-Ezn[9], Goltz[10] Steiner[11] Schrader[12] and Merzbacher[13], [14] furnish anexcellent basis for the interpretation of the results of thereaction-time studies. 

 [4] Helmholtz, H. : 'Vorläufiger Bericht über die Portpflanzungsgeschwindigkeit der Nervenreizung. ' _Arch. F. Anal. U. Physiol. _, 1850, S. 71-73. 

 [5] Exner, S. : 'Experimentelle Untersuchung der einfachsten psychischen Processe. ' _Pflüger's Arch. _, Bd. 8. 1874, S. 526-537. 

 [6] Wundt, W. : 'Untersuchungen zur Mechanik der Nerven und Nervencentren. ' Stuttgart, 1876. 

 [7] Krawzoff, L. , und Langendorff, O. : 'Zur elektrischen Reizung des Froschgehirns. ' _Arch. F. Anal. U. Physiol. _, Physiol. Abth. , 1879, S. 90-94. 

 [8] Wilson, W. H. : 'Note on the Time Relations of Stimulation of the Optic Lobes of the Frog. '_Jour. Of Physiol. _, Vol. XI. , 1890, pp. 504-508. 

 [9] Sanders-Ezn: 'Vorarbeit für die Erforschung des Reflexmechanismus in Lendentmark des Frosches. ' _Berichte über die Verhandlungen der Kgl. Sächs. Gesellsch. D. Wissensch. Zu Leipzig_, 1867, S. 3. 

 [10] Goltz, F. : 'Beiträge zur Lehre von den Functionen der Nervencentren des Frosches. ' Berlin, 1869, 130 S. 

 [11] Steiner, J. : 'Untersuchungen über die Physiologie des Froschhirns. ' Braunschweig, 1885, 127 S. 

 [12] Schrader, M. G. : 'Zur Physiologie des Froschgehirns. ' _Pflüger's Arch. _, Bd. 41, 1887, S. 75-90. 

 [13] Merzbacher, L. : 'Ueber die Beziebungen der Sinnesorgane zu den Reflexbewegungen des Frosches. ' _Pflüger's Arch. _, Bd. 81, 1900, S. 223-262. 

 [14] Merzbacher, L. : 'Untersuchungen über die Regulation der Bewegungen der Wirbelthiere. I. Beobachtungen an Fröschen. ' _Pflüger's Arch. _, Bd. 88, 1901, S. 453-474, 11 Text-figuren. 

In the present investigation it has been my purpose to study thereactions of the normal frog by the reaction-time methods of thepsychologist. Hitherto the amount of work done, the extent ofmovements or some other change has been taken as a measure of theinfluence of a stimulus. My problem is, What are the time relations ofall these reactions? With this problem in mind I enter upon thefollowing program: (1) Determination of reaction time to electricalstimuli: (_a_) qualitative, (_b_) quantitative, (_c_) for differentstrengths of current; (2) Determination of reaction time to tactualstimuli (with the same variations); (3) Auditory: (_a_) qualitative, (_b_) quantitative, with studies on the sense of hearing; (4) Visual:(_a_) qualitative, (_b_) quantitative, with observations concerningthe importance of this sense in the life of the frog, and (5)Olfactory: (_a_) qualitative, (_b_) quantitative. 

The present paper presents in rather bare form the results thus farobtained on electrical, tactual, and auditory reaction time;discussion of them will be deferred until a comparison of the resultsfor the five kinds of stimuli can be given. 

V. METHOD OF STUDY. 

The measurements of reaction time herein considered were made with theHipp Chronoscope. Cattell's 'Falling Screen' or 'Gravity Chronoscope'was used as a control for the Hipp. The Gravity Chronoscope consistsof a heavy metal plate which slides easily between two vertical posts, with electrical connections so arranged that the plate, when releasedfrom the magnet at the top of the apparatus, in its fall, at a certainpoint breaks an electric circuit and at another point further downmakes the same circuit. The rate of fall of the plate is so nearlyconstant that this instrument furnishes an accurate standard time withwhich Hipp readings may be compared, and in accordance with which theHipp may be regulated. For, since the rate of a chronoscope varieswith the strength of the current in use, with the variations intemperature and with the positions of the springs on the magnetic bar, it is always necessary to have some standard for corrections. In theseexperiments the time of fall of the gravity chronoscope plate, asdetermined by the graphic method with a 500 S. V. Electric tuning fork, was 125[sigma] (_i. E. _, thousandths of a second). 

This period, 125[sigma], was taken as a standard, and each hour, before the beginning of reaction-time experiments, the time of theplate's fall was measured ten times with the Hipp, and for anyvariation of the average thus obtained from 125[sigma], the standard, the necessary corrections were made by changing the position of thechronoscope springs or the strength of the current. 

The standard of comparison, 125[sigma], is shorter than most of thereaction times recorded, but since the time measured was always thatfrom the breaking to the making of the circuit passing through thechronoscope it cannot be urged that there were errors resulting fromthe difference of magnetization which was caused by variations in thereaction time. But it is evident that the danger from differences inmagnetization, if such exists, is not avoided in this way; instead, itis transferred from the reaction time proper to the period ofpreparation immediately preceding the reaction; for, from the momentthe chronoscope is started until the stimulus is given a current isnecessarily passing through the instrument. At a verbal signal fromthe operator the assistant started the chronoscope; the stimulus wasthen given by the operator, and the instrument recorded the time fromthe breaking of the circuit, effected by the stimulating apparatus, tothe making of the circuit by the reaction of the animal. Despiteprecautions to prevent it, the period from the starting of thechronoscope to the giving of the stimulus was variable, and errorswere anticipated, but a number of the tests proved that variations ofeven a second did not cause any considerable error. 

A fairly constant current for the chronoscope was supplied by asix-cell 'gravity battery' in connection with two storage cells, _GB_(Fig. 6). This current could be used for two hours at a time withoutany objectionable diminution in its strength. The introduction ofresistance by means of the rheostat, _R_, was frequently a convenientmethod of correcting the chronoscope. 

[Illustration: FIG. 6. General Plan of Apparatus in Diagram. _H_, HippChronoscope; _R_, rheostat; _C_, commutator; _SC_, storage cells;_GB_, 'Excello' gravity battery; _F_, Cattell's falling screen; _T_, reaction table; _RK_, reaction key; _SK_, Stimulating apparatus; _K_, key in chronoscope circuit; _S_, stimulus circuit. ]

Fig. 6 represents the general plan of the apparatus used in theseexperiments. 

The general method of experimentation is in outline as follows:

1. At a 'ready' signal from the operator the assistant makes thechronoscope circuit by closing a key, _K_ (Fig. 6), and thenimmediately starts the chronoscope. 

2. Stimulus is given by the operator as soon as the chronoscope isstarted, and by this act the chronoscope circuit is broken and therecord begun. 

3. Animal reacts and by its movements turns a key, _RK_ (Fig. 6), thusmaking the chronoscope circuit and stopping the record. 

4. Assistant stops chronoscope and takes reading. 

[Illustration: FIG. 7. Reaction Key. _l_, lever swung on pivot; _p, p_, posts for contacts with platinum plates on base; _b_, upright barfor string; _s_, spring for clamping string; _w_, wheel to carrystring; _c, c_, chronoscope circuit; 1 and 2, points which are broughtinto contact by animal's reaction. ]

The steps of this process and the parts of the apparatus concerned ineach may be clearly conceived by reference to the diagram given inFig. 6. The various forms of stimulating apparatus used and themodification of the method will be described in the sections dealingwith results. The same reaction key was used throughout (see Fig. 7). Its essential features are a lever _l_, pivoted in the middle andbearing a post at either end, _p, p_. From the middle of this leverthere projected upward a small metal bar, _b_, through the upper partof which a string to the animal ran freely except when it was clampedby the spring, _s_. This string, which was attached to the subject'sleg by means of a light elastic band, after passing through the barran over a wheel, _w_, and hung tense by reason of a five-gram weightattached to the end. Until everything was in readiness for anexperiment the string was left free to move through the bar so thatmovement of the animal was not hindered, but the instant before theready-signal was given it was clamped by pressure on _s_. The diagramshows the apparatus arranged for a reaction. The current is broken, since 1 and 2 are not in contact, but a slight movement of the animalturns the lever enough to bring 1 against 2, thus making the circuitand stopping the chronoscope. When the motor reaction of the subjectwas violent the string pulled out of the clamp so that the animal wasfree from resistance, except such as the string and weight offered. The five-gram weight served to give a constant tension and thusavoided the danger of error from this source. Between experiments theweight was placed on the table in order that there might be no strainupon the subject. 

That the subject might be brought into a favorable position for anexperiment without being touched by the operator a special reactionbox was devised. 

The animals used in these studies were specimens of _Rana clamitans_which were kept in a tank in the laboratory throughout the year. 

VI. ELECTRIC REACTION TIME. 

The reaction time to electrical stimuli was determined first becauseit seemed probable that this form of the pain reaction would be mostuseful for comparison with the auditory, visual, olfactory and tactualreactions. In this paper only the electrical and the tactual reactiontimes will be considered. The former will be divided into two groups:(1) Those resulting from a stimulus given by touching electrodes tothe leg of the frog, and (2) those gotten by having the frog restingupon wires through which a current could be passed at any time. 

_Group 1 of the electrical reactions_ were taken under the followingconditions. A reaction box about 40 cm. In diameter was used. The meantemperature of the experimenting room was about 20° C. In all casesthe string was attached to the left hind leg of the frog, and thestimulus applied to the middle of the gastrocnemius muscle of theright hind leg. Reaction times were taken in series of ten, excludingthose which were imperfect. As the moistness of the skin affects thestrength of the electric stimulus received, it was necessary tomoisten the animal occasionally, but as it did not seem advisable todisturb it after each experiment this was done at intervals of fiveminutes throughout the series. Were it not for this precaution itmight be said that lengthening of the reaction times toward the end ofa series simply indicated the weakening of the stimulus which resultedfrom the gradual drying of the skin. The stimulus in this group wasapplied by means of the stimulating apparatus of Fig. 6. It is merelytwo wire electrodes which could be placed upon the animal, with theadditional device of a key for the breaking of the chronoscope circuitthe instant the stimulus was given. The most serious objection to thismethod of stimulating is that there is a tactual as well as anelectrical stimulus. 

Before presenting averages, two representative series of reactions maybe considered. 

SERIES I. FROG B. APRIL 9, 1900. 10 A. M. 

 Temperature 19° C. String to left hind leg. Stimulus to right hind leg. 

 Strength of stimulating current 1. 0 volt, . 0001 ampčre. 

 Number of Experiment. Hour. Reaction Time. Remarks. 

 1 10. 25 No reaction. 2 10. 27 No reaction. 3 10. 30 139[sigma] 4 10. 34 164 5 10. 35 102 6 10. 37 169 7 10. 39 151 8 10. 40 152 9 10. 42 144 10 10. 43 152 11 10. 45 122 12 10. 51 179 13 10. 54 No reaction. 

 Average of 10, 147. 4[sigma]

 SERIES 2. FROG F. ELECTRICAL STIMULUS. 

 No. Hour. Reaction Time. Remarks. Deviation from Mean. 

 1 10. 19 35[sigma] Probable reaction to visual stim. 2 10. 22 173 4. 7 3 10. 24 161 - 7. 3 4 10. 25 133 -35. 3 5 10. 26 199 30. 7 6 10. 28 130 -38. 3 7 10. 32 179 10. 7 8 10. 34 187 18. 7 9 10. 35 60 Probable reflex. 10 10. 37 183 14. 7 11 10. 38 166 - 2. 3 12 10. 39 172 3. 7

 Average of 10, 168. 3[sigma] Average of first 5, 159. 2[sigma] Average Variation, 16. 64[sigma] Average of second 5, 177. 4[sigma]

Both are fairly representative series. They show the extremely largevariations, in the case of series 1, from 102 to 179[sigma]. In allthese experiments such variation is unavoidable because it isimpossible to have the conditions uniform. A very slight difference inthe frog's position, which could not be detected by the operator, might cause considerable difference in the time recorded. Efforts weremade to get uniform conditions, but the results seem to show thatthere is still much to be desired in this direction. 

Tables VII. Contains the results of four series of ten reactions eachfor frog _A_. It will be noticed that the time for the first five ineach series is much shorter than that for the last five; this isprobably indicative of fatigue. 

TABLE VII. 

 REACTION TIME OF FROG _A_ TO ELECTRICAL STIMULI. 

 Series of Averages Averages of Averages of ten reactions. Of series. First five. Second five. 1 163. 1[sigma] 134. 6[sigma] 191. 6[sigma] 2 186. 2 176. 2 196. 2 3 161. 1 125. 2 197. 0 4 158. 3 101. 6 215. 0 General averages 167. 2[sigma] 134. 4[sigma] 199. 9[sigma]

 TABLE VIII. 

 REACTION TIME OF FROG _B_ TO ELECTRICAL STIMULI. 

 1 132. 7[sigma] 118. 2[sigma] 147. 4[sigma] 2 196. 6 167. 8 225. 4 3 147. 4 145. 5 149. 8 4 157. 5 152. 0 163. 0 General averages 158. 6[sigma] 145. 9[sigma] 171. 4[sigma]

TABLE IX. 

 NORMAL AND REFLEX REACTION TIME OF SIX ANIMALS TO ELECTRICAL STIMULUS. 

 Normal. Reflex. Average for 20 Average for 20 Frog. Reactions. Mean Var. Reactions. Mean Var. _A_ 149. 5[sigma] 24. 0[sigma] _B_ 158. 3 16. 0 51. 5[sigma] 8. 0[sigma] _C_ 191. 0 24. 3 _D_ 167. 0 10. 1 _E_ 182. 4 28. 0 45. 1 5. 5 _F_ 176. 3 10. 2 46. 0 4. 5 General Average. 167. 9[sigma] 18. 8[sigma] 47. 5[sigma] 6. 0[sigma]

 For _D_ the average is for ten reactions. 

 _B_ and _E_ were males, _F_ a female; the sex of the others was not determined by dissection and is uncertain. 

Early in the experiments it became evident that there were threeclearly defined types of reactions: there were a number of reactionswhose time was shorter than that of the ordinary quick voluntary painreaction, and there were also many whose time was considerably longer. The first type it was thought might represent the spinal reflexreaction time. For the purpose of determining whether the suppositionwas true, at the end of the series of experiments three of the frogswere killed and their reflex reaction time noted. This was done bycutting the spinal cord just back of the medulla, placing the animalon an experimenting board close to the reaction key with the threadfrom the key fastened to the left leg as in case of the previous workand stimulating the gastrocnemius with an induced current by theapplication of wire electrodes. 

In Table IX. The reflex reaction times for the three animals aregiven. 

The following results obtained with frog _E_ show that the time ofreaction increases with the increase in the time after death. Theaverage of 20 reactions by _E_ taken an hour after the cord had beencut was 45. 5[sigma]; the average of 20 taken twenty hours later was55. 85[sigma]. 

As a rule the reflex reactions were but slightly variable in time asis indicated by the accompanying series. 

 SERIES OF REFLEX REACTIONS OF FROG _F_. Taken at rate of one per minute. 

 1 50[sigma] 2 58 3 55 4 59 5 48 6 46 7 45 8 51 9 42 10 44

Throughout these experiments it was noticed that any stimulus mightcause (1) a twitch in the limb stimulated, or (2) a twitch followed bya jump, or (3) a sudden jump previous to which no twitch could bedetected. And it soon appeared that these types of reaction, as itseems proper to call them, would have to be considered in anydetermination of the mean reaction time. As proof of the type theorythere is given (Fig. 8) a graphic representation of 277 reactions tothe electrical stimulus. 

[Illustration: FIG 8: Distribution of 277 reactions. ]

The column of figures at the left indicates the number of reactions atany point. Below the base line are the classes. For convenience ofplotting the reactions have been grouped into classes which areseparated by 25[sigma]. Class 1 includes all reactions between1[sigma] and 25[sigma], class 2 all from 25[sigma] to 50[sigma], andso on to 400[sigma], thereafter the classes are separated by100[sigma]. It is noticeable that there is one well-marked mode at75[sigma]. A second mode occurs at 175[sigma]. This is the primary andin our present work the chiefly significant mode, since it is that ofthe quick instinctive reaction to a stimulus. At 500[sigma] there is athird mode; but as such this has little meaning, since the reactionsare usually pretty evenly distributed from 300[sigma] on to2000[sigma]; if there is any grouping, however, it appears to be about500[sigma] and 800[sigma]. 

The first mode has already been called the reflex mode. The shortreactions referred to usually lie between 40[sigma] and 80[sigma], andsince experiment has shown conclusively that the spinal reflexoccupies about 50[sigma], there can be little doubt that the firstmode is that of the reflex reaction time. 

The second mode represents those reactions which are the result ofcentral activity and control. I should be inclined to argue that theyare what we usually call the instinctive and impulsive actions. Andthe remaining reactions represent such as are either purely voluntary, if any frog action can be so described, or, in other words, dependupon such a balancing of forces in the brain as leads to delay andgives the appearance of deliberate choice. 

Everything points to some such classification of the types as follows:(1) Stimuli strong enough to be injurious cause the shortest possiblereaction by calling the spinal centers into action, or if not spinalcenters some other reflex centers; (2) slightly weaker stimuli are notsufficient to affect the reflex mechanism, but their impulse passes onto the brain and quickly discharges the primary center. There is nohesitation, but an immediate and only slightly variable reaction; justthe kind that is described as instinctive. As would be expected, themajority of the frog's responses are either of the reflex or of thisinstinctive type. (3) There is that strength of stimulus which is notsufficient to discharge the primary center, but may pass to centers ofhigher tension and thus cause a response. This increase in thecomplexity of the process means a slower reaction, and it is such wecall a deliberate response. Precisely this kind of change in neuralaction and in reaction time is at the basis of voluntary action. And(4) finally, the stimulus may be so weak that it will not induce areaction except by repetition. Just above this point lies thethreshold of sensibility, the determination of which is ofconsiderable interest and importance. 

_Group 2 of the electrical reactions_ consists of three series takento determine the relation of strength of stimulus to reaction time. The conditions of experimentation differed from those for group 1 inthe following points: (1) The stimulus was applied directly by themaking of a circuit through wires upon which the subject rested (Fig. 9); (2) the thread was attached to the right hind leg; (3) the thread, instead of being kept at the tension given by the 5-gram weight as inthe former reactions, was slackened by pushing the upright lever ofthe reaction key one eighth of an inch toward the animal. This wasdone in order to avoid the records given by the slight twitches of thelegs which precede the motor reaction proper. For this reason thereactions of group 2 are not directly comparable with those of group1. Fig. 9 is the plan of the bottom of a reaction box 15 cm. At oneend, 30 cm. At the other, 60 cm. Long and 45 cm. Deep. On the bottomof this, at one end, a series of interrupted circuits were arranged asshown in the figure. The wires were 1. 2 cm. Apart, and an animalsitting anywhere on the series necessarily touched two or more, sothat when the stimulus key, X, was closed the circuit was completed bythe animal's body; hence, a stimulus resulted. The stimulus key, X, was a simple device by which the chronoscope circuit, _c_, _c_, wasbroken at the instant the stimulus circuit, _s_, _c_, was made. 

Cells of 'The 1900 Dry Battery' furnished the current used as astimulus. Three different strengths of stimulus whose relative valueswere 1, 2 and 4, were employed in the series 1, 2 and 3. Carefulmeasurement by means of one of Weston's direct-reading voltmeters gavethe following values: 1 cell, 0. 2 to 0. 5 volt, 0. 00001 to 0. 00003ampčre. This was used as the stimulus for series 1. 2 cells, 0. 5 to1. 0 volt, 0. 00003 to 0. 00006 ampčre. This was used for series 2. 4cells, 1. 2 to 1. 8 volt, 0. 00007 to 0. 0001 ampčre. This was used forseries 3. 

[Illustration: Fig. 9. Ground Plan of Reaction Box for ElectricalStimuli (Group 2). _IC_, interrupted circuits; _CC_, chronoscopecircuit; _X_, key for making stimulus circuit and breaking chronoscopecircuit; _B_, stimulus battery; _S_, string from reaction key toanimal. Scale 1/2. ]

The reactions now under consideration were taken in sets of 24 inorder to furnish evidence on the problem of fatigue. The stimulus wasgiven at intervals of one minute, and the subject was moistened atintervals of ten minutes. To obtain 24 satisfactory reactions it wasusually necessary to give from thirty to forty stimulations. Fiveanimals, numbers 1, 2, 4, 5, and 6, served as subjects. They weregreen frogs whose size and sex were as follows:

 Length. Weight. Sex. Number 1 7. 5 cm. 35 grams. Male. Number 2 7. 3 " 37 " Male. Number 4 8. 2 " 50. 4 " Female? Number 5 7. 1 " 25 " Female. Number 6 7. 8 " 42 " Male. 

For most of these frogs a one-cell stimulus was near the threshold, and consequently the reaction time is extremely variable. In Table X. An analysis of the reactions according to the number of repetitions ofthe stimulus requisite for a motor reaction has been made. Numbers 1and 5 it will be noticed reacted most frequently to the firststimulus, and for them 48 satisfactory records were obtained; but incase of the others there were fewer responses to the first stimulus, and in the tabulation of series 1 (Table XI. ) averages are given forless than the regular sets of 24 reactions each. 

TABLE X. 

 ANALYSIS OF REACTIONS TO ONE-CELL STIMULUS. 

 Frog. Reactions to To 2d. To 3d. To 4th. To 5th. More. Total No. First Stimulus. Of Reactions. 1 53 2 1 0 0 1 57 2 20 12 5 5 4 12 58 4 31 15 1 0 2 8 57 5 51 11 1 2 0 1 66 6 45 15 6 3 1 5 75 Totals, 200 55 14 10 7 27 313

Table XI. Is self-explanatory. In addition to the usual averages, there is given the average for each half of the sets, in order thatthe effect of fatigue may be noted. In general, for this series, thesecond half is in its average about one third longer than the firsthalf. There is, therefore, marked evidence of tiring. The meanreaction time for this strength of stimulus is difficult to determinebecause of the extremely great variations. At one time a subject mayreact immediately, with a time of not over a fifth of a second, and atanother it may hesitate for as much as a second or two beforereacting, thus giving a time of unusual length. Just how many andwhich of these delayed responses should be included in a series forthe obtaining of the mean reaction time to this particular stimulus isan extremely troublesome question. It is evident that the mode shouldbe considered in this case rather than the mean, or at least that themean should be gotten by reference to the mode. For example, althoughthe reaction times for the one-cell stimulus vary all the way from150[sigma] to 1000[sigma] or more, the great majority of them liebetween 200[sigma] and 400[sigma]. The question is, how much deviationfrom the mode should be allowed? Frequently the inclusion of a singlelong reaction will lengthen the mean by 10[sigma] or even 20[sigma]. What is meant by the modal condition and the deviation therefrom isillustrated by the accompanying curve of a series of reaction timesfor the electric stimulus of group I. 

___________________________________________________________________________8_|_______________________________________________________________________7_|_____________________________________|_________________________________6_|_____________________________________|_________________________________5_|_____________________________________|_________________________________4_|________________________________|____|____|____________________________3_|____________|___________________|____|____|____________________________2_|_______|____|____|_________|____|____|____|____|_______________________1_|__|____|____|____|_________|____|____|____|____|____|____|____|____|__ 100 110 120 130 140 150 160 170 180 190 200 210 220 230

The column of figures at the left indicates the number of reactions;that below the base line gives the reaction times in classes separatedby 10[sigma]. Of thirty-one reactions, seven are here in the class170[sigma]. This is the model class, and the mean gotten by taking theaverage of 31 reactions is 162[sigma]. If the mode had been taken torepresent the usual reaction time in this case, there would have beenno considerable error. But suppose now that in the series there hadoccurred a reaction of 800[sigma]. Should it have been used in thedetermination of the mean? If so, it would have made it almost30[sigma] greater, thus removing it considerably from the mode. Ifnot, on what grounds should it be discarded? The fact that widelyvarying results are gotten in any series of reactions, points, itwould seem, not so much to the normal variability as to accidentaldifferences in conditions; and the best explanation for isolatedreactions available is that they are due to such disturbing factors aswould decrease the strength of the stimulus or temporarily inhibit theresponse. During experimentation it was possible to detect manyreactions which were unsatisfactory because of some defect in themethod, but occasionally when everything appeared to be all right anexceptional result was gotten. There is the possibility of any or allsuch results being due to internal factors whose influence it shouldbe one of the objects of reaction-time work to determine; but in viewof the fact that there were very few of these questionable cases, andthat in series I, for instance, the inclusion of two or threereactions which stood isolated by several tenths of a second from themode would have given a mean so far from the modal condition that theresults would not have been in any wise comparable with those of otherseries, those reactions which were entirely isolated from the mode andremoved therefrom by 200[sigma] have been omitted. In series I alonewas this needful, for in the other series there was comparativelylittle irregularity. 

The results of studies of the reaction time for the one-cell electricstimulus appear in Table XI. The first column of this table containsthe average reaction time or mean for each subject. Nos. 2 and 4appeared to be much less sensitive to the current than the others, andfew responses to the first stimulus could be obtained. Their time islonger than that of the others, and their variability on the wholegreater. Individual differences are very prominent in the studies thusfar made on the frog. The one-cell stimulus is so near the thresholdthat it is no easy matter to get a mean which is significant. Couldthe conditions be as fully controlled as in human reaction time itwould not be difficult, but in animal work that is impossible. Noattempt has thus far been made to get the reaction time in case ofsummation effects except in occasional instances, and in so far asthose are available they indicate no great difference between thenormal threshold reaction and the summation reaction, but on thisproblem more work is planned. 

There are large mean variations in Table XI. , as would be anticipated. Since the reactions were taken in sets of 24, the means of each set aswell as that of the total are given, and also, in columns 4 and 5, themeans of the first half and the last half of each set. 

A comparison of Tables XI. , XII. And XIII. Makes clear the differencesin reaction time correlated with differences in the strength of anelectric stimulus. For Table XI. , series I, the relative value of thestimulus was I; for Table XII. , series 2, it was 2, and for TableXIII. , series 3, it was 4. Throughout the series from I to 3 there isa rapid decrease in the reaction time and in the variability of thesame. The reaction time for stimulus I, the so-called threshold, isgiven as 300. 9[sigma]; but of the three it is probably the leastvaluable, for reasons already mentioned. The mean of the secondseries, stimulus 2, is 231. 5[sigma] while that of the third, stimulus4, is only 103. 1[sigma]. This great reduction in reaction time for thefour-cell stimulus apparently shows the gradual transition from thedeliberate motor reaction, which occurs only after complex and variedcentral neural activities, and the purely reflex reaction, which takesplace as soon as the efferent impulse can cause changes in the spinalcenters and be transmitted as an afferent impulse to the muscularsystem. 

TABLE XI. 

 ELECTRICAL STIMULUS REACTION TIME. SERIES 1. 

 Average Average of Average Average Mean Var Frog. Of all. Mean Var. Sets. Of 1st h. Of 2d h. Of Sets. 

 1 238. 5* 33. 3* 216. 0* 205. 6* 226. 7* 33. 2* 261. 0 248. 0 274. 1 33. 3 2 458. 0 219. 0 458. 0 270. 4 643. 8 219. 0 4 273. 4 59. 9 273. 4 245. 7 301. 1 59. 9 5 263. 9 50. 5 268. 6 244. 7 292. 5 44. 9 259. 2 236. 0 282. 4 56. 1 6 271. 1 65. 1 322. 6 273. 2 372. 0 87. 9 219. 6 208. 5 230. 6 42. 3 Gen Av. 300. 9 85. 5 300. 9 244. 8 356. 8 85. 5

 Totals. For No. 1 the averages are for 2 sets of 24 reactions each, 48 " 2 " " one set of 12 " " 12 " 4 " " one set of 24 " " 24 " 5 " " two sets of 24 " " 48 " 6 " " two sets of 24 and 12 reactions, respectively, 36

 *Transcriber's Note: All values in [sigma], 1/1000ths of a second. 

TABLE XII. 

 ELECTRICAL STIMULUS REACTION TIME. SERIES 2. 

 Average Average of Average Average Mean Var Frog. Of all. Mean Var. Sets. Of 1st h. Of 2d h. Of Sets. 

 1 227. 3* 33. 7* 229. 4* 209. 1* 249. 6* 25. 5* 225. 2 207. 3 243. 0 42. 1 2 240. 1 30. 9 239. 0 222. 3 255. 1 29. 0 241. 3 220. 2 262. 4 32. 8 4 270. 3 56. 5 298. 5 285. 3 311. 4 62. 8 242. 2 206. 0 278. 4 50. 2 198. 5 26. 2 195. 0 197. 5 193. 0 33. 5 202. 0 195. 2 209. 0 18. 8 6 224. 4 24. 4 221. 6 209. 7 233. 7 23. 6 227. 2 213. 5 241. 0 25. 1 Gen. Av. 231. 5 34. 3 231. 0 216. 6 246. 6 34. 3

 For No. 5 the averages are for two sets of 18 each; for all the others there are 24 in each set. 

 *Transcriber's Note: All values in [sigma], 1/1000ths of a second. 

TABLE XIII. 

 ELECTRICAL STIMULUS REACTION TIME. SERIES 3. 

 Average Average Average Average Mean Var. Frog. Of all. Mean Var. Of all. Of 1st h. Of 2d h. Of Sets. 1 93. 6* 13. 5* 91. 8* 93. 2* 90. 4* 13. 5* 95. 4 91. 8 99. 0 13. 5 2 99. 9 12. 8 92. 2 89. 4 95. 0 17. 4 107. 5 105. 9 109. 0 8. 2 4 125. 2 16. 3 113. 5 106. 5 120. 5 13. 6 136. 0 135. 7 138. 2 19. 0 5 94. 4 8. 0 88. 6 90. 5 88. 6 8. 2 100. 2 97. 8 102. 7 7. 9 6 102. 5 12. 2 104. 2 98. 6 109. 9 12. 8 100. 9 101. 0 108. 3 11. 6 Gen. Avs. 103. 1 12. 5 103. 1 101. 0 105. 9 12. 5

For each animal there are two sets of 24 reactions each. 

 *Transcriber's Note: All values in [sigma], 1/1000ths of a second. 

The spinal reflex for a decapitated frog, as results previouslydiscussed show, is approximately 50[sigma]; and every time thefour-cell stimulus is given this kind of a reaction results. There isa slight twitch of the legs, immediately after which the animal jumps. Now for all these series the thread was slackened by one eighth of aninch, but the reflex time was determined without this slack. Calculation of the lengthening of the reaction time due to the slackindicated it to be between 20 and 30[sigma], so if allowance be madein case of the reactions to the four-cell stimulus, the mean becomesabout 70[sigma], or, in other words, nearly the same as the spinalreflex. The conclusion seems forced, therefore, that when a stimulusreaches a certain intensity it produces the cord response, while untilthat particular point is reached it calls forth central activitieswhich result in much longer and more variable reaction times. It wassaid above that the series under consideration gave evidence of thegradual transition from the reflex to the volitional in reaction time. Is this true, or do we find that there are well-marked types, betweenwhich reactions are comparatively rare? Examination of the tablesVII. , VIII. , IX. , XI. , XII. And XIII. Will show that between 70[sigma]and 150[sigma] there is a break. (In tables XI. , XII. And XIII. , allowance must always be made for the slack in the thread, bysubtracting 30[sigma]. ) All the evidence furnished on this problem bythe electrical reaction-time studies is in favor of the type theory, and it appears fairly clear that there is a jump in the reaction timefrom the reflex time of 50-80[sigma], to 140 or 150[sigma], which mayperhaps be taken as the typical instinctive reaction time. From150[sigma] up there appears to be a gradual lengthening of the time asthe strength of the stimulus is decreased, until finally the thresholdis reached, and only by summation effect can a response be obtained. 

The most important averages for the three series have been arranged inTable XIV. For the comparison of the different subjects. Usually thereaction time for series 3 is about one half as long as that forseries 2, and its variability is also not more than half as large. Inthe small variability of series 3 we have additional reason forthinking that it represents reflexes, for Table IX. Gives the meanvariation of the reflex as not more than 8[sigma], and the fact thatthe means of this series are in certain cases much larger is fullyexplained by the greater opportunity for variation afforded by theslack in the thread. 

TABLE XIV. 

 MEANS, ETC. , FOR EACH SUBJECT FOR THE THREE SERIES. (TIME IN [sigma])

 Mean First Second Mean Frog. Half. Half. Variation. Series 1 238. 5 226. 8 259. 4 33. 3 Series 2 227. 3 208. 2 246. 3 33. 7 No. 1 Series 3 93. 6 92. 5 94. 7 13. 5

 Series 1 458. 0 270. 4 643. 8 219. 0 Series 2 240. 1 221. 2 258. 8 30. 9 No. 2 Series 3 99. 9 97. 6 102. 0 12. 8

 Series 1 273. 4 245. 7 301. 1 59. 9 Series 2 270. 3 245. 6 294. 9 56. 5 No. 4 Series 3 125. 2 121. 1 129. 3 16. 3

 Series 1 263. 9 240. 4 287. 4 50. 5 Series 2 198. 5 196. 4 201. 0 26. 2 No. 5 Series 3 94. 4 94. 2 94. 7 8. 0

 Series 1 271. 1 240. 8 301. 3 65. 1 Series 2 224. 4 211. 6 237. 3 24. 4 No. 6 Series 3 102. 5 99. 8 109. 1 12. 2

A striking fact is that the averages for the first and last half ofsets of reactions differ more for the weak than for the strongstimulus. One would naturally expect, if the increase were a fatiguephenomenon purely, that it would be greatest for the strongeststimulus; but the results force us to look for some other conditionsthan fatigue. A stimulus that is sufficiently strong to be painful andinjurious to an animal forces an immediate response so long as themuscular system is not exhausted; but where, as in series 1 and 2 ofthe electrical stimulus, the stimulus is not harmful, the reason for asudden reaction is lacking unless fear enters as an additional cause. Just as long as an animal is fresh and unfamiliar with the stimulusthere is a quick reaction to any stimulus above the threshold, and assoon as a few experiences have destroyed this freshness and taught thesubject that there is no immediate danger the response becomesdeliberate. In other words, there is a gradual transition from theflash-like instinctive reaction, which is of vast importance in thelife of such an animal as the frog, to the volitional and summationresponses. The threshold electrical stimulus does not force reactions;it is a request for action rather than a demand, and the subject, although startled at first, soon becomes accustomed to the experienceand responds, if at all, in a very leisurely fashion. The reactiontime to tactual stimuli, soon to be considered, was determined bygiving a subject only three or four stimulations a day; if more weregiven the responses failed except on repetition or pressure; for thisreason the data on fatigue, or lengthening of reaction time toward theend of a series, are wanting in touch. A few tests for the purpose ofdiscovering whether the time would lengthen in a series were made withresults very similar to those of the threshold electrical stimulus;the chief difference lies in the fact that the responses to touch failaltogether much sooner than do those to the electrical stimulus. This, however, is explicable on the ground that the latter is a stimulus towhich the animal would not be likely to become accustomed so soon asto the tactual. 

 First Half. Second Half. Second % Greater. Series 1 244. 8[sigma] 356. 8[sigma] 46 per cent Series 2 216. 6 246. 6 14 " Series 3 101. 0 105. 9 5 "

If pure fatigue, that is, the exhaustion of the nervous or muscularsystem, appears anywhere in this work, it is doubtless in series 3, for there we have a stimulus which is so strong as to force responseon penalty of death; the reaction is necessarily the shortestpossible, and, as a matter of fact, the motor reaction (jump forward)here occupies little more time than the leg-jerk of a decapitatedfrog. This probably indicates that the reaction is a reflex, and thatthe slight increase in its length over that of the spinal reflex isdue to occasional cerebellar origin; but of this there can be nocertainly from the evidence herewith presented. At any rate, there isno possibility of a voluntary reaction to the strong current, and anychanges in the general character of the reaction time in a series willhave to be attributed to fatigue of the nervous or muscular systems. The second halves of the sets of series 3 are 5 per cent. Longer thanthe first, and unless this is due to the partial exhaustion of thenervous system it is hard to find an explanation of the fact. Fatigueof the muscles concerned seems out of the question because thereactions occur at the rate of only one per minute, and during therest interval any healthy and well-nourished muscle would so farrecover from the effect of contraction that it would be able tocontinue the rhythmic action for long periods. 

To the inquiry, Does fatigue in the experiments mean tiring by theexhaustion of nerve energy, or is the lengthening in reaction timewhich would naturally be attributed to tiring due to the fact thatexperience has shown quick reaction to be unnecessary? we shall haveto reply that there is evidence in favor of both as factors. There canbe little doubt that in case of the strong stimuli there is genuinefatigue which makes quick reaction impossible; but at the same time itis certain that the 40 to 50 per cent. Increase of the second half ofsets in series 1 over the first half can not be due to fatigue, forthe strain is here evidently much less than for series 3. Rather, itwould seem that habituation instead of exhaustion is the all-importantcause of the difference in series 1 and 2. It becomes clear from theseconsiderations that the repetition of a stimulus can never mean therepetition of an effect. 

VII. TACTUAL REACTION TIME. 

In the following work on the reactions to tactual stimulation thesubject was placed in a large reaction box with a thread attached toone of its legs and passing to a reaction key, as in the experimentsalready described. The box in which the subject was confined wassurrounded by movable cloth curtains to prevent the animal's escapeand at the same time permit the experimenter to work without beingseen by the frog. 

Tactual stimulation was given by means of a hand key[15] similar tothat used for electrical stimulation which is represented in Fig. 6. The touch key ended in a hard-rubber knob which could be brought incontact with the skin of the subject. This key was fixed to a handleof sufficient length to enable the operator to reach the animalwherever it chanced to be sitting in the reaction box. Stimulation wasgiven by allowing the rubber point of the touch key to come in contactwith the skin in the middle region of the subject's back. As soon asthe point touched the animal the chronoscope circuit was broken by theraising of the upper arm of the key. 

 [15] This apparatus was essentially the same as Scripture's device for the giving of tactual stimulation. 

As a precaution against reactions to visual stimuli, which it mightwell be supposed would appear since the subject could not in everycase be prevented from seeing the approaching apparatus, the frog wasalways placed with its head away from the experimenter so that theeyes could not readily be directed toward the touch apparatus. Notwithstanding care in this matter, a reaction occasionally appearedwhich was evidently due to some disturbance preceding the tactualstimulus which served as a warning or preparation for the latter. Allsuch responses were at once marked as questionable visual reactionsand were not included in the series of touch reactions proper. 

As has been mentioned in connection with the discussion of fatigue, itwas found absolutely necessary to have the subjects perfectly freshand active, and for this purpose it was advisable to give not morethan three or four stimulations at any one time. The subject wasusually kept in the reaction box from 30 to 45 minutes, dependent uponthe success of the experiments. As the work progressed it becameevident that the responses to the stimulus were becoming less and lesscertain and slower, that the subjects were becoming accustomed to thenovel experience and no longer suffered the surprise which had beenthe cause of the prompt reactions at first. It seemed best for thisreason not to continue the work longer than two weeks, and as aconsequence it was impossible to base the averages on more than twentyreactions for each subject. 

So far as the tension of the thread is concerned, the condition forthe tactual reaction time was the same as that for the first group ofelectrical reaction-time experiments. In comparing the tactual withthe electrical of series 1, 2 and 3, allowance must be made for theslack in the latter cases. 

Selection of the tactual reaction times upon which the mean is based, has been made with reference to the mode for each set of experiments. Inspection of the curves given by the reactions of each subjectindicated that the great majority of the responses lay between 100 and300[sigma], and that those which were beyond these limits wereisolated and, in all probability, exceptional reactions due to someundetected variation in conditions which should throw them out of theregular series. On this account it was thought best to use onlyreactions between 100 and 300[sigma]. 

For convenience of comparison, again, the averages for the electricalreaction time of subjects _A_, _B_, _C_, _D_, _E_ and _F_, and thesame for the tactual reaction time of subjects 1, 2, 3, 4, 5 and 6 areherewith given together. All averages are for twenty reactions, exceptfor _D_ and 5, for which there are ten. 

Besides the usual determination for the tactual reaction-time work onthe six subjects named, there is given in Table XVI. The electricalreaction time of these animals to a two-cell current. Comparison ofthe electrical and tactual results are of interest in this casebecause the mean variation for each is about 34[sigma], being34. 3[sigma], for the electrical and 33. 8[sigma], for the tactual. 

TABLE XV. 

 Average of 20 Electrical Average of 20 Tactual Frog. Reactions. Frog. Reactions. _A_ 149. 5[sigma] 1 188. 3[sigma] _B_ 158. 3 2 199. 1 _C_ 191. 0 3 212. 1 _D_ 167. 0 4 213. 0 _E_ 182. 4 5 199. 8 _F_ 176. 3 6 221. 9 Gen. Avs. 167. 9 205. 7

TABLE XVI. 

 REACTION TIME FOR TACTUAL AND ELECTRICAL STIMULI. 

 Tactual Reaction Time. Electrical Reaction Time. 

 Frog. Average. Mean Variation. Average. Mean Variation. 

 1 188. 3[sigma] 167. 3[sigma] 2 199. 1 180. 1 3 212. 1 4 213. 0 210. 3 5¹ 199. 8 138. 5 6 221. 9 164. 4 Gen. Avs. 205. 7 33. 8 172. 1 34. 3

 ¹For 5 the average of ten instead of twenty is given. 

VIII. EQUAL VARIABILITY AS A CRITERION OF COMPARABILITY OF REACTIONTIME FOR DIFFERENT KINDS OF STIMULI. 

Since variability as indicated in the study of the influence ofdifferent strengths of electrical stimulus becomes less as thestimulus increases, parity in variability for different stimuli offersa basis for the comparison of reaction times. Certain it is that thereis no use in comparing the reaction times for different senses ordifferent qualities of stimuli unless the relative values of thestimuli are taken into consideration; but how are these values to bedetermined unless some such index as variability is available? If thereaction time to tactual stimuli as here presented is to be studied inits relation to the electrical reaction time, it will mean littlesimply to say that the former is longer than the latter, because theelectrical reaction time for a one-cell stimulus happens to besomewhat less than that for the particular tactual stimulus used. Forit is clear that this tactual reaction time is really shorter than thereaction time to a weak current. In making variability a basis ofcomparison it must be assumed that the strength of stimulus is theimportant factor, and that all other variable conditions are, so faras possible, excluded. If, now, on the basis of parity in variabilitywe compare the tactual and electrical reaction times, it is apparentthat the tactual is considerably longer. The tactual average of TableXV. Is 205. 7[sigma], while the electrical reaction time which hasapproximately the same variability is 172. 1[sigma]. It may well beobjected that I have no right to make variability the basis of mycomparison in these experiments, because the work for the variouskinds of stimuli was done under different conditions. Admitting theforce of this objection, and at the same time calling attention to thefact that I do not wish to lay any stress on the results of thecomparisons here made, I take this opportunity to call attention tothe possibility of this criterion. 

The use of variability as a basis of comparison would involve theassumptions (1) that a certain intensity of every stimulus which is tobe considered is capable of producing the shortest possible, or reflexreaction, and that this reaction is at the same time the leastvariable; (2) that as the strength of a stimulus decreases thevariability increases until the threshold is reached. 

Suppose, now, it is our desire to compare the results of reactions todifferent intensities of electrical and tactual stimuli; let thefigures be as follows:

 Reaction Time. Variability. Stimulus Strength. Elect. Touch. Elect. Touch. 8 50[sigma] 50[sigma] 10[sigma] 10[sigma]. 4 130 155 25 30 2 175 220 40 40 1 300 320 50 60

In the double columns the results for electrical stimuli are givenfirst, and in the second column are the tactual. Stimulus 8 is assumedto be of sufficient strength to induce what may be designated asforced movement, and whatever the quality of the stimulus thisreaction time is constant. I make this statement theoretically, although all the evidence which this work furnishes is in support ofit. So, likewise, is the variability of this type of reaction timesmall and nearly constant. At the other extreme, stimulus 1 is so weakas to be just sufficient to call forth a response; it is the so-calledthreshold stimulus. Whether all qualities of stimulus will give thesame result here is a question to be settled by experimentation. Wundtcontends that such is the case, but the observations I have made onthe electrical and tactual reactions of the frog cause me to doubtthis assumption. It seems probable that the 'just perceptible stimulusreaction time' is by no means the same thing for different qualitiesof stimulus. Those modifications of the vital processes which aloneenable organisms to survive, make their appearance even in theresponse to the minimal stimulus. In one case the just perceptiblestimulus may cause nothing more than slight local changes incirculation, excretion, muscular action; in another it may produce, just because of the particular significance of the stimulus to thelife of the organism, a violent and sudden motor reaction. But grant, if you will, that the threshold reaction time is the same for allkinds of stimuli, and suppose that the variability is fairly constant, then, between the two extremes of stimuli, there are gradations instrength which give reaction times of widely differing variabilities. If, now, at some point in the series, as, for instance, to stimulus 2, the variability for different kinds of stimuli is the same either withreference to the reaction time (ratio) or absolutely, whatinterpretation is to be put upon the fact? Is it to be regarded asmerely a matter of chance, and unworthy of any special attention, orshould it be studied with a view to finding out precisely whatvariability itself signifies? It is obvious that any discussion ofthis subject, even of the possible or probable value of variability asa criterion for the comparative study of stimuli, can be of littlevalue so long as we do not know what are the determining factors ofvariations of this sort. The only suggestion as to the meaning of sucha condition (_i. E. _, equal variability at some point)--and our studiesseem to show it for touch and electrical stimulation--which I feeljustified in offering at present, is that parity in variabilityindicates equality in strength of stimuli, that is, the electricalstimulus which has a reaction time of the same variability as atactual stimulus has the same effect upon the peripheral nervoussystem as the tactual, it produces the same amplitude and perhaps thesame form of wave, but the reaction times for the two stimuli differbecause of the biological significance of the stimuli. The chances arethat this is wholly dependent upon the central nervous system. 

IX. SUMMARY. 

1. This paper gives the results of some experiments on the frog todetermine its electrical and tactual reaction time. It is thebeginning of comparative reaction-time studies by which it is hopedimportant information may be gained concerning the significance andmodes of action of the nervous system. Comparative physiology hasalready made clear that the time relations of neural processes deservecareful study. 

2. According to the strength of the stimulus, electric stimulation ofthe frog causes three types of reaction: (1) A very weak or thresholdstimulus results in a deliberate or delayed reaction, the time ofwhich may be anywhere from 300[sigma] (thousandths of a second) to2, 000[sigma]. (2) A very strong stimulus causes a spinal reflex, whosetime is from 50 to 80[sigma]; and (3) a stimulus of intermediatestrength causes a quick instinctive reaction of from 150 to 170[sigma]in duration. 

3. The reaction time for electric stimuli whose relative values were1, 2 and 4 were found to be 300. 9[sigma], 231. 5[sigma] and103. 1[sigma]. 

4. The reaction time of the frog to a tactual stimulus (contact of arubber point) is about 200[sigma]. 

5. The variability of reaction times of the frog is great, andincreases as the strength of the stimulus decreases. 

6. When two kinds of stimuli (_e. G. _, electrical and tactual) givereaction times of equal variability, I consider them directlycomparable. 

7. According to this criterion of comparability the reaction time toelectric stimulation which is comparable with that to tactual is172. 1[sigma]; and it is to be compared with 205. 7[sigma]. Both ofthese have a variability of approximately 34[sigma]. On this basis onemay say that the tactual reaction time is considerably longer than theelectrical. 

PART III. AUDITORY REACTIONS OF FROGS. 

X. HEARING IN THE FROG. 

A. Influences of Sounds in the Laboratory. 

After determining the simple reaction time of the green frog totactual and electrical stimulation, I attempted to do the same in caseof auditory stimuli. In this I was unsuccessful because of failure toget the animal to give a motor response which could be recorded. Theanimal was placed in an experimenting box with a string attached toone hind leg as in the experiments described in Part II. , and after ithad become accustomed to the situation a sound was made. A wide rangeof sounds were tried, but to none except the croak of another frog wasa motor reaction frequently given. Even a loud noise, such as theexplosion of a large pistol cap, caused a visible motor reaction onlyin rare cases. In fifty trials with this stimulus I succeeded ingetting three reactions, and since all of them measured between 230and 240[sigma] it is perhaps worth while to record the result asindicative of the auditory reaction time. As these were the onlymeasurements obtained, I have no satisfactory basis for the comparisonof auditory with other reaction times. 

The remarkable inhibition of movement shown by the frog in thepresence of strong auditory stimulation, at least what is for thehuman being a strong stimulus, led me to inquire concerning the limitsand delicacy of the sense of hearing in frogs. In the vast quantity ofliterature on the structure and functions of the sense organs of theanimal I have been able to find only a few casual remarks concerninghearing. 

In approaching the problem of frog audition we may first examine thestructure of the ear for the purpose of ascertaining what sounds arelikely to affect the organ. There is no outer ear, but the membranatympani, or ear drum, covered with skin, appears as a flat disc from 5to 10 mm. In diameter on the side of the head just back of the eye anda little below it. In the middle ear there is but one bone, thecolumella, forming the connecting link between the tympanum and theinternal ear. The inner ear, which contains the sense organs, consists of a membranous bag, the chief parts of which are theutriculus, the sacculus, the lagena, and the three semicircularcanals. The cavity of this membranous labyrinth is filled with afluid, the endolymph; and within the utriculus, sacculus and lagenaare masses of inorganic matter called the otoliths. The auditory nerveterminates in eight sense organs, which contain hair cells. There isno cochlea as in the mammalian ear. The assumption commonly made isthat vibrations in the water or air by direct contact cause thetympanic membrane to vibrate; this in turn causes a movement of thecolumella, which is transmitted to the perilymphatic fluid of theinner ear. The sensory hair cells are disturbed by the movements ofthe otoliths in the endolymph, and thus an impulse is originated inthe auditory nerve which results in a sensation more or lessresembling our auditory sensation. It is quite probable that thefrog's sense of hearing is very different from ours, and that it isaffected only by gross air vibrations. This conclusion the anatomy ofthe ear supports. 

Although there does not seem to be a structural basis for a delicatesense of hearing, one must examine the physiological facts at handbefore concluding that frogs do not possess a sense of hearing similarto our own. First, the fact that frogs make vocal sounds is evidencein favor of the hearing of such sounds at least, since it is difficultto explain the origin of the ability to make a sound except throughits utility to the species. Granting, however, that a frog is able tohear the croaks or pain-screams of its own species, the range of thesense still remains very small, for although the race of frogs makes agreat variety of sounds, any one species croaks within a narrow range. 

Having satisfied myself that motor reactions for reaction-timemeasurements could not be gotten to any ordinary sounds in thelaboratory, I tried the effect of the reflex croaking of another frogof the same species. In attempting to get frogs to croak regularly, Itested the effect of removing the brain. The animals are said to croakreflexly after this operation whenever the back is stroked; but forsome reason I have never been successful in getting the reactionuniformly. In many cases I was able to make normal animals croak byrubbing the back or flanks, and to this sound the animals underobservation occasionally responded by taking what looked like anattitude of attention. They straightened up and raised the head as iflistening. In no case have other motor responses been noticed; and theabove response was so rare that no reaction-time measurements could bemade. 

Again, while working with the green frog on habit formation, I one dayplaced two animals in a labyrinth from which they could escape byjumping into a tank of water. Several times when one frog jumped intothe water I noticed the other one straighten up and hold the'listening' or 'attentive' attitude for some seconds. As the animalscould not see one another this is good evidence of their ability tohear the splash made by a frog when it strikes the water. 

B. Influence of Sounds in Nature. 

In order to learn how far fear and artificial conditions were causesof the inhibition of response to sounds in the laboratory, and how farthe phenomenon was indicative of the animal's inability to perceivesounds, I observed frogs in their native haunts. 

By approaching a pond quietly, it is easy to get within a few yards offrogs sitting on the banks. In most cases they will not jump untilthey have evidence of being noticed. Repeatedly I have noted that itis never possible to get near to any frogs in the same region afterone has jumped in. In this we have additional proof that they hear thesplash-sound. To make sure that sight was not responsible for thison-guard condition in which one finds the frogs after one of theirnumber has jumped into the water, I made observations on animals thatwere hidden from one another. The results were the same. I thereforeconclude that the splash of a frog jumping into the water is not onlyperceived by other frogs in the vicinity, but that it is a peculiarlysignificant sound for them, since it is indicative of danger, andserves to put them 'on watch. '

A great variety of sounds, ranging in pitch from a low tone inimitation of the bull frog's croak to a shrill whistle, and inloudness from the fall of a pebble to the report of a pistol, weretried for the purpose of testing their effects upon the animals intheir natural environment. To no sound have I ever seen a motorresponse given. One can approach to within a few feet of a green frogor bull frog and make all sorts of noises without causing it to giveany signs of uneasiness. Just as soon, however, as a quick movement ismade by the observer the animal jumps. I have repeatedly crept up veryclose to frogs, keeping myself screened from them by bushes or trees, and made various sounds, but have never succeeded in scaring an animalinto a motor response so long as I was invisible. Apparently theydepend almost entirely upon vision for the avoidance of dangers. Sounds like the splash of a plunging frog or the croak or pain-screamof another member of the species serve as warnings, but the animals donot jump into the water until they see some sign of an unusual ordangerous object. On one occasion I was able to walk to a spot where alarge bull frog was sitting by the edge of the water, after the frogsabout it had plunged in. This individual, although it seemed to be onthe alert, let me approach close to it. I then saw that the eye turnedtoward me was injured. The animal sat still, despite the noise I made, simply because it was unable to see me; as soon as I brought myselfwithin the field of vision of the functional eye the frog was off likea flash. 

Many observers have told me that frogs could hear the human voice andthat slight sounds made by a passer-by would cause them to stopcroaking. In no case, however, have such observers been able to assertthat the animals were unaffected by visual stimuli at the same time. Ihave myself many times noticed the croaking stop as I approached apond, but could never be certain that none of the frogs had seen me. It is a noteworthy fact that when one frog in a pond begins to croakthe others soon join it. Likewise, when one member of such a chorus isfrightened and stops the others become silent. This indicates that thecessation of croaking is a sign of danger and is imitated just as isthe croaking. There is in this fact conclusive evidence that theanimals hear one another, and the probability is very great that theyhear a wide range of sounds to which they give no motor reactions, since they do not depend upon sound for escaping their enemies. 

The phenomenon of inhibition of movement in response to sounds whichwe have good reason to think the frogs hear, and to which such ananimal as a turtle or bird would react by trying to escape, is thusshown to be common for frogs in nature as well as in the laboratory. This inhibition is in itself not surprising, since many animalshabitually escape certain of their enemies by remaining motionless, but it is an interesting phenomenon for the physiologist. We have toinquire, for instance, what effects sounds which stimulate theauditory organs and cause the animal to become alert, watchful, yetmake it remain rigidly motionless, have on the primary organic rhythmsof the organism, such as the heart-beat, respiration, and peristalsis. It is also directly in the line of our investigation to inquire howthey affect reflex movements, or the reaction time for any otherstimulus--what happens to the reaction time for an electricalstimulus, for example, if a loud noise precede or accompany theelectrical stimulus. 

For the purpose of determining the range of hearing in the frog, I wasdriven to study the influence of sounds upon respiration. Although theanimals did not make any detectable movement, not even of an eyelid, in response to noises, it seemed not improbable that if the soundsacted as auditory stimuli at all, they would in some degree modify theform or rate of the respiratory movement. 

C. Influence of Sounds on Respiration. [16]

 [16] For full discussion of the normal respiratory movements of the frog see Martin, _Journal of Physiology, _ Vol. 1. , 1878, pp. 131-170. 

The method of recording the respiration was the direct transference ofthe movement of the throat by means of a pivoted lever, one end ofwhich rested against the throat, while the other served as a marker ona revolving drum carrying smoked paper. The frog was put into a smallbox, visual stimuli were, so far as possible, excluded and the leverwas adjusted carefully; a record was then taken for at least half aminute to determine the normal rate of respiration in the absence ofthe stimulus whose effect it was the chief purpose of the experimentto discover. Then, as soon as everything was running smoothly, theauditory stimulus was given. The following records indicate theeffects of a few stimuli upon the rate of breathing:

1. Stimulus, 100 V. Tuning fork. 

Number of respirations for 10 cm. _before_ stimulus 18. 0, 17. 0; numberof respirations for 10 cm. _after_ stimulus 19. 0, 17. 3. 

The records indicate very little change, and contradict one another. For the same stimulus the experiment was tried of taking the normalrespiration record for a complete revolution of the drum, and then atonce taking the record for the same length of time (about two minutes)with the tuning-fork vibrating close to the frog. The following resultis typical and proves that the sound has little effect. 

Number of respirations in a revolution _before_ stimulus: First rev. 88; second rev. 88. Number of respirations in a revolution _during_stimulus: First rev. 87; second rev. 88. 

Concerning the influence of tuning-fork stimuli more will be saidlater in a consideration of the effects of auditory stimuli uponreactions to visual stimuli. 

2. The influence of falling water as an auditory stimulus. Water wasallowed to fall about two feet in imitation, first, of a plungingfrog, and second, of water falling over rocks. In representing theeffect of the stimulus on the rate of respiration, I have given thedistance on the drum covered by the ten complete respirations justpreceding the stimulus and the ten following it. 

 10 Respirations. 10 Respirations. _Before_ Stimulus. _After_ Stimulus. 1st Stim. 13. 0 cm. 11. 8 cm. 2d Stim. 12. 7 cm. 12. 7 cm. 

 With a smaller animal. 

 1st Stim. 5. 4 cm. 4. 8 cm. 2d Stim. 4. 9 cm. 4. 7 cm. Average for 5 5. 00 cm. 4. 86 cm. 

_These records show a marked increase in the rate of respiration justafter the auditory stimulus is given for the first time. _ The stimulushas less effect when repeated after an interval of one or two minutes, and if repeated several times it finally causes no noticeable change. On the whole, the sound of falling water seems to arouse the animalsto fuller life. The stimulus appears to interest them, and itcertainly accelerates respiration. This is precisely what one wouldexpect from a sound which is of special significance in the life ofthe animal. 

3. In case of a loud shrill whistle inhibition of respirationresulted. This probably means that the frogs were frightened by thesound. Falling water served rather to excite their natural-habitatassociations, whereas, the whistle, being an uncommon and unassociatedsound, caused fear. It is evident to the casual observer that the frogsometimes inhibits and sometimes increases its respiratory movementswhen frightened, so the result in this experiment is in no waysurprising. I am by no means certain, however, that a longer series ofobservations on several individuals would give constant inhibitoryresults. My immediate purpose in the work was to get evidence ofhearing; the respiratory changes were of secondary importance, although of such great interest that I have planned a more thoroughspecial study of them for the future. 

A few sample results showing the influence of the whistle upon a smallbull-frog follow:

 Length of 10 Resps. Length of 10 Resps. _Before_ Stimulus in cm. _After_ Stimulus in cm. 1st Stim. 6. 0 6. 7 2d " 5. 4 6. 0 3d " 5. 9 5. 8 1st " 4. 7 5. 4 2d " 4. 4 4. 6

As a test-check observation for comparison, the influence of a visualstimulus upon respiration was noted under the same conditions as forthe auditory. Effect of turning on electric light over box. 

 Length in cm. Of 10 Resps. Length in cm. Of 10 Resps. _Before_ Stimulus. _After_ Stimulus. 4. 8 4. 4 5. 3 4. 6 4. 5 4. 0

These results indicate an increase in the respiration rate due to thevisual stimulus. 

4. Of the other auditory stimuli used, the pistol-cap explosion gavevery irregular results. For one animal it caused acceleration, foranother inhibition. There is, however, good evidence that the soundswere heard. 

5. The ringing of a bell gave results similer to those for a whistle, and the sound of a 500 S. V. Tuning fork usually caused a slightincrease in the rate of breathing. In these experiments I thereforehave evidence, through their effects upon respiration, of the frog'sability to hear sounds ranging from 50 V. To at least 1, 000 V. 

The croak of the green frog ranges from 100 to 200 V. , so far as Ihave been able to determine. That of the bull frog is lower, from 50to 75; and in the leopard frog the range is from 80 to 125. The latteris very different from the green frog in its croaking, in that itcroaks whenever disturbed, whereas, the green frog rarely responds inthat way to a stimulus. 

We are now in a position to say that the failure of frogs to givemotor reactions to strong auditory stimuli is not due to theirinability to be affected by the stimuli, but is a genuine inhibitionphenomenon. 

XI. THE EFFECTS OF AUDITORY STIMULI ON VISUAL REACTIONS. 

Further experimental evidence of hearing was gotten from some workdone to test the influence of sounds upon motor reactions to visualstimuli. Frogs, like most other amphibians, reptiles and fishes, areattracted by any small moving object and usually attempt to seize it. They never, so far as I have noticed, feed upon motionless objects, but, on the other hand, will take almost anything which moves. Apparently the visual stimulus of movement excites a reflex. A verysurprising thing to those who are unfamiliar with frog habits is thefear which small frogs have of large ones. Put some green frogs orsmall bull frogs into a tank with large bull frogs, and the littleones will at once show signs of extreme fear; they jump about in themost excited manner and try hard to escape. The cause of their fearsoon appears, since it is usually only a few minutes until the littleones are swallowed by their wide-mouthed, cannibalistic fellows. 

It is, moreover, well known that a bit of red flannel fastened to ahook attracts frogs and is an excellent method of capturing them. Redseems to be the color which they most readily notice. 

This tendency of the frog to attempt to seize any moving object I madeuse of to test the value of sounds. By placing a frog in a glassaquarium which was surrounded by a screen, back of which I could workand through a small hole in which I was able to watch the animalwithout being noticed by it, and then moving a bit of red cardboardalong one side of the aquarium, I could get the frog to jump at itrepeatedly. In each attempt to get the moving object, the animalstruck its head forcibly against the glass side of the aquarium. Therewas, therefore, reason to think that a few trials would lead to theinhibition of the reaction. Experiment discovered the fact that ahungry frog would usually jump at the card as many as twenty times inrapid succession. 

In this reaction to a visual stimulus there appeared good material fortesting audition. I therefore arranged a 500 S. V. Tuning fork over theaquarium and compared the reactions of animals to the visual stimulusalone, with that to the visual stimulus when accompanied by anauditory stimulus. The tuning-fork sound was chosen because it seemedmost likely to be significant to the frog. It is similar to the soundsmade by the insects upon which frogs feed. For this reason one wouldexpect that the sight of a moving object and the sound of atuning-fork would tend to reėnforce one another. 

The experiments were begun with observations on the effects of movingobjects on the respiration. In case of a normal rate of 54respirations per minute sight of the red object caused an increase to58. Then the same determination was made for the auditory stimulus. The tuning-fork usually caused an increase in rate. In a typicalexperiment it was from 65 per minute to 76. The observations proveconclusively that the 500 S. V. Sound is heard. My attention was turnedto the difference of the environment of the ear in its relation tohearing. Apparently frogs hear better when the tympanum is partiallyunder water than when it is fully exposed to the air. 

Having discovered by repeated trials about how vigorously andfrequently a frog would react to the moving red card, I tried theeffect of setting the fork in vibration a half minute before showingthe card. It was at once evident that the sound put the frog on thealert, and, when the object came into view, it jumped at it morequickly and a greater number of times than when the visual stimuluswas given without the auditory. This statement is based on the studyof only two animals, since I was unable to get any other frogs thatwere in the laboratory at the time to take notice of the redcardboard. This was probably because of the season being winter. Iventure to report the results simply because they were so definite asto point clearly to the phenomenon of the reėnforcement of thevisual-stimulus reaction by an auditory stimulus. 

Concerning the influence of this combining of stimuli on the reactiontime, I am only able to say that the reaction to the moving objectoccurred quicker in the presence of the auditory stimulus. When thered card was shown it was often several seconds before the frog wouldnotice it and attempt to get it, but when the sound also was given theanimal usually noticed and jumped toward the moving card almostimmediately. 

Unfortunately I have thus far been unable to get chronoscopicmeasurements of the reaction times in this reėnforcement phenomenon. Ihope later to be able to follow out the interesting suggestions ofthese few experiments in the study of reėnforcement and inhibition ascaused by simultaneously given stimuli. 

A few observations made in connection with these experiments are ofgeneral interest. The frog, when it first sees a moving object, usually draws the nictitating membrane over the eye two or three timesas if to clear the surface for clearer vision. Frequently this actionis the only evidence available that the animal has noticed an object. This movement of the eye-lids I have noticed in other amphibians andin reptiles under similar conditions, and since it always occurs whenthe animals have need of the clearest possible vision, I think theabove interpretation of the action is probably correct. 

Secondly, the frog after getting a glimpse of an object orientsitself by turning its head towards the object, and then waits for afavorable chance to spring. The aiming is accurate, and as previouslystated the animal is persistent in its attempts to seize an object. 

XII. THE PAIN-SCREAM OF FROGS. 

While making measurements of the frog's reaction time to electricalstimulation, I noticed that after a few repetitions of a 2-volt, . 0001-ampčre stimulus an animal would frequently make a very peculiarnoise. The sound is a prolonged scream, like that of a child, made byopening the mouth widely. The ordinary croak and grunt are made withclosed or but slightly opened mouth. The cry at once reminds one ofthe sounds made by many animals when they are frightened. The rabbit, for example, screams in much the same way when it is caught, as doalso pigs, dogs, rats, mice and many other animals. The questionarises, is this scream indicative of pain? While studying reactiontime I was able to make some observations on the relation of thescream to the stimulus. 

First, the scream is not given to weak stimuli, even upon manyrepetitions. Second, it is given to such strengths of an electricalstimulus as are undoubtedly harmful to the animal. Third, after a froghas been stimulated with a strong current (two volts), until thescream is given with almost every repetition, it will scream in thesame way when even a weak stimulus is applied. If, for instance, aftera two-volt stimulus has been given a few times, the animal be merelytouched with a stick, it will scream. It thus appears as if the strongstimulus increases the irritability of the center for thescream-reflex to such an extent that even weak stimuli are sufficientto cause the reaction. Are we to say that the weak stimulus is painfulbecause of the increased irritability, or may it be concluded that thereflex is in this case, like winking or leg-jerk or the head-loweringand puffing, simply a forced movement, which is to be explained as anhereditary protective action, but not as necessarily indicative of anysort of feeling. Clearly if we take this stand it may at once be saidthat there is no reason to believe the scream indicative of pain atany time. And it seems not improbable that this is nearer the truththan one who hears the scream for the first time is likely to think. 

The pain-scream is of interest in this consideration of auditoryreactions because it increases the range of sounds which we shouldexpect frogs to hear if we grant the probability of them hearing theirown voices. 

It may be worth while to recall at this point the fact that a whistlefrom the human lips--the nearest approach to the pain-scream among thesounds which were used as stimuli in the experiments onrespiration--caused marked inhibition of respiration. Perhaps thisfact may be interpreted in the light of the pain-scream reaction. Imay add that I have never seen a frog give a motor reaction to thepain-scream. Thinking it would certainly alarm the animals and causethem to make some movement which would serve for reaction-timemeasurements, I made repeated trials of its effects, but could neverdetect anything except respiratory changes. 

 * * * * *

 STUDIES IN PSYCHOLOGICAL THEORY. 

 * * * * *

THE POSITION OF PSYCHOLOGY IN THE SYSTEM OF KNOWLEDGE. 

BY HUGO MÜNSTERBERG. 

The modern efforts to bring all sciences into a system or at least toclassify them, from Bacon to Spencer, Wundt and Pearson have never, ifwe abstract here from Hegel, given much attention to those questionsof principle which are offered by the science of psychology. Of coursethe psychological separation of different mental functions has oftengiven the whole scheme for the system, the classification thus beingtoo often more psychological than logical. Psychology itself, moreover, has had for the most part a dignified position in thesystem; even when it has been fully subordinated to the biologicalsciences, it was on the other hand placed superior to the totality ofmental and moral sciences, which then usually have found their unityunder the positivistic heading 'sociology. ' And where the independentposition of psychology is acknowledged and the mental and moralsciences are fully accredited, as for instance with Wundt, psychologyremains the fundamental science of all mental sciences; the objectswith which philology, history, economics, politics, jurisprudence, theology deal are the products of the processes with which psychologydeals, and philology, history, theology, etc. , are thus related topsychology, as astronomy, geology, zoölogy are related to physics. There is thus nowhere a depreciation of psychology, and yet it is notin its right place. Such a position for psychology at the head of all'Geisteswissenschaften' may furnish a very simple classification forit, but it is one which cannot express the difficult character ofpsychology and the complex relations of the system of mental sciences. The historical and philological and theological sciences cannot besubordinated to psychology if psychology as science is to becoördinated with physics, that is, if it is a science which describesand explains the psychical objects in the way in which physicsdescribes and explains the physical objects. On the other hand, if itmeans in this central position of mental sciences a science which doesnot consider the inner life as an object, but as subjective activityneeding to be interpreted and subjectively understood, not as to itselements, but as to its meaning, then we should have two kinds ofpsychology, one which explains and one which interprets. They wouldspeak of different facts, the one of the inner life as objectivecontent of consciousness, as phenomenon, the other of the inner lifeas subjective attitude, as purpose. 

The fact is, that these two sciences exist to-day. There arepsychologists who recognize both and keep them separated, others whohold to the one or the other as the only possible view; they arephenomenalists or voluntarists. Mostly both views are combined, eitheras psychological voluntarism with interposed concessions tophenomenalism or as phenomenalism with the well-known concessions tovoluntarism at the deciding points. Further, those who claim thatpsychology must be phenomenalistic--and that is the opinion of thepresent writer--do not on that account hold that the propositions ofvoluntarism are wrong. On the contrary: voluntarism, we say, is rightin every respect except in believing itself to be psychology. Voluntarism, we say, is the interpretative account of the real life, of immediate experience, whose reality is understood by understandingits meaning sympathetically, but we add that in this way an objectivedescription can never be reached. Description presupposesobjectivation; another aspect, not the natural aspect of life, must bechosen to fulfill the logical purposes of psychology: thevoluntaristic inner life must be considered as content ofconsciousness while consciousness is then no longer an active subjectbut a passive spectator. Experience has then no longer any meaning ina voluntaristic sense; it is merely a complex of elements. We claimthat every voluntaristic system as far as it offers descriptions andexplanations has borrowed them from phenomenalistic psychology and isfurther filled up by fragments of logic, ethics and ęsthetics, all ofwhich refer to man in his voluntaristic aspect. We claim, therefore, that such a voluntaristic theory has no right to the name psychology, while we insist that it gives a more direct account of man's real lifethan psychology can hope to give, and, moreover, that it is thevoluntaristic man whose purpose creates knowledge and thus creates thephenomenalistic aspect of man himself. 

We say that the voluntaristic theory, the interpretation of our realattitudes, in short teleological knowledge, alone can account for thevalue and right of phenomenalistic psychology and it thus seems unfairto raise the objection of 'double bookkeeping. ' These two aspects ofinner life are not ultimately independent and exclusive; thesubjective purposes of real life necessarily demand the labors ofobjectivistic psychology. The last word is thus not dualistic butmonistic and the two truths supplement each other. But thissupplementation must never be misinterpreted as meaning that the twosciences divide inner experience, as if, for instance, thephenomenalistic study dealt with perceptions and ideas, thevoluntaristic with feelings and volitions. No, it is really adifference of logical purpose of treatment and thus a difference ofpoints of view only; the whole experience without exception must bepossible material for both. There is no feeling and no volition whichis not for the phenomenalist a content of consciousness and nothingelse. There is, on the other hand, no perception and no idea which isnot, or better, ought not to be for the voluntarist a means, an aim, atool, an end, an ideal. In that real life experience of which thevoluntarist is speaking, every object is the object of will and thosereal objects have not been differentiated into physical things underthe abstract categories of mechanics on the one hand, and psychicalideas of them in consciousness on the other; the voluntarist, if he isconsistent, knows neither physical nor psychical phenomena. Phenomenalist and voluntarist thus do not see anything under the sameaspect, neither the ideas nor the will. 

This difference is wrongly set forth if the antithesis to voluntarismis called intellectualism. Intellectualism is based on the category ofjudgment, and judgment too is a ideological attitude. Phenomenalismdoes not presuppose a subject which knows its contents but a subjectwhich simply _has_ its contents; the consciousness which has thethought as content does not take through that the voluntaristicattitude of knowing it and the psychologist has therefore no reason toprefer the thought to the volition and thus to play theintellectualist. If the psychologist does emphasize the idea and itselements, the sensations, it is not because they are vehicles ofthought but because their relations to physical objects make themvehicles of communication. The elements of ideas are negotiable andthus through their reference to the common physical world indirectlydescribable; as the elements of ideas are alone in this position, thepsychologist is obliged to consider all contents of consciousness, ideas and volitions alike, as complexes of sensations. 

The antithesis is also misinterpreted, or at least wrongly narrowed, if it is called voluntarism _versus_ associationism. Recentdiscussions have sufficiently shown that the principle of associationis not the only possible one for phenomenalistic theories. Ifassociationism is identified with objective psychology, all thewell-founded objections to the monopoly of the somewhat sterileprinciple of association appear as objections to phenomenalism inpsychology, and voluntaristic theories, especially those which workwith the teleological category of apperception, are put in its place. But without returning to apperceptionism we can overcome theone-sidedness of associationism if full use is made of the means whichthe world of phenomena offers to theory. The insufficiency ofassociationism disappears if the content of consciousness isconsidered as variable not only as to quality and intensity but alsoas to vividness. This variation of vividness, on the other hand, is noexception from the psychophysical parallelism as soon as the psychicalprocess is considered as dependent not only upon the local andquantitative differences of the sensory process but also upon themotor function of the central physical process. The one-sidedness ofthe physiological sensory theories has been the hidden reason for theone-sidedness of associationism. The sensory-motor system must beunderstood as the physical basis of the psychophysical process and thevariations in the motor discharge then become conditions of thosepsychical variations of vividness which explain objectively all thosephenomena in whose interest associationism is usually supplemented byapperceptionism. The association theory must thus be given up in favorof an 'action-theory'[1] which combines the consistency ofphenomenalistic explanation with a full acknowledgment of theso-called apperceptive processes; it avoids thus the deficiency ofassociationism and the logical inconsistency of apperceptionism. 

 [1] H. Münsterberg, 'Grundzüge der Psychologie. ' Bd. I. , Leipzig, 1900, S. 402-562. 

Only if in this way the sciences of voluntaristic type, including allhistorical and normative sciences, are fully separated fromphenomenalistic psychology, will there appear on the psychologicalside room for a scientific treatment of the phenomena of social life, that is, for sociology, social psychology, folk-psychology, psychicalanthropology and many similar sciences. All of them have been in theusual system either crowded out by the fact that history and the othermental sciences have taken all the room or have been simply identifiedwith the mental sciences themselves. And yet all those sciences exist, and a real system of sciences must do justice to all of them. A modernclassification has perhaps no longer the right as in Bacon's time toimprove the system by inventing new sciences which have as yet noexistence, but it has certainly the duty not to ignore importantdepartments of knowledge and not to throw together different scienceslike the descriptive phenomenalistic account of inner life and itsinterpretative voluntaristic account merely because each sometimescalls itself psychology. A classification of sciences which is to bemore than a catalogue fulfills its logical function only by a carefuldisentanglement of logically different functions which are externallyconnected. Psychology and the totality of psychological, philosophicaland historical sciences offer in that respect far more difficulty thanthe physical sciences, which have absorbed up to this time the chiefinterest of the classifier. It is time to follow up the ramificationsof knowledge with special interest for these neglected problems. It isclear that in such a system sciences which refer to the same objectsmay be widely separated, and sciences whose objects are unlike may begrouped together. This is not an objection; it indicates that asystem is more than a mere pigeon-holing of scholarly work, that itdetermines the logical relations; in this way only can it indeedbecome helpful to the progress of science itself. 

The most direct way to our end is clearly that of graphicrepresentation wherein the relations are at once apparent. Of coursesuch a map is a symbol and not an argument; it indicates the resultsof thought without any effort to justify them. I have given myarguments for the fundamental principles of the divisions in my'Grundzüge der Psychologie' and have repeated a few points morepopularly in 'Psychology and Life, ' especially in the chapter on'Psychology and History. ' And yet this graphic appendix to theGrundzüge may not be superfluous, as the fulness of a bulky volumecannot bring out clearly enough the fundamental relations; the detailhides the principles. The parallelism of logical movements in thedifferent fields especially becomes more obvious in the graphic form. Above all, the book discussed merely those groups which had directrelation to psychology; a systematic classification must leave noremainder. Of course here too I have not covered the whole field ofhuman sciences, as the more detailed ramification offers for ourpurpose no logical interest; to subdivide physics or chemistry, thehistory of nations or of languages, practical jurisprudence ortheology, engineering or surgery, would be a useless overburdening ofthe diagram without throwing new light on the internal relations ofknowledge. 

Without now entering more fully into any arguments, I may indicate ina few words the characteristic features of the graphically presentedproposition. At the very outset we must make it clear that phenomenaand voluntaristic attitudes are not coördinated, but that the realityof phenomena is logically dependent upon voluntaristic attitudesdirected towards the ideal of knowledge. And yet it would bemisleading to place the totality of phenomenalistic sciences as asubdivision under the teleological sciences. Possible it would be; wemight have under the sciences of logical attitudes not only logic andmathematics but as a subdivision of these, again, the sciences whichconstruct the logical system of a phenomenalistic world--physicsbeing in this sense merely mathematics with the conception ofsubstance added. And yet we must not forget that the teleologicalattitudes, to become a teleological science, must be also logicallyreconstructed, as they must be teleologically connected, and thus inthis way the totality of purpose-sciences might be, too, logicallysubordinated to the science of logic. Logic itself would thus become asubdivision of logic. We should thus move in a circle, from which theonly way out is to indicate the teleological character of all sciencesby starting not with science but with the strictly teleologicalconception of life--life as a system of purposes, felt in immediateexperience, and not as the object of phenomenalistic knowledge. Lifeas activity divides itself then into different purposes which wediscriminate not by knowledge but by immediate feeling; one of them isknowledge, that is, the effort to make life, its attitudes, its meansand ends a connected system of overindividual value. In the service ofthis logical task we connect the real attitudes and thus come to theknowledge of purposes: and we connect the means and ends--byabstracting from our subjective attitudes, considering the objects ofwill as independent phenomena--and thus come to phenomenalisticknowledge. At this stage the phenomenalistic sciences are no longerdependent upon the teleological ones, but coördinated with them;physics, for instance, is a logical purpose of life, but not a branchof logic: the only branch of logic in question is the philosophy ofphysics which examines the logical conditions under which physics ispossible. 

One point only may at once be mentioned in this connection. While wehave coördinated the knowledge of phenomena with the knowledge ofpurposes we have subordinated mathematics to the latter. As a matterof course much can be said against such a decision, and the authorityof most mathematicians would be opposed to it. They would say that themathematical objects are independent realities whose properties westudy like those of nature, whose relations we 'observe, ' whoseexistence we 'discover' and in which we are interested because theybelong to the real world. All that is true, and yet the objects of themathematician are objects made by the will, by the logical will, only, and thus different from all phenomena into which sensationenters. The mathematician, of course, does not reflect on the purelylogical origin of the objects which he studies, but the system ofknowledge must give to the study of the mathematical objects its placein the group where the functions and products of logical thought areclassified. The arithmetical or geometrical material is a freecreation, and a creation not only as to the combination ofelements--that would be the case with many laboratory substances ofthe chemist too--but a creation as to the elements themselves, and thevalue of the creation, its 'mathematical interest, ' is to be judged byideals of thought, that is, by logical purposes. No doubt this logicalpurpose is its application in the world of phenomena, and themathematical concept must thus fit the world so absolutely that it canbe conceived as a description of the world after abstracting not onlyfrom the will relations, as physics does, but also from the content. Mathematics would then be the phenomenalistic science of the form andorder of the world. In this way mathematics has a claim to places inboth fields: among the phenomenalistic sciences if we emphasize itsapplicability to the world, and among the teleological sciences if weemphasize the free creation of its objects by the logical will. Itseems to me that a logical system as such has to prefer the latteremphasis; we thus group mathematics beside logic and the theory ofknowledge as a science of objects freely created for purposes ofthought. 

All logical knowledge is divided into Theoretical and Practical. Themodern classifications have mostly excluded the practical sciencesfrom the system, rightly insisting that no facts are known in thepractical sciences which are not in principle covered by thetheoretical sciences; it is art which is superadded, but not a newkind of knowledge. This is quite true so far as a classification ofobjects of knowledge is in question, but as soon as logical tasks assuch are to be classified and different aspects count as differentsciences, then it becomes desirable to discriminate between thesciences which take the attitude of theoretical interest and thosewhich consider the same facts as related to certain human ends. But wemay at first consider the theoretical sciences only. They deal eitherwith the objectified world, with objects of consciousness which aredescribable and explainable, or with the subjectivistic world of reallife in which all reality is experienced as will and as object ofwill, in which everything is to be understood by interpretation of itsmeaning. In other words, we deal in one case with phenomena and in theother with purposes. 

The further subdivision must be the same for both groups--that whichis merely individual and that which is 'overindividual'; we prefer thelatter term to the word 'general, ' to indicate at once that not anumerical but a teleological difference is in question. A phenomenonis given to overindividual consciousness if it is experienced with theunderstanding that it can be an object for every one whom weacknowledge as subject; and a purpose is given to overindividual willin so far as it is conceived as ultimately belonging to every subjectwhich we acknowledge. The overindividual phenomena are, of course, thephysical objects, the individual phenomena the psychical objects, theoverindividual purposes are the norms, the individual purposes are theacts which constitute the historical world. We have thus fourfundamental groups: the physical, the psychological, the normative andthe historical sciences. 

Whoever denies overindividual reality finds himself in the world ofphenomena a solipsist and in the world of purposes a sceptic: there isno objective physical world, everything is my idea, and there is noobjective value, no truth, no morality, everything is my individualdecision. But to deny truth and morality means to contradict the verydenial, because the denial itself as judgment demands acknowledgmentof this objective truth and as action demands acknowledgment of themoral duty to speak the truth. And if an overindividual purpose cannotbe denied, it follows that there is a community of individual subjectswhose phenomena cannot be absolutely different: there must be anobjective world of overindividual objects. 

In each of the four groups of sciences we must consider the factseither with regard to the general relations or with regard to thespecial material; the abstract general relations refer to everypossible material, the concrete facts which fall under them demandsciences of their own. In the world of phenomena the general relationsare causal laws--physical or psychical laws; in the world of purposestheories of teleological interrelations--normative or historical; thespecific concrete facts are in the world of phenomena objects, physical or psychical objects, in the world of purposes acts ofwill--specific norms or historical acts. If we turn first tophenomena, the laws thereof are expressed in the physical sciences, bymechanics, physics, chemistry, and we make mechanics the superior aschemistry must become ultimately the mechanics of atoms. In thepsychological sciences the science of laws is psychology, with theside-branch of animal psychology, while human psychology refers toindividuals and to social groups. Social psychology, as over againstindividual psychology, is thus a science of general laws, the laws ofthose psychological phenomena which result from the mutual influenceof several individuals. 

On the other hand, we have as the special concrete products of thelaws, the objects themselves, and the most natural grouping of themmay be from whole to part. In the physical world it means that westart from the concrete universe, turning then to the earth, then tothe objects on the earth, inorganic and organic. There is here nological difficulty. Each one of these objects can be considered inthree aspects, firstly as to its structure, secondly as to its speciallaws, that is, the special function of the object as related to thegeneral sciences of physics and chemistry, and thirdly as to itsnatural development. If we apply these three methods of study to thewhole universe we have astronomy, astrophysics and cosmology, to thewhole earth, geography, geophysics, geology, to animals, zoölogy, physiology, comparative anatomy, and so on. 

The special phenomena in the framework of the psychological sciencesgroup themselves in the same logical order, from the whole to thepart. The psychological totality is empirical mankind, and as weselect the earth as the one part of the universe which is the habitatof man, so our scientific interest must move from the whole psychicalhumanity to those phenomena of human life which are the vehicle of ourcivilization, from mankind to its most important function, theassociation of man; and as we moved from earth to the special objectson earth, so we may turn from association to the special phenomenawhich result from association. If we separated further the inorganicfrom the organic, we must here separate the products ofundifferentiated and of differentiated association. The science ofmankind is race psychology, the science of the association of man issociology, the science of the results of undifferentiated associationis Völkerpsychologie, folk psychology. The science of products ofdifferentiated association has no special name; its subject matter isthe whole of historical civilization considered as a psychologicalnaturalistic phenomenon. As soon as we follow the ramification stillfurther we have to do with the special kinds of these products, thatis, with the volitions, thoughts, appreciations and beliefs. In theundifferentiated associations they give us morals and habits, languages and enjoyments and mythological ideas, while theindividually differentiated association gives political, legal andeconomic life, knowledge, art and religion: all of course merely ascausal, not as teleological processes, and thus merely aspsychological and not as historical material. Here, as with thephysical phenomena, the structure, the special laws and thedevelopment must be everywhere separated, giving us three sciences inevery case. For instance, the study of mankind deals with thedifferences of mental structure in psychical anthropology, with thespecial psychical laws in race psychology and with the development incomparative psychology. The chief point for us is that socialpsychology, race psychology, sociology, folk psychology, etc. , areunder this system sharply differentiated sciences and that they do notat all overlap the real historical sciences. There is no historicalproduct of civilization which does not come under their method but itmust be conceived as a causal phenomenon, not as related to thepurposes of the real man, and thus even the development means merely agrowing complication of naturalistic processes and not history in theteleological sense. 

We turn to the normative sciences. The general theory of theoverindividual purposes is metaphysics; the special overindividualacts are those which constitute the normative volitions, connected inthe philosophy of morals, the philosophy of state and the philosophyof law, those which constitute the normative thoughts and finallythose which constitute the normative appreciations and beliefs, connected in ęsthetics and the philosophy of religion. Especialinterest belongs to the philosophy of thought. We have discussed thereasons why we group mathematics here and not among thephenomenalistic sciences. We have thus one science which dealscritically with the presuppositions of thought, _i. E. _ the theory ofknowledge or epistemology, which can be divided into the philosophy ofphysical sciences, the philosophy of psychological sciences, thephilosophy of normative sciences and the philosophy of historicalsciences. We have secondly the science of the processes of thoughtdealing with concepts, judgments and reasoning, _i. E. _, logic, and wehave finally the science of those objects which the thought createsfreely for its own purposes and which are independent from the contentof the world, _i. E. _, mathematics, which leads to the qualitativeaspect of general mathematics and the quantitative aspect of concretemathematics. For our purposes it may be sufficient to separateexternally algebra, arithmetic, analysis and geometry. In this way allthe philosophical sciences find their natural and necessary place inthe system, while it has been their usual lot to form an appendix tothe system, incommensurable with the parts of the system itself, evenin the case that the other scheme were not preferred, to make ethics, logic, ęsthetics, epistemology and metaphysics merely special branchesof positivistic sociology and thus ultimately of biology. 

In the historical sciences the general theory which stands overagainst the special acts has a special claim on our attention. We maycall it the philosophy of history. That is not identical with thephilosophy of historical sciences which we mentioned as a part ofepistemology. The philosophy of historical sciences deals with thepresuppositions by which historical teleological knowledge becomeslogically possible. The philosophy of history seeks a theory whichconnects the special historical acts into a unity. It has twobranches. It is either a theory of the personality, creating a theoryof real individual life as it enters as ideological factor intohistory, or it seeks the unity of entire humanity. The theory ofpersonality shows the teleological interrelation of our purposes; thetheory of humanity shows the teleological interrelation of allnations. The name philosophy of history has been used mostly for thetheory of humanity only, abstracting from the fact that it has beenoften misused for sociology or for the psychology of history or forthe philosophy of historical sciences--but the name belongs also tothe theory of personality. This theory of personality is exactly thatsecond kind of 'psychology' which does not describe and does notexplain but which interprets the inner teleological connections of thereal man. It is 'voluntaristic psychology' or, as others call it whosee correctly the relation of this science to history, 'historicalpsychology. ' It is practically 'apperceptionistic psychology. ' Thespecial activities of the historical man divide themselves again intovolitions, thoughts, appreciations and beliefs, with their realizationin the state, law, economical systems, knowledge, art and religion. Each of these special realizations must allow the same manifoldness intreatment which we found with the special physical or psychicalobjects; we can ask as to structure, relation to the general view anddevelopment. But in accordance with the teleological material thestudy of the structure here means 'interpretation, ' the study of thegeneral relations here means study of the relation to civilization, and the study of the development here means the real history. We have, thus, for the state or law or economy or knowledge or art or religionalways one science which interprets the historical systems of state, etc. , in a systematic and philological way, one science which dealswith its function in the historical world and one which studiesbiographically and nationally the history of state, law, economicallife, science, art or religion. 

In the sphere of the practical sciences the divisions of thetheoretical sciences must repeat themselves. We have thus appliedphysical, applied psychological, applied normative and appliedhistorical sciences, and it is again the antithesis of psychologicaland of historical sciences which is of utmost importance and yet toooften neglected. The application of physical sciences, as inengineering, medicine, etc. , or the application of normativeknowledge in the sciences of criticism do not offer logicaldifficulty, but the application of psychological and historicalknowledge does. Let us take the case of pedagogy or of penology, merely as illustrations. Is the application of phenomenalisticpsychology or the application of teleological voluntarism in question?Considering the child, the criminal, any man, as psychophysicalapparatus which must be objectively changed and treated, we haveapplied psychology; considering him as subject with purposes, asbearer of an historical civilization whose personalities must beinterpreted and understood and appreciated, then we need appliedhistorical knowledge. In the first case the science of pedagogy is apsycho-technical discipline which makes education mechanical anddeprives the teacher of the teleological attitude of innerunderstanding; in the second case it is a science of real educationfar removed from psychology. All the sciences which deal with servicein the system of civilization, service as teacher, as judge, as socialhelper, as artist, as minister, are sciences which apply theteleological historical knowledge, and their meaning is lost if theyare considered as psycho-technical sciences only. 

LIFE (in its immediate reality, felt as a system of telelogical| experiences, involving the acknowledgement of other subjects of| experiences)||-VOLITION (will aiming towards new experiences). | |-Individual: _Practical Life. _| |-Overindividual: _Mortality. _||-THOUGHT (will acknowledging the connection of experiences). | |-Individual: _Judgement_| |-Overindividual: TRUTH| |-THEORETICAL KNOWLEDGE (connection of experiences determined by| | | pure experience). | | || | |-KNOWLEDGE OF PHENOMENA (connection of experiences after| | | | abstracting their will relations). | | | |-Knowledge of Phenomena Given to Overindividual Consciousness. | | | | |-I. PHYSICAL SCIENCES. | | | | |-A. GENERAL LAWS. | | | | | |-Mechanics. | | | | | |-Physics. | | | | | |-Chemistry. | | | | || | | | |-B. SPECIAL OBJECTS. | | | | |-1. Universe. | | | | | |-Astronomy _a, b, c_. | | | | || | | | |-2. Special Parts. | | | | | |-Geography _a, b, c_. | | | | || | | | |-3. Special Objects on Earth. | | | | |-Inorganic. | | | | | |-Mineralogy _a, b, c_. | | | | || | | | |-Organic. | | | | |-Plants. | | | | | |-Botany _a, b, c_. | | | | || | | | |-Animals. | | | | |-Zoology _a, b, c_. | | | | |-Anthropology _a, b, c_. | | | || | | |-Knowledge of Phenomena given to Indiviual Consciousness. | | | |-II. PSYCHOLOGICAL SCIENCES. | | | |-A. GENERAL LAWS. | | | | |-PHENOMENALISTIC PSYCHOLOGY| | | | |-Animal Psychology. | | | | |-Human psychology. | | | | |-Individual Ps. | | | | |-Normal. | | | | | |-Child. | | | | | |-Adult. | | | | || | | | |-Abnormal. | | | || | | |-B. SPECIAL OBJECTS. | | | |-1. Mankind. | | | | |-Race Psychology _a, b, c_. | | | |-2. Special Functions. | | | | |-Association of Men. | | | | |-Sociology _a, b, c_. | | | || | | |-3. Special Products of Association of Men| | | | (considered as natural phenomena). | | | |-Products of Undiffereniated Association of Men| | | | | (Folk Psychology). | | | | |-Volition. | | | | | |-Morals _a, b, c_. | | | | | |-Habits _a, b, c_. | | | | || | | | |-Thoughts. | | | | | |-Languages _a, b, c_. | | | | || | | | |-Appreciation. | | | | | |-Enjoyment _a, b, c_. | | | | || | | | |-Belief. | | | | |-Mythology _a, b, c_. | | | || | | |-Products of Individual Differentiation| | | | (casual phenomenalistic sciences of civilization| | | | and its development). | | | |-Volition. | | | | |-State _a, b, c_. | | | | |-Law _a, b, c_. | | | | |-Economy _a, b, c_. | | | || | | |-Thoughts. | | | | |-Sciences _a, b, c_. | | | || | | |-Appreciation. | | | | |-Art _a, b, c_. | | | || | | |-Belief. | | | |-Religion _a, b, c_. | | || | |-KNOWLEDGE OF PURPOSES (connection of experiences in their| | | telelogical reality). | | || | |-Knowledge of Purposes of the Overindividual Will. | | | |-III. NORMATIVE SCIENCES| | | |-A. GENERAL THEORY of absolute values. | | | | |-Metaphysics. | | | || | | |-B. SPECIAL ACTS. | | | |-Volition. | | | | |-Philosophy of Morals (Ethics). | | | | |-Philosophy of Law. | | | | |-Philosophy of State. | | | || | | |-Thoughts. | | | | |-Presuppositions of Thought. | | | | | |-Theory of Knowledge. | | | | | |-Phil. Of Physics. | | | | | |-Phil. Of Psych. | | | | | |-Phil. Of Normative Sciences. | | | | | |-Phil. Of Historical Sciences. | | | | || | | | |-Processes of Thought. | | | | | |-Logic. | | | | || | | | |-Objects Created by Thought. | | | | |-Mathematics. | | | | |-Algebra. | | | | |-Arithmetic. | | | | |-Analysis. | | | | |-Geometry. | | | || | | |-Appreciation. | | | | |-Philosophy of Art (Ęsthetics). | | | || | | |-Belief. | | | |-Philosophy of Religion. | | || | |-Knowledge of Purposes of the Individual Will. | | |-IV. HISTORICAL SCIENCES. | | |-A. GENERAL THEORY of real life. | | | |-Philosophy of History. | | | |-Theory of Personality. | | | | |-(Theory of selves. )| | | | |-("Historical Psychology. ")| | | | |-("VOLUNTARISTIC Psychology. ")| | | | |-("Apperceptional Psychology. ")| | | |-Theory of Humanity. | | || | |-B. SPECIAL ACTS (telelogical interpretative sciences of| | | civilization and history. )| | |-Volition. | | | |-Politics, _a, b, c_. | | | |-Law, _a, b, c_. | | | |-Economy, _a, b, c_. | | || | |-Thoughts. | | | |-Science, _a, b, c_. | | || | |-Appreciation. | | | |-Art, _a, b, c_. | | || | |-Belief. | | |-Religion, _a, b, c_. | || |-PRACTICAL KNOWLEDGE. | |-APPLIED KNOWLEDGE OF PHENOMENA. | | |-V. APPLIED PHYSICAL SCIENCES. | | | |-Technical Sciences. | | | | |-Applied Physics. | | | | |-Applied Chemistry. | | | | |-Applied Biology. | | | || | | |-Medicine. | | || | |-VI. APPLIED PSYCHOLOGICAL SCIENCES. | | |-Psychotechnical Sciences. | | | |-Psychological Pedagogy. | | | |-Psychological Penology. | | || | |-Psychiatry. | || |-APPLIED KNOWLEDGE OF PURPOSES. | |-VII. APPLIED NORMATIVE SCIENCES. | | |-Volition. | | | |-Politics. | | | | |-Science of Public Service. | | | || | | |-Law. | | | | |-Science of Legal Service. (Practical Jurisprudence. )| | | || | | |-Economy. | | | |-Science of Social Service. | | || | |-Thoughts. | | | |-Science of Teaching. (Education. )| | || | |-Appreciation. | | | |-Science of Artistic Production. | | || | |-Belief. | | |-Science of Religious Service. (Practical Theology. )| || |-VIII. APPLIED HISTORICAL SCIENCES. | |-Volition. | | |-Criticism of State. | | |-Criticism of Law. | || |-Thoughts. | | |-Criticism of Science. | || |-Appreciation. | | |-Criticism of Art. | || |-Belief. | |-Criticism of Religion. ||-APPRECIATION (will resting in isolated experiences). | |-Individual: _Enjoyment. _| |-Overindividual: _Beauty. _||-BELIEF (will resting in the supplements of experience). |-Individual: _Creed. _ |-Overindividual: _Religion. 

NOTE: The letters _a, b, c_ below the sciences of Special Objects andSpecial Acts indicate the three subdivisions that results from thethreefold aspects;--of structure(_a_), of relation to the general lawsor theories(_b_), and of development(_c_). With regards to physicalphenomena, for instances, we have astronomy(_a_), astrophysics(_b_), and cosmology(_c_); or geography(_a_), geophysics(_b_), geology(_c_);or botany(_a_), plant physiology(_b_), phylogenetic development ofplants(_c_). In the same way for psychical objects; for instance:structural sociology(_a_), functional sociology(_b_), comparativesociology(_c_); or structure (grammar and syntax) of languages(_a_), psychology of languages(_b_), comparative study of languages(_c_). With regard to the telelogical historical sciences the study ofstructure takes on here the character of intrepretation; the relationto the general view is here the dependence on civilization and thedevelopment is here the real history. We have thus, for instance, theintepretation of Roman law(_a_), dependence of Roman law uponcivilization(_b_), history of Roman law(_c_).