SIX LECTURES ON LIGHT

DELIVERED IN THE UNITED STATESIN1872-1873

BY

JOHN TYNDALL, D. C. L. , LL, D. , F. R. S. 

LATE PROFESSOR OF NATURAL PHILOSOPHY IN THEROYAL INSTITUTION OF GREAT BRITAIN

[Illustration: Sir Thomas Laurence PRA Pinx

Henry Adlarc. Sc. 

Signature: Thomas Young]

London: Longmans & Co. 

_SIXTH IMPRESSION_

LONGMANS, GREEN, AND CO. 

39 PATERNOSTER ROW, LONDON

NEW YORK AND BOMBAY

1906

PREFACE TO THE FOURTH EDITION. 

In these Lectures I have sought to render clear a difficult butprofoundly interesting subject. My aim has been not only to describeand illustrate in a familiar manner the principal laws and phenomenaof light, but to point out the origin, and show the application, ofthe theoretic conceptions which underlie and unite the whole, andwithout which no real interpretation is possible. 

The Lectures, as stated on the title-page, were delivered in theUnited States in 1872-3. I still retain a vivid and gratefulremembrance of the cordiality with which they were received. 

My scope and object are briefly indicated in the 'Summary andConclusion, ' which, as recommended in a former edition, might be, notunfitly, read as an introduction to the volume. 

J. T. 

ALP LUSGEN: _October_ 1885. 

CONTENTS. 

LECTURE I. 

 Introductory Uses of Experiment Early Scientific Notions Sciences of Observation Knowledge of the Ancients regarding Light Defects of the Eye Our Instruments Rectilineal Propagation of Light Law of Incidence and Reflection Sterility of the Middle Ages Refraction Discovery of Snell Partial and Total Reflection Velocity of Light Roemer, Bradley, Foucault, and Fizeau Principle of Least Action Descartes and the Rainbow Newton's Experiments on the Composition of Solar Light His Mistake regarding Achromatism Synthesis of White Light Yellow and Blue Lights produce White by their Mixture Colours of Natural Bodies Absorption Mixture of Pigments contrasted with Mixture of Lights

LECTURE II. 

 Origin of Physical Theories Scope of the Imagination Newton and the Emission Theory Verification of Physical Theories The Luminiferous Ether Wave-theory of Light Thomas Young Fresnel and Arago Conception of Wave-motion Interference of Waves Constitution of Sound-waves Analogies of Sound and Light Illustrations of Wave-motion Interference of Sound Waves Optical Illustrations Pitch and Colour Lengths of the Waves of Light and Rates of Vibration of the Ether-particles Interference of Light Phenomena which first suggested the Undulatory Theory Boyle and Hooke The Colours of thin Plates The Soap-bubble Newton's Rings Theory of 'Fits' Its Explanation of the Rings Overthrow of the Theory Diffraction of Light Colours produced by Diffraction Colours of Mother-of-Pearl. 

LECTURE III. 

 Relation of Theories to Experience Origin of the Notion of the Attraction of Gravitation Notion of Polarity, how generated Atomic Polarity Structural Arrangements due to Polarity Architecture of Crystals considered as an Introduction to their Action upon Light Notion of Atomic Polarity applied to Crystalline Structure Experimental Illustrations Crystallization of Water Expansion by Heat and by Cold Deportment of Water considered and explained Bearings of Crystallization on Optical Phenomena Refraction Double Refraction Polarization Action of Tourmaline Character of the Beams emergent from Iceland Spar Polarization by ordinary Refraction and Reflection Depolarization. 

LECTURE IV. 

 Chromatic Phenomena produced by Crystals in Polarized Light The Nicol Prism Polarizer and Analyzer Action of Thick and Thin Plates of Selenite Colours dependent on Thickness Resolution of Polarized Beam into two others by the Selenite One of them more retarded than the other Recompounding of the two Systems of Waves by the Analyzer Interference thus rendered possible Consequent Production of Colours Action of Bodies mechanically strained or pressed Action of Sonorous Vibrations Action of Glass strained or pressed by Heat Circular Polarization Chromatic Phenomena produced by Quartz The Magnetization of Light Rings surrounding the Axes of Crystals Biaxal and Uniaxal Crystals Grasp of the Undulatory Theory The Colour and Polarization of Sky-light Generation of Artificial Skies. 

LECTURE V. 

 Range of Vision not commensurate with Range of Radiation The Ultra-violet Rays Fluorescence The rendering of invisible Rays visible Vision not the only Sense appealed to by the Solar and Electric Beam Heat of Beam Combustion by Total Beam at the Foci of Mirrors and Lenses Combustion through Ice-lens Ignition of Diamond Search for the Rays here effective Sir William Herschel's Discovery of dark Solar Rays Invisible Rays the Basis of the Visible Detachment by a Ray-filter of the Invisible Rays from the Visible Combustion at Dark Foci Conversion of Heat-rays into Light-rays Calorescence Part played in Nature by Dark Rays Identity of Light and Radiant Heat Invisible Images Reflection, Refraction, Plane Polarization, Depolarization, Circular Polarization, Double Refraction, and Magnetization of Radiant Heat

LECTURE VI. 

 Principles of Spectrum Analysis Prismatic Analysis of the Light of Incandescent Vapours Discontinuous Spectra Spectrum Bands proved by Bunsen and Kirchhoff to be characteristic of the Vapour Discovery of Rubidium, Cæsium, and Thallium Relation of Emission to Absorption The Lines of Fraunhofer Their Explanation by Kirchhoff Solar Chemistry involved in this Explanation Foucault's Experiment Principles of Absorption Analogy of Sound and Light Experimental Demonstration of this Analogy Recent Applications of the Spectroscope Summary and Conclusion

APPENDIX. 

On the Spectra of Polarized Light

Measurement of the Waves of Light

INDEX

ON LIGHT

LECTURE I. 

 INTRODUCTORY USES OF EXPERIMENT EARLY SCIENTIFIC NOTIONS SCIENCES OF OBSERVATION KNOWLEDGE OF THE ANCIENTS REGARDING LIGHT DEFECTS OF THE EYE OUR INSTRUMENTS RECTILINEAL PROPAGATION OF LIGHT LAW OF INCIDENCE AND REFLECTION STERILITY OF THE MIDDLE AGES REFRACTION DISCOVERY OF SNELL PARTIAL AND TOTAL REFLECTION VELOCITY OF LIGHT ROEMER, BRADLEY, FOUCAULT, AND FIZEAU PRINCIPLE OF LEAST ACTION DESCARTES AND THE RAINBOW NEWTON'S EXPERIMENTS ON THE COMPOSITION OF SOLAR LIGHT HIS MISTAKE AS REGARDS ACHROMATISM SYNTHESIS OF WHITE LIGHT YELLOW AND BLUE LIGHTS PRODUCE WHITE BY THEIR MIXTURE COLOURS OF NATURAL BODIES ABSORPTION MIXTURE OF PIGMENTS CONTRASTED WITH MIXTURE OF LIGHTS. 

§ 1. _Introduction_. 

Some twelve years ago I published, in England, a little book entitledthe 'Glaciers of the Alps, ' and, a couple of years subsequently, asecond book, entitled 'Heat a Mode of Motion. ' These volumes werefollowed by others, written with equal plainness, and with a similaraim, that aim being to develop and deepen sympathy between science andthe world outside of science. I agreed with thoughtful men[1] whodeemed it good for neither world to be isolated from the other, orunsympathetic towards the other, and, to lessen this isolation, atleast in one department of science, I swerved, for a time, from thoseoriginal researches which have been the real pursuit and pleasure ofmy life. 

The works here referred to were, for the most part, republished by theMessrs. Appleton of New York, [2] under the auspices of a man who isuntiring in his efforts to diffuse sound scientific knowledge amongthe people of the United States; whose energy, ability, andsingle-mindedness, in the prosecution of an arduous task, have won forhim the sympathy and support of many of us in 'the old country. ' Iallude to Professor Youmans. Quite as rapidly as in England, the aimof these works was understood and appreciated in the United States, and they brought me from this side of the Atlantic innumerableevidences of good-will. Year after year invitations reached me[3] tovisit America, and last year (1871) I was honoured with a request socordial, signed by five-and-twenty names, so distinguished in science, in literature, and in administrative position, that I at once resolvedto respond to it by braving not only the disquieting oscillations ofthe Atlantic, but the far more disquieting ordeal of appearing inperson before the people of the United States. 

This invitation, conveyed to me by my accomplished friend ProfessorLesley, of Philadelphia, and preceded by a letter of the same purportfrom your scientific Nestor, the celebrated Joseph Henry, ofWashington, desired that I should lecture in some of the principalcities of the Union. This I agreed to do, though much in the dark asto a suitable subject. In answer to my inquiries, however, I was givento understand that a course of lectures, showing the uses ofexperiment in the cultivation of Natural Knowledge, would materiallypromote scientific education in this country. And though such lecturesinvolved the selection of weighty and delicate instruments, and theirtransfer from place to place, I determined to meet the wishes of myfriends, as far as the time and means at my disposal would allow. 

§ 2. _Subject of the Course. Source of Light employed. _

Experiments have two great uses--a use in discovery, and a use intuition. They were long ago defined as the investigator's languageaddressed to Nature, to which she sends intelligible replies. Thesereplies, however, usually reach the questioner in whispers too feeblefor the public ear. But after the investigator comes the teacher, whose function it is so to exalt and modify the experiments of hispredecessor, as to render them fit for public presentation. Thissecondary function I shall endeavour, in the present instance, tofulfil. 

Taking a single department of natural philosophy as my subject, Ipropose, by means of it, to illustrate the growth of scientificknowledge under the guidance of experiment. I wish, in the firstplace, to make you acquainted with certain elementary phenomena; thento point out to you how the theoretical principles by which phenomenaare explained take root in the human mind, and finally to apply theseprinciples to the whole body of knowledge covered by the lectures. Thescience of optics lends itself particularly well to this mode oftreatment, and on it, therefore, I propose to draw for the materialsof the present course. It will be best to begin with the few simplefacts regarding light which were known to the ancients, and to passfrom them, in historic gradation, to the more abstruse discoveries ofmodern times. 

All our notions of Nature, however exalted or however grotesque, havetheir foundation in experience. The notion of personal volition inNature had this basis. In the fury and the serenity of naturalphenomena the savage saw the transcript of his own varying moods, andhe accordingly ascribed these phenomena to beings of like passionswith himself, but vastly transcending him in power. Thus the notion of_causality_--the assumption that natural things did not come ofthemselves, but had unseen antecedents--lay at the root of even thesavage's interpretation of Nature. Out of this bias of the human mindto seek for the causes of phenomena all science has sprung. 

We will not now go back to man's first intellectual gropings; muchless shall we enter upon the thorny discussion as to how the gropingman arose. We will take him at that stage of his development, when hebecame possessed of the apparatus of thought and the power of usingit. For a time--and that historically a long one--he was limited tomere observation, accepting what Nature offered, and confiningintellectual action to it alone. The apparent motions of sun and starsfirst drew towards them the questionings of the intellect, andaccordingly astronomy was the first science developed. Slowly, andwith difficulty, the notion of natural forces took root in the humanmind. Slowly, and with difficulty, the science of mechanics had togrow out of this notion; and slowly at last came the full applicationof mechanical principles to the motions of the heavenly bodies. Wetrace the progress of astronomy through Hipparchus and Ptolemy; and, after a long halt, through Copernicus, Galileo, Tycho Brahe, andKepler; while from the high table-land of thought occupied by thesemen, Newton shoots upwards like a peak, overlooking all others fromhis dominant elevation. 

But other objects than the motions of the stars attracted theattention of the ancient world. Light was a familiar phenomenon, andfrom the earliest times we find men's minds busy with the attempt torender some account of it. But without _experiment_, which belongs toa later stage of scientific development, little progress could be heremade. The ancients, accordingly, were far less successful in dealingwith light than in dealing with solar and stellar motions. Still theydid make some progress. They satisfied themselves that light moved instraight lines; they knew also that light was reflected from polishedsurfaces, and that the angle of incidence was equal to the angle ofreflection. These two results of ancient scientific curiosityconstitute the starting-point of our present course of lectures. 

But in the first place it will be useful to say a few words regardingthe source of light to be employed in our experiments. The rusting ofiron is, to all intents and purposes, the slow burning of iron. Itdevelops heat, and, if the heat be preserved, a high temperature maybe thus attained. The destruction of the first Atlantic cable wasprobably due to heat developed in this way. Other metals are stillmore combustible than iron. You may ignite strips of zinc in a candleflame, and cause them to burn almost like strips of paper. But we mustnow expand our definition of combustion, and include under this term, not only combustion in air, but also combustion in liquids. Water, forexample, contains a store of oxygen, which may unite with, andconsume, a metal immersed in it; it is from this kind of combustionthat we are to derive the heat and light employed in our presentcourse. 

The generation of this light and of this heat merits a moment'sattention. Before you is an instrument--a small voltaic battery--inwhich zinc is immersed in a suitable liquid. An attractive force is atthis moment exerted between the metal and the oxygen of the liquid;actual combination, however, being in the first instance avoided. Uniting the two ends of the battery by a thick wire, the attraction issatisfied, the oxygen unites with the metal, zinc is consumed, andheat, as usual, is the result of the combustion. A power which, forwant of a better name, we call an electric current, passes at the sametime through the wire. 

Cutting the thick wire in two, let the severed ends be united by athin one. It glows with a white heat. Whence comes that heat? Thequestion is well worthy of an answer. Suppose in the first instance, when the thick wire is employed, that we permit the action to continueuntil 100 grains of zinc are consumed, the amount of heat generated inthe battery would be capable of accurate numerical expression. Letthe action then continue, with the thin wire glowing, until 100 grainsof zinc are consumed. Will the amount of heat generated in the batterybe the same as before? No; it will be less by the precise amountgenerated in the thin wire outside the battery. In fact, by adding theinternal heat to the external, we obtain for the combustion of 100grains of zinc a total which never varies. We have here a beautifulexample of that law of constancy as regards natural energies, theestablishment of which is the greatest achievement of modern science. By this arrangement, then, we are able to burn our zinc at one place, and to exhibit the effects of its combustion at another. In New York, for example, we may have our grate and fuel; but the heat and light ofour fire may be made to appear at San Francisco. 

[Illustration: Fig. 1. ]

Removing the thin wire and attaching to the severed ends of the thickone two rods of coke we obtain, on bringing the rods together (as infig. 1), a small star of light. Now, the light to be employed in ourlectures is a simple exaggeration of this star. Instead of beingproduced by ten cells, it is produced by fifty. Placed in a suitablecamera, provided with a suitable lens, this powerful source will giveus all the light necessary for our experiments. 

And here, in passing, I am reminded of the common delusion that theworks of Nature, the human eye included, are theoretically perfect. The eye has grown for ages _towards_ perfection; but ages ofperfecting may be still before it. Looking at the dazzling light fromour large battery, I see a luminous globe, but entirely fail to seethe shape of the coke-points whence the light issues. The cause may bethus made clear: On the screen before you is projected an image of thecarbon points, the _whole_ of the glass lens in front of the camerabeing employed to form the image. It is not sharp, but surrounded by ahalo which nearly obliterates the carbons. This arises from animperfection of the glass lens, called its _spherical aberration_, which is due to the fact that the circumferential and central rayshave not the same focus. The human eye labours under a similar defect, and from this, and other causes, it arises that when the naked lightfrom fifty cells is looked at the blur of light upon the retina issufficient to destroy the definition of the retinal image of thecarbons. A long list of indictments might indeed be brought againstthe eye--its opacity, its want of symmetry, its lack of achromatism, its partial blindness. All these taken together caused Helmholt to saythat, if any optician sent him an instrument so defective, he would bejustified in sending it back with the severest censure. But the eye isnot to be judged from the standpoint of theory. It is not perfect, but is on its way to perfection. As a practical instrument, and takingthe adjustments by which its defects are neutralized into account, itmust ever remain a marvel to the reflecting mind. 

§ 3. _Rectilineal Propagation of Light. Elementary Experiments. Law ofReflection. _

The ancients were aware of the rectilineal propagation of light. Theyknew that an opaque body, placed between the eye and a point of light, intercepted the light of the point. Possibly the terms 'ray' and'beam' may have been suggested by those straight spokes of lightwhich, in certain states of the atmosphere, dart from the sun at hisrising and his setting. The rectilineal propagation of light may beillustrated by permitting the solar light to enter, through a smallaperture in a window-shutter, a dark room in which a little smoke hasbeen diffused. In pure _air_ you cannot see the beam, but in smoky airyou can, because the light, which passes unseen through the air, isscattered and revealed by the smoke particles, among which the beampursues a straight course. 

The following instructive experiment depends on the rectilinealpropagation of light. Make a small hole in a closed window-shutter, before which stands a house or a tree, and place within the darkenedroom a white screen at some distance from the orifice. Every straightray proceeding from the house, or tree, stamps its colour upon thescreen, and the sum of all the rays will, therefore, be an image ofthe object. But, as the rays cross each other at the orifice, theimage is inverted. At present we may illustrate and expand thesubject thus: In front of our camera is a large opening (L, fig. 2), from which the lens has been removed, and which is closed at presentby a sheet of tin-foil. Pricking by means of a common sewing-needle asmall aperture in the tin-foil, an inverted image of the carbon-pointsstarts forth upon the screen. A dozen apertures will give a dozenimages, a hundred a hundred, a thousand a thousand. But, as theapertures come closer to each other, that is to say, as the tin-foilbetween the apertures vanishes, the images overlap more and more. Removing the tin-foil altogether, the screen becomes uniformlyilluminated. Hence the light upon the screen may be regarded as theoverlapping of innumerable images of the carbon-points. In like mannerthe light upon every white wall, on a cloudless day, may be regardedas produced by the superposition of innumerable images of the sun. 

[Illustration: Fig. 2. ]

The law that the angle of incidence is equal to the angle ofreflection has a bearing upon theory, to be subsequently mentioned, which renders its simple illustration here desirable. A straight lath(pointing to the figure 5 on the arc in fig. 3) is fixed as an indexperpendicular to a small looking-glass (M), capable of rotation. Webegin by receiving a beam of light upon the glass which is reflectedback along the line of its incidence. The index being then turned, themirror turns with it, and at each side of the index the incident andthe reflected beams (L _o_, _o_ R) track themselves through the dustof the room. The mere inspection of the two angles enclosed betweenthe index and the two beams suffices to show their equality; while ifthe graduated arc be consulted, the arc from 5 to _m_ is foundaccurately equal to the arc from 5 to _n_. The complete expression ofthe law of reflection is, not only that the angles of incidence andreflection are equal, but that the incident and reflected rays alwayslie in a plane perpendicular to the reflecting surface. 

[Illustration: Fig. 3. ]

This simple apparatus enables us to illustrate another law of greatpractical importance, namely, that when a mirror rotates, the angularvelocity of a beam reflected from it is twice that of the reflectingmirror. A simple experiment will make this plain. The arc (_m n_, fig. 3) before you is divided into ten equal parts, and when the incidentbeam and the index cross the zero of the graduation, both the incidentand reflected beams are horizontal. Moving the index of the mirror to1, the reflected beam cuts the arc at 2; moving the index to 2, thearc is cut at 4; moving the index to 3, the arc is cut at 6; movingthe index at 4, the arc is cut at 8; finally, moving the index to 5, the arc is cut at 10 (as in the figure). In every case the reflectedbeam moves through twice the angle passed over by the mirror. 

One of the principal problems of science is to help the senses of man, by carrying them into regions which could never be attained withoutthat help. Thus we arm the eye with the telescope when we want tosound the depths of space, and with the microscope when we want toexplore motion and structure in their infinitesimal dimensions. Now, this law of angular reflection, coupled with the fact that a beam oflight possesses no weight, gives us the means of magnifying smallmotions to an extraordinary degree. Thus, by attaching mirrors to hissuspended magnets, and by watching the images of divided scalesreflected from the mirrors, the celebrated Gauss was able to detectthe slightest thrill of variation on the part of the earth's magneticforce. By a similar arrangement the feeble attractions and repulsionsof the diamagnetic force have been made manifest. The minuteelongation of a bar of metal, by the mere warmth of the hand, may beso magnified by this method, as to cause the index-beam to movethrough 20 or 30 feet. The lengthening of a bar of iron when it ismagnetized may be also thus demonstrated. Helmholtz long ago employedthis method of rendering evident to his students the classicalexperiments of Du Bois Raymond on animal electricity; while in SirWilliam Thomson's reflecting galvanometer the principle receives oneof its latest and most important applications. 

§ 4. _The Refraction of Light. Total Reflection. _

For more than a thousand years no step was taken in optics beyond thislaw of reflection. The men of the Middle Ages, in fact, endeavoured, on the one hand, to develop the laws of the universe _à priori_ out oftheir own consciousness, while many of them were so occupied with theconcerns of a future world that they looked with a lofty scorn on allthings pertaining to this one. Speaking of the natural philosophers ofhis time, Eusebius says, 'It is not through ignorance of the thingsadmired by them, but through contempt of their useless labour, that wethink little of these matters, turning our souls to the exercise ofbetter things. ' So also Lactantius--'To search for the causes ofthings; to inquire whether the sun be as large as he seems; whetherthe moon is convex or concave; whether the stars are fixed in the sky, or float freely in the air; of what size and of what material are theheavens; whether they be at rest or in motion; what is the magnitudeof the earth; on what foundations is it suspended or balanced;--todispute and conjecture upon such matters is just as if we chose todiscuss what we think of a city in a remote country, of which we neverheard but the name. '

As regards the refraction of light, the course of real inquiry wasresumed in 1100 by an Arabian philosopher named Alhazen. Then it wastaken up in succession by Roger Bacon, Vitellio, and Kepler. One ofthe most important occupations of science is the determination, byprecise measurements, of the quantitative relations of phenomena; thevalue of such measurements depending greatly upon the skill andconscientiousness of the man who makes them. Vitellio appears to havebeen both skilful and conscientious, while Kepler's habit was torummage through the observations of his predecessors, to look at themin all lights, and thus distil from them the principles which unitedthem. He had done this with the astronomical measurements of TychoBrahe, and had extracted from them the celebrated 'laws of Kepler. ' Hedid it also with Vitellio's measurements of refraction. But in thiscase he was not successful. The principle, though a simple one, escaped him, and it was first discovered by Willebrord Snell, aboutthe year 1621. 

Less with the view of dwelling upon the phenomenon itself than ofintroducing it in a form which will render subsequently intelligibleto you the play of theoretic thought in Newton's mind, the fact ofrefraction may be here demonstrated. I will not do this by drawing thecourse of the beam with chalk on a black board, but by causing it tomark its own white track before you. A shallow circular vessel (RIG, fig. 4), half filled with water, rendered slightly turbid by theadmixture of a little milk, or the precipitation of a little mastic, is placed with its glass front vertical. By means of a small planereflector (M), and through a slit (I) in the hoop surrounding thevessel, a beam of light is admitted in any required direction. Itimpinges upon the water (at O), enters it, and tracks itself throughthe liquid in a sharp bright band (O G). Meanwhile the beam passesunseen through the air above the water, for the air is not competentto scatter the light. A puff of smoke into this space at once revealsthe track of the incident-beam. If the incidence be vertical, the beamis unrefracted. If oblique, its refraction at the common surface ofair and water (at O) is rendered clearly visible. It is also seen that_reflection_ (along O R) accompanies refraction, the beam dividingitself at the point of incidence into a refracted and a reflectedportion. [4]

[Illustration: Fig. 4. ]

The law by which Snell connected together all the measurementsexecuted up to his time, is this: Let A B C D (fig. 5) represent theoutline of our circular vessel, A C being the water-line. When thebeam is incident along B E, which is perpendicular to A C, there is norefraction. When it is incident along _m_ E, there is refraction: itis bent at E and strikes the circle at _n_. When it is incident along_m'_ E there is also refraction at E, the beam striking the point_n'_. From the ends of the two incident beams, let the perpendiculars_m_ _o_, _m'_ _o'_ be drawn upon B D, and from the ends of therefracted beams let the perpendiculars _p_ _n_, _p'_ _n'_ be alsodrawn. Measure the lengths of _o m_ and of _p_ _n_, and divide the oneby the other. You obtain a certain quotient. In like manner divide_m'_ _o'_ by the corresponding perpendicular _p'_ _n'_; you obtainprecisely the same quotient. Snell, in fact, found this quotient to be_a constant quantity_ for each particular substance, though it variedin amount from one substance to another. He called the quotient the_index of refraction_. 

[Illustration Fig. 5]

In all cases where the light is incident from air upon the surface ofa solid or a liquid, or, to speak more generally, when the incidenceis from a less highly refracting to a more highly refracting medium, the reflection is _partial_. In this case the most powerfullyreflecting substances either transmit or absorb a portion of theincident light. At a perpendicular incidence water reflects only 18rays out of every 1, 000; glass reflects only 25 rays, while mercuryreflects 666 When the rays strike the surface obliquely the reflectionis augmented. At an incidence of 40°, for example, water reflects 22rays, at 60° it reflects 65 rays, at 80° 333 rays; while at anincidence of 89½°, where the light almost grazes the surface, itreflects 721 rays out of every 1, 000. Thus, as the obliquityincreases, the reflection from water approaches, and finally quiteovertakes, the perpendicular reflection from mercury; but at noincidence, however great, when the incidence is from air, is thereflection from water, mercury, or any other substance, _total_. 

Still, total reflection may occur, and with a view to understandingits subsequent application in the Nicol's prism, it is necessary tostate when it occurs. This leads me to the enunciation of a principlewhich underlies all optical phenomena--the principle ofreversibility. [5] In the case of refraction, for instance, when theray passes obliquely from air into water, it is bent _towards_ theperpendicular; when it passes from water to air, it is bent _from_ theperpendicular, and accurately reverses its course. Thus in fig. 5, if_m_ E _n_ be the track of a ray in passing from air into water, _n_ E_m_ will be its track in passing from water into air. Let us push thisprinciple to its consequences. Supposing the light, instead of beingincident along _m_ E or _m'_ E, were incident as close as possiblealong C E (fig. 6); suppose, in other words, that it just grazes thesurface before entering the water. After refraction it will pursuesay the course E _n_''. Conversely, if the light start from _n_'', andbe incident at E, it will, on escaping into the air, just graze thesurface of the water. The question now arises, what will occursupposing the ray from the water to follow the course _n_''' E, whichlies beyond _n_'' E? The answer is, it will not quit the water at all, but will be _totally_ reflected (along E _x_). At the under surface ofthe water, moreover, the law is just the same as at its upper surface, the angle of incidence (D E _n_''') being equal to the angle ofreflection (D E _x_). 

[Illustration: Fig. 6]

Total reflection may be thus simply illustrated:--Place a shilling ina drinking-glass, and tilt the glass so that the light from theshilling shall fall with the necessary obliquity upon the watersurface above it. Look upwards through the water towards that surface, and you see the image of the shilling shining there as brightly as theshilling itself. Thrust the closed end of an empty test-tube intowater, and incline the tube. When the inclination is sufficient, horizontal light falling upon the tube cannot enter the air within it, but is totally reflected upward: when looked down upon, such a tubelooks quite as bright as burnished silver. Pour a little water intothe tube; as the liquid rises, total reflection is abolished, and withit the lustre, leaving a gradually diminishing shining zone, whichdisappears wholly when the level of the water within the tube reachesthat without it. Any glass tube, with its end stopped water-tight, will produce this effect, which is both beautiful and instructive. 

Total reflection never occurs except in the attempted passage of a rayfrom a more refracting to a less refracting medium; but in this case, when the obliquity is sufficient, it always occurs. The mirage of thedesert, and other phantasmal appearances in the atmosphere, are inpart due to it. When, for example, the sun heats an expanse of sand, the layer of air in contact with the sand becomes lighter and lessrefracting than the air above it: consequently, the rays from adistant object, striking very obliquely on the surface of the heatedstratum, are sometimes totally reflected upwards, thus producingimages similar to those produced by water. I have seen the image of arock called Mont Tombeline distinctly reflected from the heated air ofthe strand of Normandy near Avranches; and by such delusiveappearances the thirsty soldiers of the French army in Egypt weregreatly tantalised. 

The angle which marks the limit beyond which total reflection takesplace is called the _limiting angle_ (it is marked in fig. 6 by thestrong line E _n_''). It must evidently diminish as the refractiveindex increases. For water it is 48½°, for flint glass 38°41', and fordiamond 23°42'. Thus all the light incident from two completequadrants, or 180°, in the case of diamond, is condensed into anangular space of 47°22' (twice 23°42') by refraction. Coupled with itsgreat refraction, are the great dispersive and great reflectivepowers of diamond; hence the extraordinary radiance of the gem, bothas regards white light and prismatic light. 

§ 5. _Velocity of Light. Aberration. Principle of least Action. _

In 1676 a great impulse was given to optics by astronomy. In that yearOlav Roemer, a learned Dane, was engaged at the Observatory of Parisin observing the eclipses of Jupiter's moons. The planet, whosedistance from the sun is 475, 693, 000 miles, has four satellites. Weare now only concerned with the one nearest to the planet. Roemerwatched this moon, saw it move round the planet, plunge into Jupiter'sshadow, behaving like a lamp suddenly extinguished: then at the otheredge of the shadow he saw it reappear, like a lamp suddenly lighted. The moon thus acted the part of a signal light to the astronomer, andenabled him to tell exactly its time of revolution. The period betweentwo successive lightings up of the lunar lamp he found to be 42 hours, 28 minutes, and 35 seconds. 

This measurement of time was so accurate, that having determined themoment when the moon emerged from the shadow, the moment of itshundredth appearance could also be determined. In fact, it would be100 times 42 hours, 28 minutes, 35 seconds, after the firstobservation. 

Roemer's first observation was made when the earth was in the part ofits orbit nearest Jupiter. About six months afterwards, the earthbeing then at the opposite side of its orbit, when the little moonought to have made its hundredth appearance, it was found unpunctual, being fully 15 minutes behind its calculated time. Its appearance, moreover, had been growing gradually later, as the earth retreatedtowards the part of its orbit most distant from Jupiter. Roemerreasoned thus: 'Had I been able to remain at the other side of theearth's orbit, the moon might have appeared always at the properinstant; an observer placed there would probably have seen the moon 15minutes ago, the retardation in my case being due to the fact that thelight requires 15 minutes to travel from the place where my firstobservation was made to my present position. '

This flash of genius was immediately succeeded by another. 'If thissurmise be correct, ' Roemer reasoned, 'then as I approach Jupiteralong the other side of the earth's orbit, the retardation ought tobecome gradually less, and when I reach the place of my firstobservation, there ought to be no retardation at all. ' He found thisto be the case, and thus not only proved that light required time topass through space, but also determined its rate of propagation. 

The velocity of light, as determined by Roemer, is 192, 500 miles in asecond. 

For a time, however, the observations and reasonings of Roemer failedto produce conviction. They were doubted by Cassini, Fontenelle, andHooke. Subsequently came the unexpected corroboration of Roemer by theEnglish astronomer, Bradley, who noticed that the fixed stars did notreally appear to be fixed, but that they describe little orbits in theheavens every year. The result perplexed him, but Bradley had a mindopen to suggestion, and capable of seeing, in the smallest fact, apicture of the largest. He was one day upon the Thames in a boat, andnoticed that as long as his course remained unchanged, the vane uponhis masthead showed the wind to be blowing constantly in the samedirection, but that the wind appeared to vary with every change in thedirection of his boat. 'Here, ' as Whewell says, 'was the image of hiscase. The boat was the earth, moving in its orbit, and the wind wasthe light of a star. '

We may ask, in passing, what, without the faculty which formed the'image, ' would Bradley's wind and vane have been to him? A wind andvane, and nothing more. You will immediately understand the meaning ofBradley's discovery. Imagine yourself in a motionless railway-train, with a shower of rain descending vertically downwards. The moment thetrain begins to move, the rain-drops begin to slant, and the quickerthe motion of the train the greater is the obliquity. In a preciselysimilar manner the rays from a star, vertically overhead, are causedto slant by the motion of the earth through space. Knowing the speedof the train, and the obliquity of the falling rain, the velocity ofthe drops may be calculated; and knowing the speed of the earth in herorbit, and the obliquity of the rays due to this cause, we cancalculate just as easily the velocity of light. Bradley did this, andthe 'aberration of light, ' as his discovery is called, enabled him toassign to it a velocity almost identical with that deduced by Roemerfrom a totally different method of observation. Subsequently Fizeau, and quite recently Cornu, employing not planetary or stellardistances, but simply the breadth of the city of Paris, determined thevelocity of light: while Foucault--a man of the rarest mechanicalgenius--solved the problem without quitting his private room. Owingto an error in the determination of the earth's distance from the sun, the velocity assigned to light by both Roemer and Bradley is toogreat. With a close approximation to accuracy it may be regarded as186, 000 miles a second. 

By Roemer's discovery, the notion entertained by Descartes, andespoused by Hooke, that light is propagated instantly through space, was overthrown. But the establishment of its motion through stellarspace led to speculations regarding its velocity in transparentterrestrial substances. The 'index of refraction' of a ray passingfrom air into water is 4/3. Newton assumed these numbers to mean thatthe velocity of light in water being 4, its velocity in air is 3; andhe deduced the phenomena of refraction from this assumption. Huyghenstook the opposite and truer view. According to this great man, thevelocity of light in water being 3, its velocity in air is 4; but bothin Newton's time and ours the same great principle determined, anddetermines, the course of light in all cases. In passing from point topoint, whatever be the media in its path, or however it may berefracted or reflected, light takes the course which occupies _leasttime_. Thus in fig. 4, taking its velocity in air and in water intoaccount, the light reaches G from I more rapidly by travelling firstto O, and there changing its course, than if it proceeded straightfrom I to G. This is readily comprehended, because, in the lattercase, it would pursue a greater distance through the water, which isthe more retarding medium. 

§ 6. _Descartes' Explanation of the Rainbow_. 

Snell's law of refraction is one of the corner-stones of opticalscience, and its applications to-day are million-fold. Immediatelyafter its discovery Descartes applied it to the explanation of therainbow. A beam of solar light falling obliquely upon a rain-drop isrefracted on entering the drop. It is in part reflected at the back ofthe drop, and on emerging it is again refracted. By these tworefractions, and this single reflection, the light is sent to the eyeof an observer facing the drop, and with his back to the sun. 

Conceive a line drawn from the sun, through the back of his head, tothe observer's eye and prolonged beyond it. Conceive a second linedrawn from the shower to the eye, and enclosing an angle of 42½° withthe line drawn from the sun. Along this second line a rain-drop whenstruck by a sunbeam will send red light to the eye. Every other dropsimilarly situated, that is, every drop at an angular distance of 42½°from the line through the sun and eye, will do the same. A circularband of red light is thus formed, which may be regarded as theboundary of the base of a cone, with its apex at the observer's eye. Because of the magnitude of the sun, the angular width of this redband will be half a degree. 

From the eye of the observer conceive another line to be drawn, enclosing an angle, not of 42½°, but of 40½°, with the prolongation ofthe line drawn from the sun. Along this other line a rain-drop, at itsremote end, when struck by a solar beam, will send violet light to theeye. All drops at the same angular distance will do the same, and weshall therefore obtain a band of violet light of the same width as thered band. These two bands constitute the limiting colours of therainbow, and between them the bands corresponding to the other colourslie. 

Thus the line drawn from the eye to the _middle_ of the bow, and theline drawn through the eye to the sun, always enclose an angle ofabout 41°. To account for this was the great difficulty, whichremained unsolved up to the time of Descartes. 

Taking a pen in hand, and calculating by means of Snell's law thetrack of every ray through a raindrop, Descartes found that, at oneparticular angle, the rays, reflected at its back, emerged from thedrop _almost parallel to each other_. They were thus enabled topreserve their intensity through long atmospheric distances. At allother angles the rays quitted the drop _divergent_, and through thisdivergence became so enfeebled as to be practically lost to the eye. The angle of parallelism here referred to was that of forty-onedegrees, which observation had proved to be invariably associated withthe rainbow. 

From what has been said, it is clear that two observers standingbeside each other, or one above the other, nay, that even the two eyesof the same observer, do not see exactly the same bow. The position ofthe base of the cone changes with that of its apex. And here we haveno difficulty in answering a question often asked--namely, whether arainbow is ever seen reflected in water. Seeing two bows, the one inthe heavens, the other in the water, you might be disposed to inferthat the one bears the same relation to the other that a tree upon thewater's edge bears to its reflected image. The rays, however, whichreach an observer's eye after reflection from the water, and whichform a bow in the water, would, were their course from the showeruninterrupted, converge to a point vertically under the observer, andas far below the level of the water as his eye is above it. But underno circumstances could an eye above the water-level and one below itsee the same bow--in other words, the self-same drops of rain cannotform the reflected bow and the bow seen directly in the heavens. Thereflected bow, therefore, is not, in the usual optical sense of theterm, the _image_ of the bow seen in the sky. 

§ 7. _Analysis and Synthesis of Light. Doctrine of Colours_. 

In the rainbow a new phenomenon was introduced--the phenomenon ofcolour. And here we arrive at one of those points in the history ofscience, when great men's labours so intermingle that it is difficultto assign to each worker his precise meed of honour. Descartes was atthe threshold of the discovery of the composition of solar light; butfor Newton was reserved the enunciation of the true law. He went towork in this way: Through the closed window-shutter of a room hepierced an orifice, and allowed a thin sunbeam to pass through it. Thebeam stamped a round white image of the sun on the opposite wall ofthe room. In the path of this beam Newton placed a prism, expecting tosee the beam refracted, but also expecting to see the image of thesun, after refraction, still round. To his astonishment, it was drawnout to an image with a length five times its breadth. It was, moreover, no longer white, but divided into bands of differentcolours. Newton saw immediately that solar light was _composite_, notsimple. His elongated image revealed to him the fact that someconstituents of the light were more deflected by the prism thanothers, and he concluded, therefore, that white light was a mixture oflights of different colours, possessing different degrees ofrefrangibility. 

Let us reproduce this celebrated experiment. On the screen is nowstamped a luminous disk, which may stand for Newton's image of thesun. Causing the beam (from the aperture L, fig. 7) which produces thedisk to pass through a lens (E), we form a sharp image of theaperture. Placing in the track of the beam a prism (P), we obtainNewton's coloured image, with its red and violet ends, which he calleda _spectrum_. Newton divided the spectrum into seven parts--red, orange, yellow, green, blue, indigo, violet; which are commonly calledthe seven primary or prismatic colours. The drawing out of the whitelight into its constituent colours is called _dispersion_. 

[Illustration: Fig. 7. ]

This was the first _analysis_ of solar light by Newton; but thescientific mind is fond of verification, and never neglects it whereit is possible. Newton completed his proof by _synthesis_ in this way:The spectrum now before you is produced by a glass prism. Causing thedecomposed beam to pass through a second similar prism, but so placedthat the colours are refracted back and reblended, the perfectly whiteluminous disk is restored. 

[Illustration: Fig. 8. ]

In this case, refraction and dispersion are simultaneously abolished. Are they always so? Can we have the one without the other? It wasNewton's conclusion that we could not. Here he erred, and his error, which he maintained to the end of his life, retarded the progress ofoptical discovery. Dollond subsequently proved that by combining twodifferent kinds of glass, the colours can be extinguished, stillleaving a residue of refraction, and he employed this residue in theconstruction of achromatic lenses--lenses yielding no colour--whichNewton thought an impossibility. By setting a water-prism--watercontained in a wedge-shaped vessel with glass sides (B, fig. 8)--inopposition to a wedge of glass (to the right of B), this point can beillustrated before you. We have first of all the position (dotted) ofthe unrefracted beam marked upon the screen; then we produce thenarrow water-spectrum (W); finally, by introducing a flint-glassprism, we refract the beam back, until the colour disappears (at A). The image of the slit is now _white_; but though the dispersion isabolished, there remains a very sensible amount of refraction. 

This is the place to illustrate another point bearing upon theinstrumental means employed in these lectures. Bodies differ widelyfrom each other as to their powers of refraction and dispersion. Notethe position of the water-spectrum upon the screen. Altering in noparticular the wedge-shaped vessel, but simply substituting for thewater the transparent bisulphide of carbon, you notice how much higherthe beam is thrown, and how much richer is the display of colour. Toaugment the size of our spectrum we here employ (at L) a slit, insteadof a circular aperture. [6]

[Illustration: Fig. 9. ]

The synthesis of white light may be effected in three ways, all ofwhich are worthy of attention: Here, in the first instance, we have arich spectrum produced by the decomposition of the beam (from L, fig. 9). One face of the prism (P) is protected by a diaphragm (not shownin the figure), with a longitudinal slit, through which the beampasses into the prism. It emerges decomposed at the other side. Ipermit the colours to pass through a cylindrical lens (C), which sosqueezes them together as to produce upon the screen a sharply definedrectangular image of the longitudinal slit. In that image the coloursare reblended, and it is perfectly white. Between the prism and thecylindrical lens may be seen the colours, tracking themselves throughthe dust of the room. Cutting off the more refrangible fringe by acard, the rectangle is seen red: cutting off the less refrangiblefringe, the rectangle is seen blue. By means of a thin glass prism(W), I deflect one portion of the colours, and leave the residualportion. On the screen are now two coloured rectangles produced inthis way. These are _complementary_ colours--colours which, by theirunion, produce white. Note, that by judicious management, one of thesecolours is rendered _yellow_, and the other _blue_. I withdraw thethin prism; yellow and blue immediately commingle, and we have _white_as the result of their union. On our way, then, we remove the fallacy, first exposed by Wünsch, and afterwards independently by Helmholtz, that the mixture of blue and yellow lights produces green. 

Restoring the circular aperture, we obtain once more a spectrum likethat of Newton. By means of a lens, we can gather up these colours, and build them together, not to an image of the aperture, but to animage of the carbon-points themselves. 

Finally, by means of a rotating disk, on which are spread in sectorsthe colours of the spectrum, we blend together the prismatic coloursin the eye itself, and thus produce the impression of whiteness. 

Having unravelled the interwoven constituents of white light, we havenext to inquire, What part the constitution so revealed enables thisagent to play in Nature? To it we owe all the phenomena of colour, andyet not to it alone; for there must be a certain relationship betweenthe ultimate particles of natural bodies and white light, to enablethem to extract from it the luxury of colour. But the function ofnatural bodies is here _selective_, not _creative_. There is no colour_generated_ by any natural body whatever. Natural bodies have showeredupon them, in the white light of the sun, the sum total of allpossible colours; and their action is limited to the sifting of thattotal--the appropriating or absorbing of some of its constituents, and the rejecting of others. It will fix this subject in your minds ifI say, that it is the portion of light which they reject, and not thatwhich they appropriate or absorb, that gives bodies their colours. 

Let us begin our experimental inquiries here by asking, What is themeaning of blackness? Pass a black ribbon through the colours of thespectrum; it quenches all of them. The meaning of blackness is thusrevealed--it is the result of the absorption of all the constituentsof solar light. Pass a red ribbon through the spectrum. In the redlight the ribbon is a vivid red. Why? Because the light that entersthe ribbon is not quenched or absorbed, but in great part sent back tothe eye. Place the same ribbon in the green of the spectrum; it isblack as jet. It absorbs the green light, and renders the space onwhich that light falls a space of intense darkness. Place a greenribbon in the green of the spectrum. It shines vividly with its propercolour; transfer it to the red, it is black as jet. Here it absorbsall the light that falls upon it, and offers mere darkness to the eye. 

Thus, when white light is employed, the red sifts it by quenching thegreen, and the green sifts it by quenching the red, both exhibitingthe residual colour. The process through which natural bodies acquiretheir colours is therefore a _negative_ one. The colours are producedby subtraction, not by addition. This red glass is red because itdestroys all the more refrangible rays of the spectrum. This blueliquid is blue because it destroys all the less refrangible rays. Bothtogether are opaque because the light transmitted by the one isquenched by the other. In this way, by the union of two transparentsubstances, we obtain a combination as dark as pitch to solar light. This other liquid, finally, is purple because it destroys the greenand the yellow, and allows the terminal colours of the spectrum topass unimpeded. From the blending of the blue and the red thisgorgeous purple is produced. 

One step further for the sake of exactness. The light which falls upona body is divided into two portions, one of which is reflected fromthe surface of the body; and this is of the same colour as theincident light. If the incident light be white, the superficiallyreflected light will also be white. Solar light, for example, reflected from the surface of even a black body, is white. Theblackest camphine smoke in a dark room, through which a sunbeam passesfrom an aperture in the window-shutter, renders the track of the beamwhite, by the light scattered from the surfaces of the soot particles. The moon appears to us as if

 'Clothed in white samite, mystic, wonderful;'

but were it covered with the blackest velvet it would still hang as awhite orb in the heavens, shining upon our world substantially as itdoes now. 

§ 8. _Colours of Pigments as distinguished from Colours of Light_. 

The second portion of the incident light enters the body, and upon itstreatment there the colour of the body depends. And here a moment mayproperly be given to the analysis of the action of pigments uponlight. They are composed of fine particles mixed with a vehicle; buthow intimately soever the particles may be blended, they still remainparticles, separated, it may be, by exceedingly minute distances, butstill separated. To use the scientific phrase, they are not opticallycontinuous. Now, wherever optical continuity is ruptured we havereflection of the incident light. It is the multitude of reflectionsat the limiting surfaces of the particles that prevents light frompassing through snow, powdered glass, or common salt. The light hereis exhausted in echoes, not extinguished by true absorption. It is thesame kind of reflection that renders the thunder-cloud so imperviousto light. Such a cloud is composed of particles of water, mixed withparticles of air, both separately transparent, but practically opaquewhen thus mixed together. 

In the case of pigments, then, the light is _reflected_ at thelimiting surfaces of the particles, but it is in part _absorbed_within the particles. The reflection is necessary to send the lightback to the eye; the absorption is necessary to give the body itscolour. The same remarks apply to flowers. The rose is red, in virtue, not of the light reflected from its surface, but of light which hasentered its substance, which has been reflected from surfaces within, and which, in returning _through_ the substance, has had its greenextinguished. A similar process in the case of hard green leavesextinguishes the red, and sends green light from the body of theleaves to the eye. 

All bodies, even the most transparent, are more or less absorbent oflight. Take the case of water. A glass cell of clear water interposedin the track of our beam does not perceptibly change any one of thecolours of the spectrum. Still absorption, though insensible, hashere occurred, and to render it sensible we have only to increase thedepth of the water through which the light passes. Instead of a cellan inch thick, let us take a layer, ten or fifteen feet thick: thecolour of the water is then very evident. By augmenting the thicknesswe absorb more of the light, and by making the thickness very great weabsorb the light altogether. Lampblack or pitch can do no more, andthe only difference in this respect between them and water is that avery small depth in their case suffices to extinguish all the light. The difference between the highest known transparency and the highestknown opacity is one of degree merely. 

If, then, we render water sufficiently deep to quench all the light;and if from the interior of the water no light reaches the eye, wehave the condition necessary to produce blackness. Looked properlydown upon, there are portions of the Atlantic Ocean to which one wouldhardly ascribe a trace of colour: at the most a tint of dark indigoreaches the eye. The water, in fact, is practically _black_, and thisis an indication both of its depth and purity. But the case isentirely changed when the ocean contains solid particles in a state ofmechanical suspension, capable of sending the light impinging on themback to the eye. 

Throw, for example, a white pebble, or a white dinner plate, into theblackest Atlantic water; as it sinks it becomes greener and greener, and, before it disappears, it reaches a vivid blue green. Break such apebble, or plate, into fragments, these will behave like the unbrokenmass: grind the pebble to powder, every particle will yield itsmodicum of green; and if the particles be so fine as to remainsuspended in the water, the scattered light will be a uniform green. Hence the greenness of shoal water. You go to bed with the black waterof the Atlantic around you. You rise in the morning, find it a vividgreen, and correctly infer that you are crossing the Bank ofNewfoundland. Such water is found charged with fine matter in a stateof mechanical suspension. The light from the bottom may sometimes comeinto play, but it is not necessary. The subaqueous foam, generated bythe screw or paddle-wheels of a steamer, also sends forth a vividgreen. The foam here furnishes a _reflecting surface_, the waterbetween the eye and it the _absorbing medium_. 

Nothing can be more superb than the green of the Atlantic waves whenthe circumstances are favourable to the exhibition of the colour. Aslong as a wave remains unbroken no colour appears, but when the foamjust doubles over the crest like an Alpine snow-cornice, under thecornice we often see a display of the most exquisite green. It ismetallic in its brilliancy. The foam is first illuminated, and itscatters the light in all directions; the light which passes throughthe higher portion of the wave alone reaches the eye, and gives tothat portion its matchless colour. The folding of the wave, producing, as it does, a series of longitudinal protuberances and furrows whichact like cylindrical lenses, introduces variations in the intensity ofthe light, and materially enhances its beauty. 

We are now prepared for the further consideration of a point alreadyadverted to, and regarding which error long found currency. You willfind it stated in many books that blue light and yellow light mixedtogether, produce green. But blue and yellow have been just proved tobe complementary colours, producing white by their mixture. Themixture of blue and yellow _pigments_ undoubtedly produces green, butthe mixture of pigments is a totally different thing from the mixtureof lights. 

Helmholtz has revealed the cause of the green produced by a mixture ofblue and yellow pigments. No natural colour is _pure_. A blue liquid, or a blue powder, permits not only the blue to pass through it, but aportion of the adjacent green. A yellow powder is transparent not onlyto the yellow light, but also in part to the adjacent green. Now, whenblue and yellow are mixed together, the blue cuts off the yellow, theorange, and the red; the yellow, on the other hand, cuts off theviolet, the indigo, and the blue. Green is the only colour to whichboth are transparent, and the consequence is that, when white lightfalls upon a mixture of yellow and blue powders, the green alone issent back to the eye. You have already seen that the fine blueammonia-sulphate of copper transmits a large portion of green, whilecutting off all the less refrangible light. A yellow solution ofpicric acid also allows the green to pass, but quenches all the morerefrangible light. What must occur when we send a beam through bothliquids? The experimental answer to this question is now before you:the green band of the spectrum alone remains upon the screen. 

The impurity of natural colours is strikingly illustrated by anobservation recently communicated to me by Mr. Woodbury. On lookingthrough a blue glass at green leaves in sunshine, he saw thesuperficially reflected light blue. The light, on the contrary, whichcame from the body of the leaves was crimson. On examination, I foundthat the glass employed in this observation transmitted both ends ofthe spectrum, the red as well as the blue, and that it quenched themiddle. This furnished an easy explanation of the effect. In thedelicate spring foliage the blue of the solar light is for the mostpart absorbed, and a light, mainly yellowish green, but containing aconsiderable quantity of red, escapes from the leaf to the eye. Onlooking at such foliage through the violet glass, the green and theyellow are stopped, and the red alone reaches the eye. Thus regarded, therefore, the leaves appear like faintly blushing roses, and presenta very beautiful appearance. With the blue ammonia-sulphate of copper, which transmits no red, this effect is not obtained. 

As the year advances the crimson gradually hardens to a coppery red;and in the dark green leaves of old ivy it is almost absent. Permitting a beam of white light to fall upon fresh leaves in a darkroom, the sudden change from green to red, and from red back to green, when the violet glass is alternately introduced and withdrawn, is verysurprising. Looked at through the same glass, the meadows in Mayappear of a warm purple. With a solution of permanganate of potash, which, while it quenches the centre of the spectrum, permits its endsto pass more freely than the violet glass, excellent effects are alsoobtained. [7]

This question of absorption, considered with reference to itsmolecular mechanism, is one of the most subtle and difficult inphysics. We are not yet in a condition to grapple with it, but weshall be by-and-by. Meanwhile we may profitably glance back on the webof relations which these experiments reveal to us. We have, firstly, in solar light an agent of exceeding complexity, composed ofinnumerable constituents, refrangible in different degrees. We find, secondly, the atoms and molecules of bodies gifted with the power ofsifting solar light in the most various ways, and producing by thissifting the colours observed in nature and art. To do this they mustpossess a molecular structure commensurate in complexity with that oflight itself. Thirdly, we have the human eye and brain, so organizedas to be able to take in and distinguish the multitude of impressionsthus generated. The light, therefore, at starting is complex; to siftand select it as they do, natural bodies must be complex; while totake in the impressions thus generated, the human eye and brain, however we may simplify our conceptions of their action, [8] must behighly complex. 

Whence this triple complexity? If what are called material purposeswere the only end to be served, a much simpler mechanism would besufficient. But, instead of simplicity, we have prodigality ofrelation and adaptation--and this, apparently, for the sole purpose ofenabling us to see things robed in the splendours of colour. Would itnot seem that Nature harboured the intention of educating us for otherenjoyments than those derivable from meat and drink? At all events, whatever Nature meant--and it would be mere presumption to dogmatizeas to what she meant--we find ourselves here, as the upshot of heroperations, endowed, not only with capacities to enjoy the materiallyuseful, but endowed with others of indefinite scope and application, which deal alone with the beautiful and the true. 

LECTURE II. 

 ORIGIN OF PHYSICAL THEORIES SCOPE OF THE IMAGINATION NEWTON AND THE EMISSION THEORY VERIFICATION OF PHYSICAL THEORIES THE LUMINIFEROUS ETHER WAVE THEORY OF LIGHT THOMAS YOUNG FRESNEL AND ARAGO CONCEPTION OF WAVE-MOTION INTERFERENCE OF WAVES CONSTITUTION OF SOUND-WAVES ANALOGIES OF SOUND AND LIGHT ILLUSTRATIONS OF WAVE-MOTION INTERFERENCE OF SOUND-WAVES OPTICAL ILLUSTRATIONS PITCH AND COLOUR LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF THE ETHER-PARTICLES INTERFERENCE OF LIGHT PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY BOYLE AND HOOKE THE COLOURS OF THIN PLATES THE SOAP-BUBBLE NEWTON'S RINGS THEORY OF 'FITS' ITS EXPLANATION OF THE RINGS OVER-THROW OF THE THEORY DIFFRACTION OF LIGHT COLOURS PRODUCED BY DIFFRACTION COLOURS OF MOTHER-OF-PEARL. 

§ 1. _Origin and Scope of Physical Theories_. 

We might vary and extend our experiments on Light indefinitely, andthey certainly would prove us to possess a wonderful mastery over thephenomena. But the vesture of the agent only would thus be revealed, not the agent itself. The human mind, however, is so constituted thatit can never rest satisfied with this outward view of natural things. Brightness and freshness take possession of the mind when it iscrossed by the light of principles, showing the facts of Nature to beorganically connected. 

Let us, then, inquire what this thing is that we have been generating, reflecting, refracting and analyzing. 

In doing this, we shall learn that the life of the experimentalphilosopher is twofold. He lives, in his vocation, a life of thesenses, using his hands, eyes, and ears in his experiments: but such aquestion as that now before us carries him beyond the margin of thesenses. He cannot consider, much less answer, the question, 'What islight?' without transporting himself to a world which underlies thesensible one, and out of which all optical phenomena spring. Torealise this subsensible world the mind must possess a certainpictorial power. It must be able to form definite images of the thingswhich that world contains; and to say that, if such or such a state ofthings exist in the subsensible world, then the phenomena of thesensible one must, of necessity, grow out of this state of things. Physical theories are thus formed, the truth of which is inferred fromtheir power to explain the known and to predict the unknown. 

This conception of physical theory implies, as you perceive, theexercise of the imagination--a word which seems to render manyrespectable people, both in the ranks of science and out of them, uncomfortable. That men in the ranks of science should feel thus is, Ithink, a proof that they have suffered themselves to be misled by thepopular definition of a great faculty, instead of observing itsoperation in their own minds. Without imagination we cannot take astep beyond the bourne of the mere animal world, perhaps not even tothe edge of this one. But, in speaking thus of imagination, I do notmean a riotous power which deals capriciously with facts, but awell-ordered and disciplined power, whose sole function is to formsuch conceptions as the intellect imperatively demands. Imagination, thus exercised, never really severs itself from the world of fact. This is the storehouse from which its materials are derived; and themagic of its art consists, not in creating things anew, but in sochanging the magnitude, position, grouping, and other relations ofsensible things, as to render them fit for the requirements of theintellect in the subsensible world. [9]

Descartes imagined space to be filled with something that transmittedlight _instantaneously_. Firstly, because, in his experience, nomeasurable interval was known to exist between the appearance of aflash of light, however distant, and its effect upon consciousness;and secondly, because, as far as his experience went, no physicalpower is conveyed from place to place without a vehicle. But hisimagination helped itself farther by illustrations drawn from theworld of fact. 'When, ' he says, ' one walks in darkness with staff inhand, the moment the distant end of the staff strikes an obstacle thehand feels it. This explains what might otherwise be thought strange, that the light reaches us instantaneously from the sun. I wish thee tobelieve that light in the bodies that we call luminous is nothing morethan a very brisk and violent motion, which, by means of the air andother transparent media, is conveyed to the eye, exactly as the shockthrough the walking-stick reaches the hand of a blind man. This isinstantaneous, and would be so even if the intervening distance weregreater than that between earth and heaven. It is therefore no morenecessary that anything material should reach the eye from theluminous object, than that something should be sent from the ground tothe hand of the blind man when he is conscious of the shock of hisstaff. ' The celebrated Robert Hooke at first threw doubt upon thisnotion of Descartes, but he afterwards substantially espoused it. Thebelief in instantaneous transmission was destroyed by the discovery ofRoemer referred to in our last lecture. 

§ 2. _The Emission Theory of Light_. 

The case of Newton still more forcibly illustrates the position, thatin forming physical theories we draw for our materials upon the worldof fact. Before he began to deal with light, he was intimatelyacquainted with the laws of elastic collision, which all of you haveseen more or less perfectly illustrated on a billiard-table. Asregards the collision of sensible elastic masses, Newton knew theangle of incidence to be equal to the angle of reflection, and he alsoknew that experiment, as shown in our last lecture (fig. 3), hadestablished the same law with regard to light. He thus found in hisprevious knowledge the material for theoretic images. He had only tochange the magnitude of conceptions already in his mind to arrive atthe Emission Theory of Light. Newton supposed light to consist ofelastic particles of inconceivable minuteness, shot out withinconceivable rapidity by luminous bodies. Optical reflectioncertainly occurred _as if_ light consisted of such particles, and thiswas Newton's justification for introducing them. 

But this is not all. In another important particular, also, Newton'sconceptions regarding the nature of light were influenced by hisprevious knowledge. He had been pondering over the phenomena ofgravitation, and had made himself at home amid the operations of thisuniversal power. Perhaps his mind at this time was too freshly and toodeeply imbued with these notions to permit of his forming anunfettered judgment regarding the nature of light. Be that as it may, Newton saw in Refraction the result of an attractive force exerted onthe light-particles. He carried his conception out with the mostsevere consistency. Dropping vertically downwards towards the earth'ssurface, the motion of a body is accelerated as it approaches theearth. Dropping downwards towards a horizontal surface--say from airon to glass or water--the velocity of the light-particles, when theycame close to the surface, is, according to Newton, also accelerated. Approaching such a surface obliquely, he supposed the particles, whenclose to it, to be drawn down upon it, as a projectile is deflected bygravity to the surface of the earth. This deflection was, according toNewton, the refraction seen in our last lecture (fig. 4). Finally, itwas supposed that differences of colour might be due to differencesin the 'bigness' of the particles. This was the physical theory oflight enunciated and defended by Newton; and you will observe that itsimply consists in the transference of conceptions, born in the worldof the senses, to a subsensible world. 

But, though the region of physical theory lies thus behind the worldof senses, the verifications of theory occur in that world. Laying thetheoretic conception at the root of matters, we determine by deductionwhat are the phenomena which must of necessity grow out of this root. If the phenomena thus deduced agree with those of the actual world, itis a presumption in favour of the theory. If, as new classes ofphenomena arise, they also are found to harmonise with theoreticdeduction, the presumption becomes still stronger. If, finally, thetheory confers prophetic vision upon the investigator, enabling him topredict the occurrence of phenomena which have never yet been seen, and if those predictions be found on trial to be rigidly correct, thepersuasion of the truth of the theory becomes overpowering. 

Thus working backwards from a limited number of phenomena, the humanmind, by its own expansive force, reaches a conception which coversthem all. There is no more wonderful performance of the intellect thanthis; but we can render no account of it. Like the scriptural gift ofthe Spirit, no man can tell whence it cometh. The passage from fact toprinciple is sometimes slow, sometimes rapid, and at all times asource of intellectual joy. When rapid, the pleasure is concentrated, and becomes a kind of ecstasy or intoxication. To any one who hasexperienced this pleasure, even in a moderate degree, the action ofArchimedes when he quitted the bath, and ran naked, crying 'Eureka!'through the streets of Syracuse, becomes intelligible. 

How, then, did it fare with the Emission Theory when the deductionsfrom it were brought face to face with natural phenomena? Tested byexperiment, it was found competent to explain many facts, and withtranscendent ingenuity its author sought to make it account for all. He so far succeeded, that men so celebrated as Laplace and Malus, wholived till 1812, and Biot and Brewster, who lived till our own time, were found among his disciples. 

§ 3. _The Undulatory Theory of Light_. 

Still, even at an early period of the existence of the EmissionTheory, one or two great men were found espousing a different one. They furnish another illustration of the law that, in formingtheories, the scientific imagination must draw its materials from theworld of fact and experience. It was known long ago that sound isconveyed in waves or pulses through the air; and no sooner was thistruth well housed in the mind than it became the basis of a theoreticconception. It was supposed that light, like sound, might also be theproduct of wave-motion. But what, in this case, could be the materialforming the waves? For the waves of sound we have the air of ouratmosphere; but the stretch of imagination which filled all space witha _luminiferous ether_ trembling with the waves of light was so boldas to shock cautious minds. In one of my latest conversations with SirDavid Brewster, he said to me that his chief objection to theundulatory theory of light was, that he could not think the Creatorcapable of so clumsy a contrivance as the filling of space with etherto produce light. This, I may say, is very dangerous ground, and thequarrel of science with Sir David, on this point as with manyestimable persons on other points, is, that they profess to know toomuch about the mind of the Creator. 

This conception of an ether was advocated, and successfully applied tovarious phenomena of optics, by the illustrious astronomer, Huyghens. He deduced from it the laws of reflection and refraction, and appliedit to explain the double refraction of Iceland spar. The theory wasespoused and defended by the celebrated mathematician, Euler. Theywere, however, opposed by Newton, whose authority at the time borethem down. Or shall we say it was authority merely? Not quite so. Newton's preponderance was in some degree due to the fact that, thoughHuyghens and Euler were right in the main, they did not possesssufficient data to _prove_ themselves right. No human authority, however high, can maintain itself against the voice of Nature speakingthrough experiment. But the voice of Nature may be an uncertain voice, through the scantiness of data. This was the case at the period nowreferred to, and at such a period, by the authority of Newton, allantagonists were naturally overborne. 

The march of mind is rhythmic, not uniform, and this great EmissionTheory, which held its ground so long, resembled one of those circleswhich, according to your countryman Emerson, the intermittent force ofgenius periodically draws round the operations of the intellect, butwhich are eventually broken through by pressure from behind. In theyear 1773 was born, at Milverton, in Somersetshire, a circle-breakerof this kind. He was educated for the profession of a physician, butwas too strong to be tied down to professional routine. He devotedhimself to the study of natural philosophy, and became in all itsdepartments a master. He was also a master of letters. Languages, ancient and modern, were housed within his brain, and, to use thewords of his epitaph, 'he first penetrated the obscurity which hadveiled for ages the hieroglyphics of Egypt. ' It fell to the lot ofthis man to discover facts in optics which Newton's theory wasincompetent to explain, and his mind roamed in search of a sufficienttheory. He had made himself acquainted with all the phenomena ofwave-motion; with all the phenomena of sound; working successfully inthis domain as an original discoverer. Thus informed and disciplined, he was prepared to detect any resemblance which might reveal itselfbetween the phenomena of light and those of wave-motion. Suchresemblances he did detect; and, spurred on by the discovery, hepursued his speculations and experiments, until he finally succeededin placing on an immovable basis the Undulatory Theory of Light. 

The founder of this great theory was Thomas Young, a name, perhaps, unfamiliar to many of you, but which ought to be familiar to you all. Permit me, therefore, by a kind of geometrical construction which Ionce ventured to employ in London, to give you a notion of themagnitude of this man. Let Newton stand erect in his age, and Young inhis. Draw a straight line from Newton to Young, tangent to the headsof both. This line would slope downwards from Newton to Young, because Newton was certainly the taller man of the two. But the slopewould not be steep, for the difference of stature was not excessive. The line would form what engineers call a gentle gradient from Newtonto Young. Place underneath this line the biggest man born in theinterval between both. It may be doubted whether he would reach theline; for if he did he would be taller intellectually than Young, andthere was probably none taller. But I do not want you to rest onEnglish estimates of Young; the German, Helmholtz, a kindred genius, thus speaks of him: "His was one of the most profound minds that theworld has ever seen; but he had the misfortune to be too much inadvance of his age. He excited the wonder of his contemporaries, who, however, were unable to follow him to the heights at which his daringintellect was accustomed to soar. His most important ideas lay, therefore, buried and forgotten in the folios of the Royal Society, until a new generation gradually and painfully made the samediscoveries, and proved the exactness of his assertions and the truthof his demonstrations. "

It is quite true, as Helmholtz says, that Young was in advance of hisage; but something is to be added which illustrates the responsibilityof our public writers. For twenty years this man of genius wasquenched--hidden from the appreciative intellect of hiscountry-men--deemed in fact a dreamer, through the vigorous sarcasm ofa writer who had then possession of the public ear, and who in the_Edinburgh Review_ poured ridicule upon Young and his speculations. Tothe celebrated Frenchmen Fresnel and Arago he was first indebted forthe restitution of his rights; for they, especially Fresnel, independently remade and vastly extended his discoveries. To thestudents of his works Young has long since appeared in his true light, but these twenty blank years pushed him from the public mind, whichbecame in time filled with the fame of Young's colleague at the RoyalInstitution, Davy, and afterwards with the fame of Faraday. Carlylerefers to a remark of Novalis, that a man's self-trust is enormouslyincreased the moment he finds that others believe in him. If theopposite remark be true--if it be a fact that public disbelief weakensa man's force--there is no calculating the amount of damage thesetwenty years of neglect may have done to Young's productiveness as aninvestigator. It remains to be stated that his assailant was Mr. HenryBrougham, afterwards Lord Chancellor of England. 

§ 4. _Wave-Motion, Interference of Waves, 'Whirlpool Rapids' ofNiagara_. 

Our hardest work is now before us. But the capacity for hard workdepends in a great measure on the antecedent winding up of the will; Iwould call upon you, therefore, to gird up your loins for cominglabours. 

In the earliest writings of the ancients we find the notion that soundis conveyed by the air. Aristotle gives expression to this notion, andthe great architect Vitruvius compares the waves of sound to waves ofwater. But the real mechanism of wave-motion was hidden from theancients, and indeed was not made clear until the time of Newton. Thecentral difficulty of the subject was, to distinguish between themotion of the wave itself, and the motion of the particles which atany moment constitute the wave. 

Stand upon the seashore and observe the advancing rollers before theyare distorted by the friction of the bottom. Every wave has a back anda front, and, if you clearly seize the image of the moving wave, youwill see that every particle of water along the front of the wave isin the act of rising, while every particle along its back is in theact of sinking. The particles in front reach in succession the crestof the wave, and as soon as the crest is past they begin to fall. Theythen reach the furrow or _sinus_ of the wave, and can sink no farther. Immediately afterwards they become the front of the succeeding wave, rise again until they reach the crest, and then sink as before. Thus, while the waves pass onwards horizontally, the individual particlesare simply lifted up and down vertically. Observe a sea-fowl, or, ifyou are a swimmer, abandon yourself to the action of the waves; youare not carried forward, but simply rocked up and down. Thepropagation of a wave is the propagation of a _form_, and not thetransference of the substance which constitutes the wave. 

The _length_ of the wave is the distance from crest to crest, whilethe distance through which the individual particles oscillate iscalled the _amplitude_ of the oscillation. You will notice that inthis description the particles of water are made to vibrate _across_the line of propagation. [10]

And now we have to take a step forwards, and it is the most importantstep of all. You can picture two series of waves proceeding fromdifferent origins through the same water. When, for example, you throwtwo stones into still water, the ring-waves proceeding from the twocentres of disturbance intersect each other. Now, no matter hownumerous these waves may be, the law holds good that the motion ofevery particle of the water is the algebraic sum of all the motionsimparted to it. If crest coincide with crest and furrow with furrow, the wave is lifted to a double height above its sinus; if furrowcoincide with crest, the motions are in opposition and their sum iszero. We have then _still_ water. This action of wave upon wave istechnically called _interference_, a term, to be remembered. 

To the eye of a person conversant with these principles, nothing canbe more interesting than the crossing of water ripples. Through theirinterference the water-surface is sometimes shivered into the mostbeautiful mosaic, trembling rhythmically as if with a kind of visiblemusic. When waves are skilfully generated in a dish of mercury, astrong light thrown upon the shining surface, and reflected on to ascreen, reveals the motions of the liquid metal. The shape of thevessel determines the forms of the figures produced. In a circulardish, for example, a disturbance at the centre propagates itself as aseries of circular waves, which, after reflection, again meet at thecentre. If the point of disturbance be a little way removed from thecentre, the interference of the direct and reflected waves producesthe magnificent chasing shown in the annexed figure. [11] The lightreflected from such a surface yields a pattern of extraordinarybeauty. When the mercury is slightly struck by a needle-point in adirection concentric with the surface of the vessel, the lines oflight run round in mazy coils, interlacing and unravelling themselvesin a wonderful manner. When the vessel is square, a splendidchequer-work is produced by the crossing of the direct and reflectedwaves. Thus, in the case of wave-motion, the most ordinary causes giverise to most exquisite effects. The words of Emerson are perfectlyapplicable here:--

[Illustration: Fig. 10. ]

 'Thou can'st not wave thy staff in the air, Or dip thy paddle in the lake, But it carves the brow of beauty there. And the ripples in rhymes the oars forsake. '

The most impressive illustration of the action of waves on waves thatI have ever seen occurs near Niagara. For a distance of two miles, orthereabouts, below the Falls, the river Niagara flows unruffledthrough its excavated gorge. The bed subsequently narrows, and thewater quickens its motion. At the place called the 'Whirlpool Rapids, 'I estimated the width of the river at 300 feet, an estimate confirmedby the dwellers on the spot. When it is remembered that the drainageof nearly half a continent is compressed into this space, theimpetuosity of the river's escape through this gorge may be imagined. 

Two kinds of motion are here obviously active, a motion of translationand a motion of undulation--the race of the river through its gorge, and the great waves generated by its collision with the obstacles inits way. In the middle of the stream, the rush and tossing are mostviolent; at all events, the impetuous force of the individual waves ishere most strikingly displayed. Vast pyramidal heaps leap incessantlyfrom the river, some of them with such energy as to jerk their summitsinto the air, where they hang suspended as bundles of liquid pearls, which, when shone upon by the sun, are of indescribable beauty. 

The first impression, and, indeed, the current explanation of theseRapids is, that the central bed of the river is cumbered with largeboulders, and that the jostling, tossing, and wild leaping of thewaters there are due to its impact against these obstacles. A verydifferent explanation occurred to me upon the spot. Boulders derivedfrom the adjacent cliffs visibly cumber the _sides_ of the river. Against these the water rises and sinks rhythmically but violently, large waves being thus produced. On the generation of each wave thereis an immediate compounding of the wave-motion with the river-motion. The ridges, which in still water would proceed in circular curvesround the centre of disturbance, cross the river obliquely, and theresult is, that at the centre waves commingle which have really beengenerated at the sides. This crossing of waves may be seen on a smallscale in any gutter after rain; it may also be seen on simply pouringwater from a wide-lipped jug. Where crest and furrow cross each other, the wave is annulled; where furrow and furrow cross, the river isploughed to a greater depth; and where crest and crest aid each other, we have that astonishing leap of the water which breaks the cohesionof the crests, and tosses them shattered into the air. The phenomenaobserved at the Whirlpool Rapids constitute, in fact, one of thegrandest illustrations of the principle of interference. 

§ 5. _Analogies of Sound and Light. _

Thomas Young's fundamental discovery in optics was that the principleof Interference was applicable to light. Long prior to his time anItalian philosopher, Grimaldi, had stated that under certaincircumstances two thin beams of light, each of which, acting singly, produced a luminous spot upon a white wall, when caused to acttogether, partially quenched each other and darkened the spot. Thiswas a statement of fundamental significance, but it required thediscoveries and the genius of Young to give it meaning. How he did sowill gradually become clear to you. You know that air is compressible:that by pressure it can be rendered more dense, and that bydilatation it can be rendered more rare. Properly agitated, atuning-fork now sounds in a manner audible to you all, and most of youknow that the air through which the sound is passing is parcelled outinto spaces in which the air is condensed, followed by other spaces inwhich the air is rarefied. These condensations and rarefactionsconstitute what we call _waves_ of sound. You can imagine the air of aroom traversed by a series of such waves, and you can imagine a secondseries sent through the same air, and so related to the first thatcondensation coincides with condensation and rarefaction withrarefaction. The consequence of this coincidence would be a loudersound than that produced by either system of waves taken singly. Butyou can also imagine a state of things where the condensations of theone system fall upon the rarefactions of the other system. In thiscase (other things being equal) the two systems would completelyneutralize each other. Each of them taken singly produces sound; bothof them taken together produce no sound. Thus by adding sound to soundwe produce silence, as Grimaldi, in his experiment, produced darknessby adding light to light. 

Through his investigations on sound, which were fruitful and profound, Young approached the study of light. He put meaning into theobservation of Grimaldi, and immensely extended it. With splendidsuccess he applied the undulatory theory to the explanation of thecolours of thin plates, and to those of striated surfaces. Hediscovered and explained classes of colour which had been previouslyunnoticed or unknown. On the assumption that light was wave-motion, all his experiments on interference were accounted for; on theassumption that light was flying particles, nothing was explained. Inthe time of Huyghens and Euler a medium had been assumed for thetransmission of the waves of light; but Newton raised the objectionthat, if light consisted of the waves of such a medium, shadows couldnot exist. The waves, he contended, would bend round opaque bodies andproduce the motion of light behind them, as sound turns a corner, oras waves of water wash round a rock. It was proved that the bendinground referred to by Newton actually occurs, but that the inflectedwaves abolish each other by their mutual interference. Young alsodiscerned a fundamental difference between the waves of light andthose of sound. Could you see the air through which sound-waves arepassing, you would observe every individual particle of airoscillating to and fro, _in the direction of propagation_. Could yousee the luminiferous ether, you would also find every individualparticle making a small excursion to and fro; but here the motion, like that assigned to the water-particles above referred to, would be_across_ the line of propagation. The vibrations of the air are_longitudinal_, those of the ether _transversal_. 

The most familiar illustration of the interference of sound-waves isfurnished by the _beats_ produced by two musical sounds slightly outof unison. When two tuning-forks in perfect unison are agitatedtogether the two sounds flow without roughness, as if they were butone. But, by attaching with wax to one of the forks a little weight, we cause it to vibrate more slowly than its neighbour. Suppose thatone of them performs 101 vibrations in the time required by the otherto perform 100, and suppose that at starting the condensations andrarefactions of both forks coincide. At the 101st vibration of thequicker fork they will again coincide, that fork at this point havinggained one whole vibration, or one whole wavelength, upon the other. But a little reflection will make it clear that, at the 50thvibration, the two forks condensation where the other tends to producea rarefaction; by the united action of the two forks, therefore, thesound is quenched, and we have a pause of silence. This occurs whereone fork has gained _half a wavelength_ upon the other. At the 101stvibration, as already stated, we have coincidence, and, therefore, augmented sound; at the 150th vibration we have again a quenching ofthe sound. Here the one fork is _three half-waves_ in advance of theother. In general terms, the waves conspire when the one series is an_even_ number of half-wave lengths, and they destroy each other whenthe one series is an _odd_ number of half-wave lengths in advance ofthe other. With two forks so circumstanced, we obtain thoseintermittent shocks of sound separated by pauses of silence, to whichwe give the name of beats. By a suitable arrangement, moreover, it ispossible to make one sound wholly extinguish another. Along fourdistinct lines, for example, the vibrations of the two prongs of atuning-fork completely blot each other out. [12]

The _pitch_ of sound is wholly determined by the rapidity of thevibration, as the _intensity_ is by the amplitude. What pitch is tothe ear in acoustics, colour is to the eye in the undulatory theory oflight. Though never seen, the lengths of the waves of light have beendetermined. Their existence is proved _by their effects_, and fromtheir effects also their lengths may be accurately deduced. This may, moreover, be done in many ways, and, when the different determinationsare compared, the strictest harmony is found to exist between them. This consensus of evidence is one of the strongest points of theundulatory theory. The shortest waves of the visible spectrum arethose of the extreme violet; the longest, those of the extreme red;while the other colours are of intermediate pitch or wavelength. Thelength of a wave of the extreme red is such, that it would require39, 000 such waves, placed end to end, to cover one inch, while 64, 631of the extreme violet waves would be required to span the samedistance. 

Now, the velocity of light, in round numbers, is 186, 000 miles persecond. Reducing this to inches, and multiplying the number thus foundby 39, 000, we find the number of waves of the extreme red, in 186, 000miles, to be four hundred and sixty millions of millions. _All thesewaves enter the eye, and strike the retina at the back of the eye inone second_. In a similar manner, it may be found that the number ofshocks corresponding to the impression of violet is six hundred andseventy-eight millions of millions. 

All space is filled with matter oscillating at such rates. From everystar waves of these dimensions move, with the velocity of light, likespherical shells in all directions. And in ether, just as in water, the motion of every particle is the algebraic sum of all the separatemotions imparted to it. One motion does not blot out the other; or, ifextinction occur at one point, it is strictly atoned for, by augmentedmotion, at some other point. Every star declares by its light itsundamaged individuality, as if it alone had sent its thrills throughspace. 

§ 6. _Interference of Light_. 

[Illustration: Fig. 11. ]

The principle of interference, as just stated, applies to the waves oflight as it does to the waves of water and the waves of sound. And theconditions of interference are the same in all three. If two series oflight-waves of the same length start at the same moment from a commonorigin (say A, fig. 11), crest coincides with crest, sinus with sinus, and the two systems blend together to a single system (A _m_ _n_) ofdouble amplitude. If both series start at the same moment, one of thembeing, at starting, a whole wavelength in advance of the other, theyalso add themselves together, and we have an augmented luminouseffect. The same occurs when the one system of waves is any _even_number of semi-undulations in advance of the other. But if the onesystem be half a wave-length (as at A' _a_', fig. 12), or any _odd_number of half wavelengths, in advance, then the crests of the onefall upon the sinuses of the other; the one system, in fact, tends to_lift_ the particles of ether at the precise places where the othertends to _depress_ them; hence, through the joint action of theseopposing forces (indicated by the arrows) the light-ether remainsperfectly still. This stillness of the ether is what we call darkness, which corresponds with a dead level in the case of water. 

[Illustration: Fig. 12. ]

It was said in our first lecture, with reference to the coloursproduced by absorption, that the function of natural bodies isselective, not creative; that they extinguish certain constituents ofthe white solar light, and appear in the colours of the unextinguishedlight. It must at once occur to you that, inasmuch as we have ininterference an agency by which light may be self-extinguished, we mayhave in it the conditions for the production of colour. But this wouldimply that certain constituents are quenched by interference, whileothers are permitted to remain. This is the fact; and it is entirelydue to the difference in the lengths of the waves of light. 

§ 7. _Colours of thin Films. Observations of Boyle and Hooke_. 

This subject may be illustrated by the phenomena which first suggestedthe undulatory theory to the mind of Hooke. These are the colours ofthin transparent films of all kinds, known as the _colours of thinplates_. In this relation no object in the world possesses a deeperscientific interest than a common soap-bubble. And here let me sayemerges one of the difficulties which the student of pure scienceencounters in the presence of 'practical' communities like those ofAmerica and England; it is not to be expected that such communitiescan entertain any profound sympathy with labours which seem so farremoved from the domain of practice as are many of the labours of theman of science. Imagine Dr. Draper spending his days in blowingsoap-bubbles and in studying their colours! Would you show him thenecessary patience, or grant him the necessary support? And yet be itremembered it was thus that minds like those of Boyle, Newton andHooke were occupied; and that on such experiments has been founded atheory, the issues of which are incalculable. I see no other way foryou, laymen, than to trust the scientific man with the choice of hisinquiries; he stands before the tribunal of his peers, and by theirverdict on his labours you ought to abide. 

Whence, then, are derived the colours of the soap-bubble? Imagine abeam of white light impinging on the bubble. When it reaches the firstsurface of the film, a known fraction of the light is reflected back. But a large portion of the beam enters the film, reaches its secondsurface, and is again in part reflected. The waves from the secondsurface thus turn back and hotly pursue the waves from the firstsurface. And, if the thickness of the film be such as to cause thenecessary retardation, the two systems of waves interfere with eachother, producing augmented or diminished light, as the case may be. 

But, inasmuch as the waves of light are of different lengths, it isplain that, to produce extinction in the case of the longer waves, agreater thickness of film is necessary than in the case of the shorterones. Different colours, therefore, must appear at differentthicknesses of the film. 

Take with you a little bottle of spirit of turpentine, and pour itinto one of your country ponds. You will then see the glowing of thosecolours over the surface of the water. On a small scale we producethem thus: A common tea-tray is filled with water, beneath the surfaceof which dips the end of a pipette. A beam of light falls upon thewater, and is reflected by it to the screen. Spirit of turpentine ispoured into the pipette; it descends, issues from the end in minutedrops, which rise in succession to the surface. On reaching it, eachdrop spreads suddenly out as a film, and glowing colours immediatelyflash forth upon the screen. The colours change as the thickness ofthe film changes by evaporation. They are also arranged in zones, inconsequence of the gradual diminution of thickness from the centreoutwards. 

Any film whatever will produce these colours. The film of air betweentwo plates of glass squeezed together, exhibits, as shown by Hooke, rich fringes of colour. A particularly fine example of these fringesis now before you. Nor is even air necessary; the rupture of opticalcontinuity suffices. Smite with an axe the black, transparentice--black, because it is pure and of great depth--under the moraineof a glacier; you readily produce in the interior flaws which no aircan reach, and from these flaws the colours of thin plates sometimesbreak like fire. But the source of most historic interest is, asalready stated, the soap-bubble. With one of the mixtures employed bythe eminent blind philosopher, Plateau, in his researches on thecohesion figures of thin films, we obtain in still air a bubble ten ortwelve inches in diameter. You may look at the bubble itself, or youmay look at its projection upon the screen; rich colours arranged inzones are, in both cases, exhibited. Rendering the beam parallel, andpermitting it to impinge upon the sides, bottom, and top of thebubble, gorgeous fans of colour, reflected from the bubble, overspreadthe screen, rotating as the beam is carried round. By this experimentthe internal motions of the film are also strikingly displayed. 

Not in a moment are great theories elaborated: the facts which demandthem become first prominent; then, to the period of observationsucceeds a period of pondering and of tentative explanation. By suchefforts the human mind is gradually prepared for the final theoreticillumination. The colours of thin plates, for example, occupied theattention of Robert Boyle. In his 'Experimental History of Colours' hecontends against the schools which affirmed that colour was 'apenetrative quality that reaches to the innermost parts of theobject, ' adducing opposing facts. 'To give you a first instance, ' hesays, 'I shall need but to remind you of what I told you a littleafter the beginning of this essay, touching the blue and red andyellow that may be produced upon a piece of tempered steel; for thesecolours, though they be very vivid, yet if you break the steel theyadorn, they will appear to be but superficial. ' He then describes, inphraseology which shows the delight he took in his work, the followingbeautiful experiment:--

'We took a quantity of clean lead, and melted it with a strong fire, and then immediately pouring it out into a clean vessel of convenientshape and matter (we used one of iron, that the great and sudden heatmight not injure it), and then carefully and nimbly taking off thescum that floated on the top, we perceived, as we expected, the smoothand glossy surface of the melted matter to be adorned with a veryglorious colour, which, being as transitory as delightful, did almostimmediately give place to another vivid colour, and that was asquickly succeeded by a third, and this, as it were, chased away by afourth; and so these wonderfully vivid colours successively appearedand vanished till the metal ceasing to be hot enough to hold anylonger this pleasing spectacle, the colours that chanced to adorn thesurface when the lead thus began to cool remained upon it, but were sosuperficial that how little soever we scraped off the surface of thelead, we did, in such places, scrape off all the colour. ' 'Thesethings, ' he adds, 'suggested to me some thoughts or ravings which Ihave not now time to acquaint you with. '[13]

He extends his observations to essential oils and spirits of wine, 'which being shaken till they have good store of bubbles, thosebubbles will (if attentively considered) appear adorned with variousand lovely colours, which all immediately vanish upon theretrogressing of the liquid which affords these bubbles their skinsinto the rest of the oil. ' He also refers to the colour of glassfilms. 'I have seen one that was skilled in fashioning glasses by thehelp of a lamp blowing some of them so strongly as to burst them;whereupon it was found that the tenacity of the metal was such thatbefore it broke it suffered itself to be reduced into films soextremely thin that they constantly showed upon their surface thevarying colours of the rainbow. '[14]

Subsequent to Boyle the colours of thin plates occupied the attentionof Robert Hooke, in whose writings we find a dawning of the undulatorytheory of light. He describes with great distinctness the coloursobtained with thin flakes of 'Muscovy glass' (talc), also thosesurrounding flaws in crystals where optical continuity is destroyed. He shows very clearly the dependence of the colour upon the thicknessof the film, and proves by microscopic observation that plates of auniform thickness yield uniform colours. 'If, ' he says, 'you take anysmall piece of the Muscovy glass, and with a needle, or some otherconvenient instrument, cleave it oftentimes into thinner and thinnerlaminæ, you shall find that until you come to a determinate thinnessof them they shall appear transparent and colourless; but if youcontinue to split and divide them further, you shall find at last thateach plate shall appear most lovely tinged or imbued with adeterminate colour. If, further, by any means you so flaw a prettythick piece that one part begins to cleave a little from the other, and between these two there be gotten some pellucid medium, thoselaminated or pellucid bodies that fill that space shall exhibitseveral rainbows or coloured lines, the colours of which will bedisposed and ranged according to the various thicknesses of theseveral parts of the plate. ' He then describes fully and clearly theexperiment with pressed glasses already referred to:--

'Take two small pieces of ground and polished looking-glass plate, each about the bigness of a shilling: take these two dry, and withyour forefingers and thumbs press them very hard and close together, and you shall find that when they approach each other very near therewill appear several irises or coloured lines, in the same manneralmost as in the Muscovy glass; and you may very easily change any ofthe colours of any part of the interposed body by pressing the platescloser and harder together, or leaving them more lax--that is, a partwhich appeared coloured with a red, may presently be tinged with ayellow, blue, green, purple, or the like. 'Any substance, ' he says, 'provided it be thin and transparent, will show these colours. ' LikeBoyle, he obtained them with glass films; he also procured them withbubbles of pitch, rosin, colophony, turpentine, solutions of severalgums, as gum arabic in water, any glutinous liquor, as wort, wine, spirit of wine, oyl of turpentine, glare of snails, &c. 

Hooke's writings show that even in his day the idea that both lightand heat are modes of motion had taken possession of many minds. 'First, ' he says, 'that all kind _of fiery burning bodies_ have theirparts in motion I think will be easily granted me. That the sparkstruck from a flint and steel is in rapid agitation I have elsewheremade probable;... That heat argues a motion of the internal parts is(as I said before) generally granted;... And that in all extremely hotshining bodies there is a very quick motion that causes light, as wellas a more robust that causes heat, may be argued from the celeritywherewith the bodies are dissolved. Next, it must be _a vibrativemotion. '_ His reference to the quick motion of light and the morerobust motion of heat is a remarkable stroke of sagacity; but Hooke'sdirect insight is better than his reasoning; for the proofs he adducesthat light is 'a vibrating motion' have no particular bearing upon thequestion. 

Still the Undulatory Theory had undoubtedly dawned upon the mind ofthis remarkable man. In endeavouring to account for the colours ofthin plates, he again refers to the relation of colour to thickness:he dwells upon the fact that the film which shows these colours mustbe transparent, proving this by showing that however thin an opaquebody was rendered no colours were produced. 'This, ' he says, 'I haveoften tried by pressing a small globule of mercury between two smoothplates of glass, whereby I have reduced that body to a much greaterthinness than was requisite to exhibit the colours with a transparentbody. ' Then follows the sagacious remark that to produce the colours'there must be a considerable reflecting body adjacent to the under orfurther side of the lamina or plate: for this I always found, that thegreater that reflection was the more vivid were the appearing colours. From which observation, ' he continues, 'it is most evident, _that thereflection from the further or under side of the body is the principalcause of the production of these colours. _'

He draws a diagram, correctly representing the reflection at the twosurfaces of the film; but here his clearness ends. He ascribes thecolours to a coalescence or confusion of the two reflecting pulses;the principal of interference being unknown to him, he could not gofurther in the way of explanation. 

§ 8. _Newton's Rings. Relation of Colour to Thickness of Film_. 

[Illustration: Fig. 13]

In this way, then, by the active operation of different minds, factsare observed, examined, and the precise conditions of theirappearance determined. All such work in science is the prelude toother work; and the efforts of Boyle and Hooke cleared the way for theoptical career of Newton. He conquered the difficulty which Hooke hadfound insuperable, and determined by accurate measurements therelation of the thickness of the film to the colour it displays. Indoing this his first care was to obtain a film of variable andcalculable depth. On a plano-convex glass lens (D B E, fig. 13) ofvery feeble curvature he laid a plate of glass (A C) with a planesurface, thus obtaining a film of air of gradually increasing depthfrom the point of contact (B) outwards. On looking at the film inmonochromatic light he saw, with the delight attendant on fulfilledprevision, surrounding the place of contact, a series of bright ringsseparated from each other by dark ones, and becoming more closelypacked together as the distance from the point of contact augmented(as in fig. 14). When he employed red light, his rings had certaindiameters; when he employed blue light, the diameters were less. Ingeneral terms, the more refrangible the light the smaller were therings. Causing his glasses to pass through the spectrum from red toblue, the rings gradually contracted; when the passage was from blueto red, the rings expanded. This is a beautiful experiment, andappears to have given Newton the most lively satisfaction. When whitelight fell upon, the glasses, inasmuch as the colours were notsuperposed, a series _of iris-coloured_ circles was obtained. Amagnified image of _Newton's rings_ is now before you, and, byemploying in succession red, blue, and white light, we obtain all theeffects observed by Newton. You notice that in monochromatic light therings run closer and closer together as they recede from the centre. This is due to the fact that at a distance the film of air thickensmore rapidly than near the centre. When white light is employed, thisclosing up of the rings causes the various colours to be superposed, so that after a certain thickness they are blended together to whitelight, the rings then ceasing altogether. It needs but a moment'sreflection to understand that the colours of thin plates, produced bywhite light, are never unmixed or monochromatic. 

[Illustration: Fig. 14]

Newton compared the tints obtained in this way with the tints of hissoap-bubble, and he calculated the corresponding thickness. How he didthis may be thus made plain to you: Suppose the water of the ocean tobe absolutely smooth; it would then accurately represent the earth'scurved surface. Let a perfectly horizontal plane touch the surface atany point. Knowing the earth's diameter, any engineer or mathematicianin this room could tell you how far the sea's surface will lie belowthis plane, at the distance of a yard, ten yards, a hundred yards, ora thousand yards from the point of contact of the plane and the sea. It is common, indeed, in levelling operations, to allow for thecurvature of the earth. Newton's calculation was precisely similar. His plane glass was a tangent to his curved one. From its refractiveindex and focal distance he determined the diameter of the sphere ofwhich his curved glass formed a segment, he measured the distances ofhis rings from the place of contact, and he calculated the depthbetween the tangent plane and the curved surface, exactly as theengineer would calculate the distance between his tangent plane andthe surface of the sea. The wonder is, that, where such infinitesimaldistances are involved, Newton, with the means at his disposal, couldhave worked with such marvellous exactitude. 

To account for these rings was the greatest optical difficulty thatNewton, ever encountered. He quite appreciated the difficulty. Overhis eagle eye there was no film--no vagueness in his conceptions. Atthe very outset his theory was confronted by the question, Why, when abeam of light is incident on a transparent body, are some of thelight-particles reflected and some transmitted? Is it that there aretwo kinds of particles, the one specially fitted for transmission andthe other for reflection? This cannot be the reason; for, if we allowa beam of light which has been reflected from one piece of glass tofall upon another, it, as a general rule, is also divided into areflected and a transmitted portion. The particles once reflected arenot always reflected, nor are the particles once transmitted alwaystransmitted. Newton saw all this; he knew he had to explain why it isthat the self-same particle is at one moment reflected and at the nextmoment transmitted. It could only he through _some change in thecondition of the particle itself_. The self-same particle, heaffirmed, was affected by 'fits' of easy transmission and reflection. 

§ 9. _Theory of 'Fits' applied to Newton's Rings_. 

If you are willing to follow me in an attempt to reveal thespeculative groundwork of this theory of fits, the intellectualdiscipline will, I think, repay you for the necessary effort ofattention. Newton was chary of stating what he considered to be thecause of the fits, but there can hardly be a doubt that his mindrested on a physical cause. Nor can there be a doubt that here, as inall attempts at theorising, he was compelled to fall back uponexperience for the materials of his theory. Let us attempt to restorehis course of thought and observation. A magnet would furnish him withthe notion of attracted and repelled poles; and he who habitually sawin the visible an image of the invisible would naturally endow hislight-particles with such poles. Turning their attracted poles towardsa transparent substance, the particles would be sucked in andtransmitted; turning their repelled poles, they would be driven awayor reflected. Thus, by the ascription of poles, the transmission andreflection of the self-same particle at different times might beaccounted for. 

Consider these rings of Newton as seen in pure red light: they arealternately bright and dark. The film of air corresponding to theoutermost of them is not thicker than an ordinary soap-bubble, and itbecomes thinner on approaching the centre; still Newton, as I havesaid, measured the thickness corresponding to every ring, and showedthe difference of thickness between ring and ring. Now, mark theresult. For the sake of convenience, let us call the thickness of thefilm of air corresponding to the first dark ring _d_; then Newtonfound the distance corresponding to the second dark ring 2 _d_; thethickness corresponding to the third dark ring 3 _d_; the thicknesscorresponding to the tenth dark ring 10 _d_, and so on. Surely theremust be some hidden meaning in this little distance, _d_, which turnsup so constantly? One can imagine the intense interest with whichNewton pondered its meaning. Observe the probable outcome of histhought. He had endowed his light-particles with poles, but now he isforced to introduce the notion of _periodic recurrence_. Here hispower of transfer from the sensible to the subsensible would render iteasy for him to suppose the light-particles animated, not only with amotion of translation, but also with a motion of rotation. Newton'sastronomical knowledge rendered all such conceptions familiar to him. The earth has such a double motion. In the time occupied in passingover a million and a half of miles of its orbit--that is, intwenty-four hours--our planet performs a complete rotation; and in thetime required to pass over the distance _d_, Newton's light-particlemight be supposed to perform a complete rotation. True, thelight-particle is smaller than the planet, and the distance _d_, instead of being a million and a half of miles, is a little over theninety thousandth of an inch. But the two conceptions are, in point ofintellectual quality, identical. 

Imagine, then, a particle entering the film of air where it possessesthis precise thickness. To enter the film, its attracted end must bepresented. Within the film it is able to turn _once_ completely round;at the other side of the film its attracted pole will be againpresented; it will, therefore, enter the glass at the opposite side ofthe film _and be lost to the eye_. All round the place of contact, wherever the film possesses this precise thickness, the light willequally disappear--we shall therefore have a ring of darkness. 

And now observe how well this conception falls in with the law ofproportionality discovered by Newton. When the thickness of the filmis 2 _d_, the particle has time to perform, _two_ complete rotationswithin the film; when the thickness is 3 _d, three_ completerotations; when 10 _d, ten_ complete rotations are performed. It ismanifest that in each of these cases, on arriving at the secondsurface of the film, the attracted pole of the particle will bepresented. It will, therefore, be transmitted; and, because no lightis sent to the eye, we shall have a ring of darkness at each of theseplaces. 

The bright rings follow immediately from the same conception. Theyoccur between the dark rings, the thicknesses to which they correspondbeing also intermediate between those of the dark ones. Take the caseof the first bright ring. The thickness of the film is ½_d_; in thisinterval the rotating particle can perform only half a rotation. When, therefore, it reaches the second surface of the film, its repelledpole is presented; it is, therefore, driven back and reaches the eye. At all distances round the centre corresponding to this thickness thesame effect is produced, and the consequence is a ring of brightness. The other bright rings are similarly accounted for. At the second one, where the thickness is 1½_d_, a rotation and a half is performed; atthe third, two rotations and a half; and at each of these places theparticles present their repelled poles to the lower surface of thefilm. They are therefore sent back to the eye, and produce there theimpression of brightness. This analysis, though involving difficultieswhen closely scrutinised, enables us to see how the theory of fits mayhave grown into consistency in the mind of Newton. 

It has been already stated that the Emission Theory assigned a greatervelocity to light in glass and water than in air or stellar space; andthat on this point it was at direct issue with the theory ofundulation, which makes the velocity in air or stellar space greaterthan in glass or water. By an experiment proposed by Arago, andexecuted with consummate skill by Foucault and Fizeau, this questionwas brought to a crucial test, and decided in favour of the theory ofundulation. 

In the present instance also the two theories are at variance. Newtonassumed that the action which produces the alternate bright and darkrings took place at a _single surface_; that is, the second surface ofthe film. The undulatory theory affirms that the rings are caused bythe interference of waves reflected from both surfaces. This also hasbeen demonstrated by experiment. By a proper arrangement, as we shallafterwards learn, we may abolish reflection from one of the surfacesof the film, and when this is done the rings vanish altogether. 

Rings of feeble intensity are also formed by _transmitted_ light. These are referred by the undulatory theory to the interference ofwaves which have passed _directly_ through the film, with others whichhave suffered _two_ reflections within the film, and are thuscompletely accounted for. 

§ 10. _The Diffraction of Light_. 

Newton's espousal of the Emission Theory is said to have retardedscientific discovery. It might, however, be questioned whether, in thelong run, the errors of great men have not really their effect inrendering intellectual progress rhythmical, instead of permitting itto remain uniform, the 'retardation' in each case being the prelude toa more impetuous advance. It is confusion and stagnation, rather thanerror, that we ought to avoid. Thus, though the undulatory theory washeld back for a time, it gathered strength in the interval, and itsdevelopment within the last half century has been so rapid andtriumphant as to leave no rival in the field. We have now to turn tothe investigation of new classes of phenomena, of which it alone canrender a satisfactory account. 

Newton, who was familiar with the idea of an ether, and who introducedit in some of his speculations, objected, as already stated, that iflight consisted of waves shadows could not exist; for that the waveswould bend round the edges of opaque bodies and agitate the etherbehind them. He was right in affirming that this bending ought tooccur, but wrong in supposing that it does not occur. The bending isreal, though in all ordinary cases it is masked by the action ofinterference. This inflection of the light receives the name of_Diffraction_. 

To study the phenomena of diffraction it is necessary that our sourceof light should be a physical point, or a fine line; for when aluminous surface is employed, the waves issuing from different pointsof the surface obscure and neutralize each other. A _point_ of lightof high intensity is obtained by admitting the parallel rays of thesun through an aperture in a window-shutter, and concentrating thebeam by a lens of short focus. The small solar image at the focusconstitutes a suitable point of light. The image of the sun formed onthe convex surface of a glass bead, or of a watch-glass blackenedwithin, though less intense, will also answer. An intense _line_ oflight is obtained by admitting the sunlight through a slit and sendingit through a strong cylindrical lens. The slice of light is contractedto a physical line at the focus of the lens. A glass tube blackenedwithin and placed in the light, reflects from its surface a luminousline which, though less intense, also answers the purpose. 

In the experiment now to be described a vertical slit of variablewidth is placed in front of the electric lamp, and this slit is lookedat from a distance through another vertical slit, also of variableaperture, and held in the hand. 

The light of the lamp being, in the first place, renderedmonochromatic by placing a pure red glass in front of the slit, whenthe eye is placed in the straight line drawn through both slits anextraordinary appearance (shown in fig. 15) is observed. Firstly, theslit in front of the lamp is seen as a vivid rectangle of light; butright and left of it is a long series of rectangles, decreasing invividness, and separated from each other by intervals of absolutedarkness. 

The breadth of these bands is seen to vary with the width of the slitheld before the eye. When the slit is widened the bands becomenarrower, and crowd more losely together; when the slit is narrowed, the individual bands widen and also retreat from each other, leavingbetween them wider spaces of darkness than before. 

[Illustration: Fig. 15. ]

Leaving everything else unchanged, let a blue glass or a solution ofammonia-sulphate of copper, which gives a very pure blue, be placed inthe path of the light. A series of blue bands is thus obtained, exactly like the former in all respects save one; the blue rectanglesare _narrower_, and they are _closer together_ than the red ones. 

If we employ colours of intermediate refrangibilities, which we may doby causing the different colours of a spectrum to shine through theslit, we obtain bands of colour intermediate in width, and occupyingintermediate positions, between those of the red and blue. The aspectof the bands in red, green, and violet light is represented in fig. 16. When _white light_, therefore, passes through the slit the variouscolours are not superposed, and instead of a series of monochromaticbands, separated from each other by intervals of darkness, we have aseries of coloured spectra placed side by side. When the distant slitis illuminated by a candle flame, instead of the more intense electriclight, or when a distant platinum wire raised to a white heat by anelectric current is employed, substantially the same effects areobserved. 

[Illustration: Fig. 16. ]

§ 11. _Application of the Wave-theory to the Phenomena ofDiffraction_. 

Of these and of a multitude of similar effects the Emission Theory isincompetent to offer any satisfactory explanation. Let us see how theyare accounted for by the Theory of Undulation. 

And here, with the view of reaching absolute clearness, I must make anappeal to that faculty the importance of which I have dwelt upon soearnestly here and elsewhere--the faculty of imagination. Figureyourself upon the sea-shore, with a well-formed wave advancing. Take aline of particles along the front of the wave, all at the samedistance below the crest; they are all rising in the same manner andat the same rate. Take a similar line of particles on the back of thewave, they are all falling in the same manner and at the same rate. Take a line of particles along the crest, they are all in the samecondition as regards the motion of the wave. The same is true for aline of particles along the furrow of the wave. 

The particles referred to in each of these cases respectively, beingin the same condition as regards the motion of the wave, are said tobe in the same _phase_ of vibration. But if you compare a particle onthe front of the wave with one at the back; or, more generally, if youcompare together any two particles not occupying the same position inthe wave, their conditions of motion not being the same, they are saidto be in different phases of vibration. If one of the particles lieupon the crest, and the other on the furrow of the wave, then, as oneis about to rise and the other about to fall, they are said to be in_opposite_ phases of vibration. 

There is still another point to be cleared up--and it is one of theutmost importance as regards our present subject. Let O (fig. 17) be aspot in still water which, when disturbed, produces a series ofcircular waves: the disturbance necessary to produce these waves issimply an oscillation up and down of the water at O. Let _m_ _n_ bethe position of the ridge of one of the waves at any moment, and _m'__n'_ its position a second or two afterwards. Now every particle ofwater, as the wave passes it, oscillates, as we have learned, up anddown. If, then, this oscillation be a sufficient origin ofwave-motion, each distinct particle of the wave _m_ _n_ ought to givebirth, to a series of circular waves. This is the important point upto which I wish to lead you. Every particle of the wave _m_ _n_ _does_act in this way. Taking each particle as a centre, and surrounding itby a circular wave with a radius equal to the distance between _m_ _n_and _m'_ _n'_, the coalescence of all these little waves would buildup the large ridge _m'_ _n'_ exactly as we find it built up in nature. Here, in fact, we resolve the wave-motion into its elements, andhaving succeeded in doing this we shall have no great difficulty inapplying our knowledge to optical phenomena. 

[Illustration: Fig. 17. ]

Now let us return to our slit, and, for the sake of simplicity, wewill first consider the case of monochromatic light. Conceive a seriesof waves of ether advancing from the first slit towards the second, and finally filling the second slit. When each wave passes through thelatter it not only pursues its direct course to the retina, butdiverges right and left, tending to throw into motion the entire massof the ether behind the slit. In fact, as already explained, _everypoint of the wave which fills the slit is itself a centre of a newwave system which is transmitted in all directions through the etherbehind the slit_. This is the celebrated principle of Huyghens: wehave now to examine how these secondary waves act upon each other. 

[Illustration: Fig. 18. ]

Let us first regard the central band of the series. Let AP (fig. 18)be the width of the aperture held before the eye, grossly exaggeratedof course, and let the dots across the aperture represent etherparticles, all in the same phase of vibration. Let E T represent aportion of the retina. From O, in the centre of the slit, let aperpendicular O R be imagined drawn upon the retina. The motioncommunicated to the point R will then be the sum of all the motionsemanating in this direction from the ether particles in the slit. Considering the extreme narrowness of the aperture, we may, withoutsensible error, regard all points of the wave A P as equally distantfrom R. No one of the partial waves lags sensibly behind the others:hence, at R, and in its immediate neighbourhood, we have no sensiblereduction of the light by interference. This undiminished lightproduces the brilliant central band of the series. 

Let us now consider those waves which diverge laterally behind thesecond slit. In this case the waves from the two sides of the slithave, in order to converge upon the retina, to pass over unequaldistances. Let A P (fig. 19) represent, as before, the width of thesecond slit. We have now to consider the action of the various partsof the wave A P upon a point R' of the retina, not situated in theline joining the two slits. 

[Illustration: Fig. 19. ]

Let us take the particular case in which the difference of path fromthe two marginal points A, P, to the retina is a whole wave-length ofthe red light; how must this difference affect the final illuminationof the retina?

Let us fix our attention upon the particular oblique line that passesthrough the _centre_ O of the slit to the retina at R'. The differenceof path between the waves which pass along this line and those fromthe two margins is, in the case here supposed, half a wavelength. Make_e_ R' equal to P R', join P and _e_, and draw O _d_ parallel to P e. A e is then the length of a wave of light, while A _d_ is half awave-length. Now the least reflection will make it clear that not onlyis there discordance between the central and marginal waves, but thatevery line of waves such as _x_ R', on the one side of O R', finds aline _x_' R' upon the other side of O R', from which its path differsby half an undulation--with which, therefore, it is in completediscordance. The consequence is, that the light on the one side of thecentral line will completely abolish the light on the other side ofthat line, absolute darkness being the result of their coalescence. The first dark interval of our series of bands is thus accounted for. It is produced by an obliquity of direction which causes the paths ofthe marginal waves to be _a whole wave-length_ different from eachother. 

When the difference between the paths of the marginal waves is _half awave-length, _ a partial destruction of the light is effected. Theluminous intensity corresponding to this obliquity is a little lessthan one-half--accurately 0. 4--that of the undiffracted light. If thepaths of the marginal waves be three semi-undulations different fromeach other, and if the whole beam be divided into three equal parts, two of these parts will, for the reasons just given, completelyneutralize each other, the third only being effective. Corresponding, therefore, to an obliquity which produces a difference of threesemi-undulations in the marginal waves, we have a luminous band, butone of considerably less intensity than the undiffracted central band. 

With a marginal difference of path of four semi-undulations we have asecond extinction of the entire beam, because here the beam can bedivided into four equal parts, every two of which quench each other. A second space of absolute darkness will therefore correspond to theobliquity producing this difference. In this way we might proceedfurther, the general result being that, whenever the direction ofwave-motion is such as to produce a marginal difference of path of an_even_ number of semi-undulations, we have complete extinction; while, when the marginal difference is an _odd_ number of semi-undulations, we have only partial extinction, a portion of the beam remaining as aluminous band. 

A moment's reflection will make it plain that the wider the slit theless will be the obliquity of direction needed to produce thenecessary difference of path. With a wide slit, therefore, the bands, as observed, will be closer together than with a narrow one. It isalso plain that the shorter the wave, the less will be the obliquityrequired to produce the necessary retardation. The maxima and minimaof violet light must therefore fall nearer to the centre than themaxima and minima of red light. The maxima and minima of the othercolours fall between these extremes. In this simple way the undulatorytheory completely accounts for the extraordinary appearance abovereferred to. 

When a slit and telescope are used, instead of the slit and naked eye, the effects are magnified and rendered more brilliant. Looking, moreover, through a properly adjusted telescope with a small circularaperture in front of it, at a distant point of light, the point isseen encircled by a series of coloured bands. If monochromatic lightbe used, these bands are simply bright and dark, but with white lightthe circles display iris-colours. If a slit be shortened so as to forma square aperture, we have two series of spectra at right angles toeach other. The effects, indeed, are capable of endless variation byvarying the size, shape, and number of the apertures through which thepoint of light is observed. Through two square apertures, with theircorners touching each other as at A, Schwerd observed the appearanceshown in fig. 20. Adding two others to them, as at B, he observed theappearance represented in fig. 21. The position of every band of lightand shade in such figures has been calculated from theory by Fresnel, Fraunhofer, Herschel, Schwerd, and others, and completely verified byexperiment. Your eyes could not tell you with greater certainty of theexistence of these bands than the theoretic calculation. 

[Illustration: Fig. 20. ]

The street-lamps at night, looked at through the meshes of ahandkerchief, show diffraction phenomena. The diffraction effectsobtained in looking through a bird's feathers are, as shown bySchwerd, very brilliant. The iridescence of certain Alpine clouds isalso an effect of diffraction which may be imitated by thespores of Lycopodium. When shaken over a glass plate these sporescause a point of light, looked at through the dusted plate, to besurrounded by coloured circles, which rise to actual splendour whenthe light becomes intense. Shaken in the air the spores produce thesame effect. The diffraction phenomena obtained during the artificialprecipitation of clouds from the vapours of various liquids in anintensely illuminated tube are, as I have elsewhere shewn, exceedinglyfine. 

[Illustration: Fig. 21. ]

One of the most interesting cases of diffraction by small particlesthat ever came before me was that of an artist whose vision wasdisturbed by vividly coloured circles. He was in great dread of losinghis sight; assigning as a cause of his increased fear that the circleswere becoming larger and the colours more vivid. I ascribed thecolours to minute particles in the humours of the eye, and ventured toencourage him by the assurance that the increase of size and vividnesson the part of the circles indicated that the diffracting particleswere becoming _smaller_, and that they might finally be altogetherabsorbed. The prediction was verified. It is needless to say one wordon the necessity of optical knowledge in the case of the practicaloculist. 

Without breaking ground on the chromatic phenomena presented bycrystals, two other sources of colour may be mentioned here. Byinterference in the earth's atmosphere, the light of a star, as shownby Arago, is self-extinguished, the twinkling of the star and thechanges of colour which it undergoes being due to this cause. Lookingat such a star through an opera-glass, and shaking the glass so as tocause the image of the star to pass rapidly over the retina, youproduce a row of coloured beads, the spaces between which correspondto the periods of extinction. Fine scratches drawn upon glass orpolished metal reflect the waves of light from their sides; and some, being reflected from the opposite sides of the same scratch, interferewith and quench each other. But the obliquity of reflection whichextinguishes the shorter waves does not extinguish the longer ones, hence the phenomena of colours. These are called the colours of_striated surfaces_. They are beautifully illustrated bymother-of-pearl. This shell is composed of exceedingly thin layers, which, when cut across by the polishing of the shell, expose theiredges and furnish the necessary small and regular grooves. The mostconclusive proof that the colours are due to the mechanical state ofthe surface is to be found in the fact, established by Brewster, thatby stamping the shell carefully upon black sealing-wax, we transferthe grooves, and produce upon the wax the colours of mother-of-pearl. 

LECTURE III. 

 RELATION OF THEORIES TO EXPERIENCE ORIGIN OF THE NOTION OF THE ATTRACTION OF GRAVITATION NOTION OF POLARITY, HOW GENERATED ATOMIC POLARITY STRUCTURAL ARRANGEMENTS DUE TO POLARITY ARCHITECTURE OF CRYSTALS CONSIDERED AS AN INTRODUCTION TO THEIR ACTION UPON LIGHT NOTION OF ATOMIC POLARITY APPLIED TO CRYSTALLINE STRUCTURE EXPERIMENTAL ILLUSTRATIONS CRYSTALLIZATION OF WATER EXPANSION BY HEAT AND BY COLD DEPORTMENT OF WATER CONSIDERED AND EXPLAINED BEARINGS OF CRYSTALLIZATION ON OPTICAL PHENOMENA REFRACTION DOUBLE REFRACTION POLARIZATION ACTION OF TOURMALINE CHARACTER OF THE BEAMS EMERGENT FROM ICELAND SPAR POLARIZATION BY ORDINARY REFRACTION AND REFLECTION DEPOLARIZATION

§ 1. _Derivation of Theoretic Conceptions from Experience. _

One of the objects of our last lecture, and that not the leastimportant, was to illustrate the manner in which scientific theoriesare formed. They, in the first place, take their rise in the desire ofthe mind to penetrate to the sources of phenomena. From itsinfinitesimal beginnings, in ages long past, this desire has grown andstrengthened into an imperious demand of man's intellectual nature. Itlong ago prompted Cæsar to say that he would exchange his victoriesfor a glimpse of the sources of the Nile; it wrought itself into theatomic theories of Lucretius; it impelled Darwin to those daringspeculations which of late years have so agitated the public mind. Butin no case, while framing theories, does the imagination _create_ itsmaterials. It expands, diminishes, moulds, and refines, as the casemay be, materials derived from the world of fact and observation. 

This is more evidently the case in a theory like that of light, wherethe motions of a subsensible medium, the ether, are presented to themind. But no theory escapes the condition. Newton took care not toencumber the idea of gravitation with unnecessary physicalconceptions; but we know that he indulged in them, though he did notconnect them with his theory. But even the theory, as it stands, didnot enter the mind as a revelation dissevered from the world ofexperience. The germ of the conception that the sun and planets areheld together by a force of attraction is to be found in the fact thata magnet had been previously seen to attract iron. The notion ofmatter attracting matter came thus from without, not from within. Inour present lecture the magnetic force must serve as the portal into anew domain; but in the first place we must master its elementaryphenomena. 

The general facts of magnetism are most simply illustrated by amagnetized bar of steel, commonly called a bar magnet. Placing such amagnet upright upon a table, and bringing a magnetic needle near itsbottom, one end of the needle is observed to retreat from the magnet, while the other as promptly approaches. The needle is held quiveringthere by some invisible influence exerted upon it. Raising the needlealong the magnet, but still avoiding contact, the rapidity of itsoscillations decreases, because the force acting upon it becomesweaker. At the centre the oscillations cease. Above the centre, theend of the needle which had been previously drawn towards the magnetretreats, and the opposite end approaches. As we ascend higher, theoscillations become more violent, because the force becomes stronger. At the upper end of the magnet, as at the lower, the force reaches amaximum; but all the lower half of the magnet, from E to S (fig. 22), attracts one end of the needle, while all the upper half, from E to N, attracts the opposite end. This _doubleness_ of the magnetic force iscalled _polarity_, and the points near the ends of the magnet in whichthe forces seem concentrated are called its _poles_. 

[Illustration: Fig. 22. ]

What, then, will occur if we break this magnet in two at the centre E?Shall we obtain two magnets, each with a single pole? No; each half isin itself a perfect magnet, possessing two poles. This may be provedby breaking something of less value than the magnet--the steel of alady's stays, for example, hardened and magnetized. It acts like themagnet. When broken, each half acts like the whole; and when theseparts are again broken, we have still the perfect magnet, possessing, as in the first instance, two poles. Push your breaking to its utmostsensible limit--you cannot stop there. The bias derived fromobservation will infallibly carry you beyond the bourne of the senses, and compel you to regard this thing that we call magnetic polarity asresident in the ultimate particles of the steel. You come to theconclusion that each molecule of the magnet is endowed with this polarforce. 

Like all other forces, this force of magnetism is amenable tomechanical laws; and, knowing the direction and magnitude of theforce, we can predict its action. Placing a small magnetic needle neara bar magnet, it takes a determinate position. That position might bededuced theoretically from the mutual action of the poles. Moving theneedle round the magnet, for each point of the surrounding space thereis a definite direction of the needle and no other. A needle of ironwill answer as well as the magnetic needle; for the needle of iron ismagnetized by the magnet, and acts exactly like a steel needleindependently magnetized. 

If we place two or more needles of iron near the magnet, the actionbecomes more complex, for then the needles are not only acted on bythe magnet, but they act upon each other. And if we pass to smallermasses of iron--to iron filings, for example--we find that they actsubstantially as the needles, arranging themselves in definite forms, in obedience to the magnetic action. 

Placing a sheet of paper or glass over a bar magnet and showering ironfilings upon the paper, I notice a tendency of the filings to arrangethemselves in determinate lines. They cannot freely follow thistendency, for they are hampered by the friction against the paper. They are helped by tapping the paper; each tap releasing them for amoment, and enabling them to follow their tendencies. But this is anexperiment which can only be seen by myself. To enable you all to seeit, I take a pair of small magnets and by a simple optical arrangementthrow the magnified images of the magnets upon the screen. Scatteringiron filings over the glass plate to which the small magnets areattached, and tapping the plate, you see the arrangement of the ironfilings in those magnetic curves which have been so long familiar toscientific men (fig. 23). 

[Illustration: Fig. 23. 

N is the nozzle of the lamp; M a plane mirror, reflecting the beamupwards. At P the magnets and iron filings are placed; L is a lenswhich forms an image of the magnets and filings; and R is a totallyreflecting prism, which casts the image G upon the screen. ]

(By a very ingenious device, Professor Mayer, of Hoboken, hassucceeded in fixing and photographing the magnetic curves. I amindebted to his kindness for the annexed beautiful illustration, fig. 24. )

The aspect of these curves so fascinated Faraday that the greaterportion of his intellectual life was devoted to pondering over them. He invested the space through which they run with a kind ofmateriality; and the probability is that the progress of science, byconnecting the phenomena of magnetism with the luminiferous ether, will prove these 'lines of force, ' as Faraday loved to call them, torepresent a condition of this mysterious substratum of all radiantaction. 

It is not, however, the magnetic curves, as such, but theirrelationship to theoretic conceptions, that we have now to consider. By the action of the bar magnet upon the needle we obtain the notionof a polar force; by the breaking of the strip of magnetized steel weattain the notion that polarity can attach itself to the ultimateparticles of matter. The experiment with the iron filings introduces anew idea into the mind; the idea, namely, of _structural arrangement_. Every pair of filings possesses four poles, two of which areattractive and two repulsive. The attractive poles approach, therepulsive poles retreat; the consequence being a certain definitearrangement of the particles with reference to each other. 

§ 2. _Theory of Crystallization. _

Now this idea of structure, as produced by polar force, opens a wayfor the intellect into an entirely new region, and the reason youare asked to accompany me into this region is, that our next inquiryrelates to the action of crystals upon light. Prior to speaking ofthis action, I wish you to realise intellectually the process ofcrystalline architecture. Look then into a granite quarry, and spend afew minutes in examining the rock. It is not of perfectly uniformtexture. It is rather an agglomeration of pieces, which, onexamination, present curiously defined forms. You have there whatmineralogists call quartz, you have felspar, you have mica. In amineralogical cabinet, where these substances are preservedseparately, you will obtain some notion of their forms. You will seethere, also, specimens of beryl, topaz, emerald, tourmaline, heavyspar, fluor-spar, Iceland spar--possibly a full-formed diamond, as itquitted the hand of Nature, not yet having got into the hands of thelapidary. 

[Illustration: Fig. 24. ]

These crystals, you will observe, are put together according to law;they are not chance productions; and, if you care to examine them moreminutely, you will find their architecture capable of being to someextent revealed. They often split in certain directions before aknife-edge, exposing smooth and shining surfaces, which are calledplanes of cleavage; and by following these planes you sometimes reachan internal form, disguised beneath the external form of the crystal. Ponder these beautiful edifices of a hidden builder. You cannot helpasking yourself how they were built; and familiar as you now are withthe notion of a polar force, and the ability of that force to producestructural arrangement, your inevitable answer will be, that thosecrystals are built by the play of polar forces with which theirmolecules are endowed. In virtue of these forces, molecule laysitself to molecule in a perfectly definite way, the final visible formof the crystal depending upon this play of its ultimate particles. 

Everywhere in Nature we observe this tendency to run into definiteforms, and nothing is easier than to give scope to this tendency byartificial arrangements. Dissolve nitre in water, and allow the waterslowly to evaporate; the nitre remains and the solution soon becomesso concentrated that the liquid condition can no longer be preserved. The nitre-molecules approach each other, and come at length within therange of their polar forces. They arrange themselves in obedience tothese forces, a minute crystal of nitre being at first produced. Onthis crystal the molecules continue to deposit themselves from thesurrounding liquid. The crystal grows, and finally we have largeprisms of nitre, each of a perfectly definite shape. Alum crystallizeswith the utmost ease in this fashion. The resultant crystal is, however, different in shape from that of nitre, because the poles ofthe molecules are differently disposed. When they are _nursed_ withproper care, crystals of these substances may be caused to grow to agreat size. 

The condition of perfect crystallization is, that the crystallizingforce shall act with deliberation. There should be no hurry in itsoperations; but every molecule ought to be permitted, withoutdisturbance from its neighbours, to exercise its own rights. If thecrystallization be too sudden, the regularity disappears. Water may besaturated with sulphate of soda, dissolved when the water is hot, andafterwards permitted to cool. When cold the solution issupersaturated; that is to say, more solid matter is contained in itthan corresponds to its temperature. Still the molecules show no signof building themselves together. 

This is a very remarkable, though a very common fact. The molecules inthe centre of the liquid are so hampered by the action of theirneighbours that freedom to follow their own tendencies is denied tothem. Fix your mind's eye upon a molecule within the mass. It wishesto unite with its neighbour to the right, but it wishes equally tounite with its neighbour to the left; the one tendency neutralizes theother and it unites with neither. But, if a crystal of sulphate ofsoda be dropped into the solution, the molecular indecision ceases. Onthe crystal the adjacent molecules will immediately precipitatethemselves; on these again others will be precipitated, and this actof precipitation will continue from the top of the flask to thebottom, until the solution has, as far as possible, assumed the solidform. The crystals here produced are small, and confusedly arranged. The process has been too hasty to admit of the pure and orderly actionof the crystallizing force. It typifies the state of a nation in whichnatural and healthy change is resisted, until society becomes, as itwere, supersaturated with the desire for change, the change being theneffected through confusion and revolution. 

Let me illustrate the action of the crystallizing force by twoexamples of it: Nitre might be employed, but another well-knownsubstance enables me to make the experiment in a better form. Thesubstance is common sal-ammoniac, or chloride of ammonium, dissolvedin water. Cleansing perfectly a glass plate, the solution of thechloride is poured over the glass, to which when the plate is set onedge, a thin film of the liquid adheres. Warming the glass slightly, evaporation is promoted, but by evaporation the water only is removed. The plate is then placed in a solar microscope, and an image of thefilm is thrown upon a white screen. The warmth of the illuminatingbeam adds itself to that already imparted to the glass plate, so thatafter a moment or two the dissolved salt can no longer exist in theliquid condition. Molecule then closes with molecule, and you have amost impressive display of crystallizing energy overspreading thewhole screen. You may produce something similar if you breathe uponthe frost ferns which overspread your window-panes in winter, and thenobserve through a pocket lens the subsequent recongelation of thefilm. 

In this case the crystallizing force is hampered by the adhesion ofthe film to the glass; nevertheless, the play of power is strikinglybeautiful. Sometimes the crystals start from the edge of the film andrun through it from that edge; for, the crystallization being oncestarted, the molecules throw themselves by preference on the crystalsalready formed. Sometimes the crystals start from definite nuclei inthe centre of the film, every small crystalline particle which restsin the film furnishing a starting-point. Throughout the process younotice one feature which is perfectly unalterable, and that is, angular magnitude. The spiculæ branch from the trunk, and from thesebranches others shoot; but the angles enclosed by the spiculæ areunalterable. In like manner you may find alum-crystals, quartz-crystals, and all other crystals, distorted in shape. They arethus far at the mercy of the accidents of crystallization; but in oneparticular they assert their superiority over all suchaccidents--_angular magnitude_ is always rigidly preserved. 

My second example of the action of crystallizing force is this: Bysending a voltaic current through a liquid, you know that we decomposethe liquid, and if it contains a metal, we liberate this metal byelectrolysis. This small cell contains a solution of acetate of lead, which is chosen for our present purpose, because lead lends itselffreely to this crystallizing power. Into the cell are dipped two verythin platinum wires, and these are connected by other wires with asmall voltaic battery. On sending the voltaic current through thesolution, the lead will be slowly severed from the atoms with which itis now combined; it will be liberated upon one of the wires, and atthe moment of its liberation it will obey the polar forces of itsatoms, and produce crystalline forms of exquisite beauty. They are nowbefore you, sprouting like ferns from the wire, appearing indeed likevegetable growths rendered so rapid as to be plainly visible to thenaked eye. On reversing the current, these wonderful lead-fronds willdissolve, while from the other wire filaments of lead dart through theliquid. In a moment or two the growth of the lead-trees recommences, but they now cover the other wire. 

In the process of crystallization, Nature first reveals herself as abuilder. Where do her operations stop? Does she continue by the playof the same forces to form the vegetable, and afterwards the animal?Whatever the answer to these questions may be, trust me that thenotions of the coming generations regarding this mysterious thing, which some have called 'brute matter, ' will be very different fromthose of the generations past. 

There is hardly a more beautiful and instructive example of this playof molecular force than that furnished by water. You have seen theexquisite fern-like forms produced by the crystallization of a film ofwater on a cold window-pane. [15] You have also probably noticed thebeautiful rosettes tied together by the crystallizing force during thedescent of a snow-shower on a very calm day. The slopes and summits ofthe Alps are loaded in winter with these blossoms of the frost. Theyvary infinitely in detail of beauty, but the same angular magnitude ispreserved throughout: an inflexible power binding spears and spiculæto the angle of 60 degrees. 

The common ice of our lakes is also ruled in its formation by the sameangle. You may sometimes see in freezing water small crystals ofstellar shapes, each star consisting of six rays, with this angle of60° between every two of them. This structure may be revealed inordinary ice. In a sunbeam, or, failing that, in our electric beam, wehave an instrument delicate enough to unlock the frozen molecules, without disturbing the order of their architecture. Cutting fromclear, sound, regularly frozen ice, a slab parallel to the planes offreezing, and sending a sunbeam through such a slab, it liquefiesinternally at special points, round each point a six-petalled liquidflower of exquisite beauty being formed. Crowds of such flowers arethus produced. From an ice-house we sometimes take blocks of icepresenting misty spaces in the otherwise continuous mass; and when weinquire into the cause of this mistiness, we find it to be due tomyriads of small six-petalled flowers, into which the ice has beenresolved by the mere heat of conduction. 

A moment's further devotion to the crystallization of water will bewell repaid; for the sum of qualities which renders this substancefitted to play its part in Nature may well excite wonder and stimulatethought. Like almost all other substances, water is expanded by heatand contracted by cold. Let this expansion and contraction be firstillustrated:--

A small flask is filled with coloured water, and stopped with a cork. Through the cork passes a glass tube water-tight, the liquid standingat a certain height in the tube. The flask and its tube resemble thebulb and stem of a thermometer. Applying the heat of a spirit-lamp, the water rises in the tube, and finally trickles over the top. Expansion by heat is thus illustrated. 

Removing the lamp and piling a freezing mixture round the flask, theliquid column falls, thus showing the contraction of the water by thecold. But let the freezing mixture continue to act: the falling of thecolumn continues to a certain point; it then ceases. The top of thecolumn remains stationary for some seconds, and afterwards begins torise. The contraction has ceased, and _expansion by cold_ sets in. Letthe expansion continue till the liquid trickles a second time over thetop of the tube. The freezing mixture has here produced to allappearance the same effect as the flame. In the case of water, contraction by cold ceases, and expansion by cold sets in at thedefinite temperature of 39° Fahr. Crystallization has virtually herecommenced, the molecules preparing themselves for the subsequent actof solidification, which occurs at 32°, and in which the expansionsuddenly culminates. In virtue of this expansion, ice, as you know, islighter than water in the proportion of 8 to 9. [16]

A molecular problem of great interest is here involved, and I wish nowto place before you, for the satisfaction of your minds, a possiblesolution of the problem:--

Consider, then, the ideal case of a number of magnets deprived ofweight, but retaining their polar forces. If we had a mobile liquid ofthe specific gravity of steel, we might, by making the magnets floatin it, realize this state of things, for in such a liquid the magnetswould neither sink nor swim. Now, the principle of gravitationenunciated by Newton is that every particle of matter, of every kind, attracts every other particle with a force varying inversely as thesquare of the distance. In virtue of the attraction of gravity, then, the magnets, if perfectly free to move, would slowly approach eachother. 

But besides the unpolar force of gravity, which belongs to matter ingeneral, the magnets are endowed with the polar force of magnetism. For a time, however, the polar forces do not come sensibly into play. In this condition the magnets resemble our water-molecules at thetemperature say of 50°. But the magnets come at length sufficientlynear each other to enable their poles to interact. From this point theaction ceases to be solely a general attraction of the masses. Attractions of special points of the masses and repulsions of otherpoints now come into play; and it is easy to see that therearrangement of the magnets consequent upon the introduction of thesenew forces may be such as to require a greater amount of room. This, Itake it, is the case with our water-molecules. Like our ideal magnets, they approach each other for a time _as wholes_. Previous to reachingthe temperature 39° Fahr. , the polar forces had doubtless begun toact, but it is at this temperature that their claim to more roomexactly balances the contraction due to cold. At lower temperatures, as regards change of volume, the polar forces predominate. But theycarry on a struggle with the force of contraction until the freezingtemperature is attained. The molecules then close up to form solidcrystals, a considerable augmentation of volume being the immediateconsequence. 

§ 3. _Ordinary Refraction of Light explained by the Wave Theory_. 

We have now to exhibit the bearings of this act of crystallizationupon optical phenomena. According to the undulatory theory, thevelocity of light in water and glass is less than in air. Consider, then, a small portion of a wave issuing from a point of light sodistant that the minute area may be regarded as practically plane. Moving vertically downwards, and impinging on a horizontal surface ofglass or water, the wave would go through the medium without change ofdirection. As, however, the velocity in glass or water is less thanthe velocity in air, the wave would be retarded on passing into thedenser medium. 

[Illustration: Fig. 25. ]

But suppose the wave, before reaching the glass, to be _oblique_ tothe surface; that end of the wave which first reaches the medium willbe the first retarded by it, the other portions as they enter theglass being retarded in succession. It is easy to see that thisretardation of the one end of the wave must cause it to swing roundand change its front, so that when the wave has fully entered theglass its course is oblique to its original direction. According tothe undulatory theory, light is thus _refracted_. 

With these considerations to guide us, let us follow the course of abeam of monochromatic light through our glass prism. The velocity inair is to its velocity in glass as 3: 2. Let A B C (fig. 25) be thesection of our prism, and _a_ _b_ the section of a plane waveapproaching it in the direction of the arrow. When it reaches _c_ _d_, one end of the wave is on the point of entering the glass. Followingit still further, it is obvious that while the portion of the wavestill in the air passes over the distance _c_ _e_, the wave in theglass will have passed over only two-thirds of this distance, or _d__f_. The line _e_ _f_ now marks the front of the wave. Immersed whollyin the glass it pursues its way to _g_ _h_, where the end _g_ of thewave is on the point of escaping into the air. During the timerequired by the end _h_ of the wave to pass over the distance _h_ _k_to the surface of the prism, the other end _g_, moving more rapidly, will have reached the point _i_. The wave, therefore, has againchanged its front, so that after its emergence from the prism it willpass on to _l_ _m_, and subsequently in the direction of the arrow. The refraction of the beam is thus completely accounted for; and itis, moreover, based upon actual experiment, which proves that theratio of the velocity of light in glass to its velocity in air is thathere mentioned. It is plain that if the change of velocity on enteringthe glass were greater, the refraction also would be greater. 

§ 4. _Double Refraction of Light explained by the Wave Theory_. 

The two elements of rapidity of propagation, both of sound and light, in any substance whatever, are _elasticity_ and _density_, the speedincreasing with the former and diminishing with the latter. Theenormous velocity of light in stellar space is attainable because theether is at the same time of infinitesimal density and of enormouselasticity. Now the ether surrounds the atoms of all bodies, but it isnot independent of them. In ponderable matter it acts as if itsdensity were increased without a proportionate increase of elasticity;and this accounts for the diminished velocity of light in refractingbodies. We here reach a point of cardinal importance. In virtue of thecrystalline architecture that we have been considering, the ether inmany crystals possesses different densities, and differentelasticities, in different directions; the consequence is, that insuch crystals light is transmitted with different velocities. And asrefraction depends wholly upon the change of velocity on entering therefracting medium, being greatest where the change of velocity isgreatest, we have in many crystals two different refractions. By suchcrystals a beam of light is divided into two. This effect is called_double refraction_. 

In ordinary water, for example, there is nothing in the grouping ofthe molecules to interfere with the perfect homogeneity of the ether;but, when water crystallizes to ice, the case is different. In a plateof ice the elasticity of the ether in a direction perpendicular to thesurface of freezing is different from what it is parallel to thesurface of freezing; ice is, therefore, a double refracting substance. Double refraction is displayed in a particularly impressive manner byIceland spar, which is crystallized carbonate of lime. The differenceof ethereal density in two directions in this crystal is very great, the separation of the beam into the two halves being, therefore, particularly striking. 

I am unwilling to quit this subject before raising it to unmistakableclearness in your minds. The vibrations of light being transversal, the elasticity concerned in the propagation of any ray is theelasticity at right angles to the direction of propagation. In Icelandspar there is one direction round which the crystalline molecules aresymmetrically built. This direction is called the axis of the crystal. In consequence of this symmetry the elasticity is the same in alldirections perpendicular to the axis, and hence a ray transmittedalong the axis suffers no double refraction. But the elasticity alongthe axis is greater than the elasticity at right angles to it. Consider, then, a system of waves crossing the crystal in a directionperpendicular to the axis. Two directions of vibration are open tosuch waves: the ether particles can vibrate parallel to the axis orperpendicular to it. _They do both_, and hence immediately dividethemselves into two systems propagated with different velocities. Double refraction is the necessary consequence. 

[Illustration: Fig. 26. ]

By means of Iceland spar cut in the proper direction, doublerefraction is capable of easy illustration. Causing the beam whichbuilds the image of our carbon-points to pass through the spar, thesingle image is instantly divided into two. Projecting (by the lens E, fig. 26) an image of the aperture (L) through which the light issuesfrom the electric lamp, and introducing the spar (P), two luminousdisks (E O) appear immediately upon the screen instead of one. 

The two beams into which the spar divides the single incident-beamhave been subjected to the closest examination. They do not behavealike. One of them obeys the ordinary law of refraction discovered bySnell, and is, therefore, called the _ordinary ray_: its index ofrefraction is 1. 654. The other does not obey this law. Its index ofrefraction, for example, is not constant, but varies from a maximum of1. 654 to a minimum of 1. 483; nor in this case do the incident andrefracted rays always lie in the same plane. It is, therefore, calledthe _extraordinary ray_. In calc-spar, as just stated, the ordinaryray is the most refracted. One consequence of this merits a passingnotice. Pour water and bisulphide of carbon into two cups of the samedepth; the cup that contains the more strongly refracting liquid willappear shallower than the other. Place a piece of Iceland spar over adot of ink; two dots are seen, the one appearing nearer than the otherto the eye. The nearest dot belongs to the most strongly refractedray, exactly as the nearest cup-bottom belongs to the most highlyrefracting liquid. When you turn the spar round, the extraordinaryimage of the dot rotates round the ordinary one, which remains fixed. This is also the deportment of our two disks upon the screen. 

§ 5. _Polarization of Light explained by the Wave Theory_. 

The double refraction of Iceland spar was first treated in a workpublished by Erasmus Bartholinus, in 1669. Huyghens sought to accountfor this phenomenon on the principles of the wave theory, and hesucceeded in doing so. He, moreover, made highly importantobservations on the distinctive character of the two beams transmittedby the spar, admitting, with resigned candour, that he had not solvedthe difficulty, and leaving the solution to future times. Newton, reflecting on the observations of Huyghens, came to the conclusionthat each of the beams transmitted by Iceland spar had two sides; andfrom the analogy of this _two-sidedness_ with the _two-endedness_ of amagnet, wherein consists its polarity, the two beams came subsequentlyto be described as _polarized_. 

We may begin the study of the polarization of light, with ease andprofit, by means of a crystal of tourmaline. But we must start with aclear conception of an ordinary beam of light. It has been alreadyexplained that the vibrations of the individual ether-particles areexecuted _across_ the line of propagation. In the case of ordinarylight we are to figure the ether-particles as vibrating in alldirections, or azimuths, as it is sometimes expressed, across thisline. 

Now, in the case of a plate of tourmaline cut parallel to the axis ofthe crystal, a beam of light incident upon the plate is divided intotwo, the one vibrating parallel to the axis of the crystal, the otherat right angles to the axis. The grouping of the molecules, and ofthe ether associated with the molecules, reduces all the vibrationsincident upon the crystal to these two directions. One of these beams, namely, that whose vibrations are perpendicular to the axis, isquenched with exceeding rapidity by the tourmaline. To such vibrationsmany specimens of the crystal are highly opaque; so that, after havingpassed through a very small thickness of the tourmaline, the lightemerges with all its vibrations reduced to a single plane. In thiscondition it is what we call _plane polarized light_. 

[Illustration: Fig. 27. ]

[Illustration: Fig. 28. ]

A moment's reflection will show that, if what is here stated becorrect, on placing a second plate of tourmaline with its axisparallel to the first, the light will pass through both; but that, ifthe axes be crossed, the light that passes through the one plate willbe quenched by the other, a total interception of the light being theconsequence. Let us test this conclusion by experiment. The image of aplate of tourmaline (_t_ _t_, fig. 27) is now before you. I placeparallel to it another plate (_t'_ _t'_): the green of the crystal isa little deepened, nothing more; this agrees with our conclusion. Bymeans of an endless screw, I now turn one of the crystals graduallyround, and you observe that as long as the two plates are oblique toeach other, a certain portion of light gets through; but that whenthey are at right angles to each other, the space common to both is aspace of darkness (fig. 28). Our conclusion, arrived at prior toexperiment, is thus verified. 

Let us now return to a single plate; and here let me say that it is onthe green light transmitted by the tourmaline that you are to fix yourattention. We have to illustrate the two-sidedness of that greenlight, in contrast to the all-sidedness of ordinary light. The whitelight surrounding the green image, being ordinary light, is reflectedby a plane glass mirror in all directions; the green light, on thecontrary, is not so reflected. The image of the tourmaline is nowhorizontal; reflected upwards, it is still green; reflected sideways, the image is reduced to blackness, because of the incompetency of thegreen light to be reflected in this direction. Making the plate oftourmaline vertical, and reflecting it as before, it is the light ofthe upper image that is quenched; the side image now shows the green. This is a result of the greatest significance. If the vibrations oflight were longitudinal, like those of sound, you could have no actionof this kind; and this very action compels us to assume that thevibrations are transversal. Picture the thing clearly. In the one casethe mirror receives, as it were, the impact of the _edges_ of thewaves, the green light being then quenched. In the other case the_sides_ of the waves strike the mirror, and the green light isreflected. To render the extinction complete, the light must bereceived upon the mirror at a special angle. What this angle is weshall learn presently. 

The quality of two-sidedness conferred upon light by bi-refractingcrystals may also be conferred upon it by ordinary reflection. Malusmade this discovery in 1808, while looking through Iceland spar at thelight of the sun reflected from the windows of the Luxembourg palacein Paris. I receive upon a plate of window-glass the beam from ourlamp; a great portion of the light reflected from the glass ispolarized. The vibrations of this reflected beam are executed, for themost part, parallel to the surface of the glass, and when the glass isheld so that the beam shall make an angle of 58° with theperpendicular to the glass, the _whole_ of the reflected beam ispolarized. It was at this angle that the image of the tourmaline wascompletely quenched in our former experiment. It is called _thepolarizing angle_. 

Sir David Brewster proved the angle of polarization of a medium to bethat particular angle at which the refracted and reflected raysinclose a right angle. [17] The polarizing angle augments with theindex of refraction. For water it is 52½°; for glass, as alreadystated, 58°; while for diamond it is 68°. 

And now let us try to make substantially the experiment of Malus. Thebeam from the lamp is received at the proper angle upon a plate ofglass and reflected through the spar. Instead of two images, you seebut one. So that the light, when polarized, as it now is byreflection, can only get through the spar in one direction, andconsequently can produce but one image. Why is this? In the Icelandspar as in the tourmaline, all the vibrations of the ordinary lightare reduced to two planes at right angles to each other; but, unlikethe tourmaline, both beams are transmitted with equal facility by thespar. The two beams, in short, emergent from the spar, are polarized, their directions of vibration being at right angles to each other. When, therefore, the light is first polarized by reflection, thedirection of vibration in the spar which coincides with the directionof vibration of the polarized beam, transmits the beam, and thatdirection only. Only one image, therefore, is possible under theconditions. 

You will now observe that such logic as connects our experiments issimply a transcript of the logic of Nature. On the screen before youare two disks of light produced by the double refraction of Icelandspar. They are, as you know, two images of the aperture through whichthe light issues from the camera. Placing the tourmaline in front ofthe aperture, two images of the crystal will also be obtained; but nowlet us reason out beforehand what is to be expected from thisexperiment. The light emergent from the tourmaline is polarized. Placing the crystal with its axis horizontal, the vibrations of itstransmitted light will be horizontal. Now the spar, as already stated, has two directions of vibration, one of which at the present momentis vertical, the other horizontal. What are we to conclude? That thegreen light will be transmitted along the latter, which is parallel tothe axis of the tourmaline, and not along the former, which isperpendicular to that axis. Hence we may infer that one image of thetourmaline will show the ordinary green light of the crystal, whilethe other image will be black. Tested by experiment, our reasoning isverified to the letter (fig. 29). 

[Illustration: Fig. 29. ]

[Illustration; Fig. 30. ]

Let us push our test still further. By means of an endless screw, thecrystal can be turned ninety degrees round. The black image, as Iturn, becomes gradually brighter, and the bright one gradually darker;at an angle of forty-five degrees both images are equally bright (fig. 30); while, when ninety degrees have been obtained, the axis of thecrystal being then vertical, the bright and black images have changedplaces, exactly as reasoning would have led us to suppose (fig. 31). 

[Illustration: Fig. 31. ]

[Illustration: Fig. 32. ]

Considering what has been already said (p. 114) regarding thereflection of light polarized by transmission through tourmaline, youwill readily foresee what must occur when we receive upon a plate ofglass, held at the polarizing angle, the two beams emergent from ourprism of Iceland spar. I cause both beams to pass side by side throughthe air, catch them on a glass plate, and seek to reflect themupwards. At the polarizing angle one beam only is capable of beingthus reflected. Which? Your prompt answer will be, The beam whosevibrations are horizontal (fig. 32). I now turn the glass plate andtry to reflect both beams laterally. One of them only is reflected;that, namely, the vibrations of which are vertical (fig. 33). It isplain that, by means either of the tourmaline or the reflecting glass, we can determine in a moment the direction of vibration in anypolarized beam. 

[Illustration: Fig. 33. ]

As already stated, the whole of a beam of ordinary light reflectedfrom glass at the polarizing angle is polarized; a word must now beadded regarding the far larger portion of the light which is_transmitted_ by the glass. The transmitted beam contains a quantityof polarized light equal to the reflected beam; but this is only afraction of the whole transmitted light. By taking two plates of glassinstead of one, we augment the quantity of the transmitted polarizedlight; and by taking _a bundle_ of plates, we so increase the quantityas to render the transmitted beam, for all practical purposes, _perfectly_ polarized. Indeed, bundles of glass plates are oftenemployed as a means of furnishing polarized light. It is important tonote that the plane of vibration of this transmitted light is at rightangles to that of the reflected light. 

One word more. When the tourmalines are crossed, the space where theycross each other is black. But we have seen that the least obliquityon the part of the crystals permits light to get through both. Nowsuppose, when the two plates are crossed, that we interpose a thirdplate of tourmaline between them, with its axis oblique to both. Aportion of the light transmitted by the first plate will get throughthis intermediate one. But, after it has got through, _its plane ofvibration is changed_: it is no longer perpendicular to the axis ofthe crystal in front. Hence it will, in part, get through thatcrystal. Thus, by pure reasoning, we infer that the interposition of athird plate of tourmaline will in part abolish the darkness producedby the perpendicular crossing of the other two plates. I have not athird plate of tourmaline; but the talc or mica which you employ inyour stoves is a more convenient substance, which acts in the sameway. Between the crossed tourmalines, I introduce a film of thiscrystal with its axis oblique to theirs. You see the edge of the filmslowly descending, and, as it descends, light takes the place ofdarkness. The darkness, in fact, seems scraped away, as if it weresomething material. This effect has been called, naturally butimproperly, _depolarization_. Its proper meaning will be disclosed inour next lecture. 

These experiments and reasonings, if only thoroughly studied andunderstood, will form a solid groundwork for the analysis of thesplendid optical phenomena next to be considered. 

LECTURE IV. 

 CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED LIGHT THE NICOL PRISM POLARIZER AND ANALYZER ACTION OF THICK AND THIN PLATES OF SELENITE COLOURS DEPENDENT ON THICKNESS RESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE SELENITE ONE OF THEM MORE RETARDED THAN THE OTHER RECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZER INTERFERENCE THUS RENDERED POSSIBLE CONSEQUENT PRODUCTION OF COLOURS ACTION OF BODIES MECHANICALLY STRAINED OR PRESSED ACTION OF SONOROUS VIBRATIONS ACTION OF GLASS STRAINED OR PRESSED BY HEAT CIRCULAR POLARIZATION CHROMATIC PHENOMENA PRODUCED BY QUARTZ THE MAGNETIZATION OF LIGHT RINGS SURROUNDING THE AXES OF CRYSTALS BIAXAL AND UNIAXAL CRYSTALS GRASP OF THE UNDULATORY THEORY THE COLOUR AND POLARIZATION OF SKY-LIGHT GENERATION OF ARTIFICIAL SKIES. 

§ 1. _Action of Crystals on Polarized Light: the Nicol Prism. _

We have this evening to examine and illustrate the chromatic phenomenaproduced by the action of crystals, and double-refracting bodiesgenerally, upon polarized light, and to apply the Undulatory Theory totheir elucidation. For a long time investigators were compelled toemploy plates of tourmaline for this purpose, and the progress theymade with so defective a means of inquiry is astonishing. But thesemen had their hearts in their work, and were on this account enabledto extract great results from small instrumental appliances. For ourpresent purpose we need far larger apparatus; and, happily, in theselater times this need has been to a great extent satisfied. We haveseen and examined the two beams emergent from Iceland spar, and haveproved them to be polarized. If, at the sacrifice of half the light, we could abolish one of these, the other would place at our disposal abeam of polarized light, incomparably stronger than any attainablefrom tourmaline. 

The beams, as you know, are refracted differently, and from this, asmade plain in §4, Lecture I. , we are able to infer that the one may betotally reflected, when the other is not. An able optician, namedNicol, cut a crystal of Iceland spar in two halves in a certaindirection. He polished the severed surfaces, and reunited them byCanada balsam, the surface of union being so inclined to the beamtraversing the spar that the ordinary ray, which is the most highlyrefracted, was totally reflected by the balsam, while theextraordinary ray was permitted to pass on. 

Let _b x, c y_ (fig. 34) represent the section of an elongated rhombof Iceland spar cloven from the crystal. Let this rhomb be cut alongthe plane _b c_; and the two severed surfaces, after having beenpolished, reunited by Canada balsam. We learned, in our first lecture, that total reflection only takes place when a ray seeks to escape froma more refracting to a less refracting medium, and that it always, under these circumstances, takes place when the obliquity issufficient. Now the refractive index of Iceland spar is, for theextraordinary ray less, and for the ordinary greater, than for Canadabalsam. Hence, in passing from the spar to the balsam, theextraordinary ray passes from a less refracting to a more refractingmedium, where total reflection cannot occur; while the ordinary raypasses from a more refracting to a less refracting medium, wheretotal reflection can occur. The requisite obliquity is secured bymaking the rhomb of such a length that the plane of which _b c_ is thesection shall be perpendicular, or nearly so, to the two end surfacesof the rhomb _b x, c y_. 

[Illustration: Fig. 34. ]

The invention of the Nicol prism was a great step in practical optics, and quite recently such prisms have been constructed of a size andpurity which enable audiences like the present to witness thechromatic phenomena of polarized light to a degree altogetherunattainable a short time ago. 

(The two prisms employed in these experiments were lent to me by mylamented friend Mr. William Spottiswoode, and they were manufacturedby Mr. Ahrens, an optician of consummate skill. )

§ 2. _Colours of Films of Selenite in Polarized Light_. 

Two Nicol prisms play the same part as the two plates of tourmaline. Placed with their directions of vibration parallel, the light passesthrough both; while when these directions are crossed the light isquenched. Introducing a film of mica between the prisms, the light, asin the case of the tourmaline, is restored. But notice, when the filmof mica is _thin_ you have sometimes not only light, but _coloured_light. Our work for some time to come will consist of the examinationof such colours. With this view, I will take a representative crystal, one easily dealt with, because it cleaves with great facility--thecrystal gypsum, or selenite, which is crystallized sulphate of lime. Between the crossed Nicols I place a thick plate of this crystal; likethe mica, it restores the light, but it produces no colour. With mypenknife I take a thin splinter from the crystal and place it betweenthe prisms; the image of the splinter glows with the richest colours. Turning the prism in front, these colours gradually fade anddisappear, but, by continuing the rotation until the vibratingsections of the prisms are parallel to each other, vivid colours againarise, but these colours are complementary to the former ones. 

Some patches of the splinter appear of one colour, some of another. These differences are due to the different thicknesses of the film. Asin the case of Hooke's thin plates, if the thickness be uniform thecolour is uniform. Here, for instance, is a stellar shape, everylozenge of the star being a film of gypsum of uniform thickness: eachlozenge, you observe, shows a brilliant and uniform colour. It iseasy, by shaping our films so as to represent flowers or otherobjects, to exhibit such objects in hues unattainable by art. Here, for example, is a specimen of heart's-ease, the colours of which youmight safely defy the artist to reproduce. By turning the front Nicol90 degrees round, we pass through a colourless phase to a series ofcolours complementary to the former ones. This change is still morestrikingly represented by a rose-tree, which is now presented in itsnatural hues--a red flower and green leaves; turning the prism 90degrees round, we obtain a green flower and red leaves. All thesewonderful chromatic effects have definite mechanical causes in themotions of the ether. The principle of interference duly applied andinterpreted explains them all. 

§ 3. _Colours of Crystals in Polarized Light explained by theUndulatory Theory_. 

By this time you have learned that the word 'light' may be used in twodifferent senses: it may mean the impression made upon consciousness, or it may mean the physical cause of the impression. It is with thiscause that we have to occupy ourselves at present. The luminiferousether is a substance which fills all space, and surrounds the atomsand molecules of bodies. To this inter-stellar and inter-atomic mediumdefinite mechanical properties are ascribed, and we deal with it inour reasonings and calculations as a body possessed of theseproperties. In mechanics we have the composition and resolution offorces and of motions, extending to the composition and resolution of_vibrations_. We treat the luminiferous ether on mechanicalprinciples, and, from the composition and resolution of itsvibrations we deduce all the phenomena displayed by crystals inpolarized light. 

[Illustration: Fig. 35. ]

Let us take, as an example, the crystal of tourmaline, with which weare now so familiar. Let a vibration cross this crystal oblique to itsaxis. Experiment has assured us that a portion of the light will passthrough. The quantity which passes we determine in this way. Let A B(fig. 35) be the axis of the tourmaline, and let _a_ _b_ represent theamplitude of an oblique ethereal vibration before it reaches A B. From_a_ and _b_ let the two perpendiculars _a_ _c_ and _b_ _d_ be drawnupon the axis: then _c_ _d_ will be the amplitude of the transmittedvibration. 

I shall immediately ask you to follow me while I endeavour to explainthe effects observed when a film of gypsum is placed between the twoNicol prisms. But, prior to this, it will be desirable to establishstill further the analogy between the action of the prisms and that ofthe two plates of tourmaline. The magnified images of these plates, with their axes at right-angles to each other, are now before you. Introducing between them a film of selenite, you observe that byturning the film round it may be placed in a position where it has nopower to abolish the darkness of the superposed portions of thetourmalines. Why is this? The answer is, that in the gypsum there aretwo directions, at right angles to each other, in which alonevibrations can take place, and that in our present experiment one ofthese directions is parallel to one of the axes of the tourmaline, andthe other parallel to the other axis. When this is the case, the filmexercises no sensible action upon the light. But now I turn the filmso as to render its directions of vibration _oblique_ to the twotourmaline axes; then, you see it exercises the power, demonstrated inthe last lecture, of partially restoring the light. 

[Illustration: Fig. 36. ]

Let us now mount our Nicol prisms, and cross them as we crossed thetourmaline. Introducing our film of gypsum between them, you noticethat in one particular position the film has no power whatever overthe field of view. But, when the film is turned a little way round, the light passes. We have now to understand the mechanism by whichthis is effected. 

First, then, we have a prism which receives the light from theelectric lamp, and which is called the _polarizer_. Then we have theplate of gypsum (supposed to be placed at S, fig. 36), and then theprism in front, which is called the _analyzer_. On its emergence fromthe first prism, the light is polarized; and, in the particular casenow before us, its vibrations are executed in a horizontal plane. Wehave to examine what occurs when the two directions of vibration inthe interposed gypsum are oblique to the horizon. Draw a rectangularcross (A B, C D, fig. 37) to represent these two directions. Draw aline (_a_ _b_) to represent the amplitude of the horizontal vibrationon the emergence of the light from the first Nicol. Let fall from eachend of this line two perpendiculars (_a_ _c_, _a_ _f_, _b_ _d_, _b__e_) on the two arms of the cross; then the distances (_c_ _d_, _e__f_) between the feet of these perpendiculars represent the amplitudesof two rectangular vibrations, which are the _components_ of the firstsingle vibration. Thus the polarized ray, when it enters the gypsum, is resolved into its two equivalents, which vibrate at right angles toeach other. 

[Illustration; Fig. 37. ]

In one of these two rectangular directions the ether within the gypsumis more sluggish than in the other; and, as a consequence, the wavesthat follow this direction are more retarded than the others. In bothcases the undulations are shortened when they enter the gypsum, butin the one case they are more shortened than in the other. You canreadily imagine that in this way the one system of waves may get halfa wave-length, or indeed any number of half wavelengths, in advance ofthe other. The possibility of interference here at once flashes uponthe mind. A little consideration, however, will render it evidentthat, as long as the vibrations are executed at right angles to eachother, they cannot quench each other, no matter what the retardationmay be. This brings us at once to the part played by the analyzer. Itssole function is to recompound the two vibrations emergent from thegypsum. It reduces them to a single plane, where, if one of them beretarded by the proper amount, extinction will occur. 

But here, as in the case of thin films, the different lengths of thewaves of light come into play. Red will require a greater thickness toproduce the retardation necessary for extinction than blue;consequently when the longer waves have been withdrawn byinterference, the shorter ones remain, the film of gypsum shining withthe colours which the short waves confer. Conversely, when the shorterwaves have been withdrawn, the thickness is such that the longer wavesremain. An elementary consideration suffices to show, that when thedirections of vibration of the prisms and the gypsum enclose an angleof forty-five degrees, the colours are at their maximum brilliancy. When the film is turned from this direction, the colours graduallyfade, until, at the point where the directions of vibration in plateand prisms are parallel, they disappear altogether. 

(The best way of obtaining a knowledge of these phenomena is toconstruct a model of thin wood or pasteboard, representing the plateof gypsum, its planes of vibration, and also those of the polarizerand analyzer. Two parallel pieces of the board are to be separated byan interval which shall represent the thickness of the film of gypsum. Between them two other pieces, intersecting each other at a rightangle, are to represent the planes of vibration within the film; whileattached to the two parallel surfaces outside are two other pieces ofboard, which represent the planes of vibration of the polarizer andanalyzer. On the two intersecting planes the waves are to be drawn, showing the resolution of the first polarized beam into two others, and then the subsequent reduction of the two systems of vibrations toa common plane by the analyzer. Following out rigidly the interactionof the two systems of waves, we are taught by such a model that allthe phenomena of colour obtained by the combination of the waves, whenthe planes of vibration of the two Nicols are parallel, are displacedby the _complementary_ phenomena, when the planes of vibration areperpendicular to each other. )

In considering the next point, we will operate, for the sake ofsimplicity, with monochromatic light--with red light, for example, which is easily obtained pure by red glass. Supposing a certainthickness of the gypsum produces a retardation of half a wave-length, twice this thickness will produce a retardation of two halfwave-lengths, three times this thickness a retardation of three halfwave-lengths, and so on. Now, when the Nicols are parallel, theretardation of half a wave-length, or of any _odd_ number of halfwave-lengths, produces extinction; at all thicknesses, on the otherhand, which correspond to a retardation of an _even_ number of halfwave-lengths, the two beams support each other, when they are broughtto a common plane by the analyzer. Supposing, then, that we take aplate of a wedge form, which grows gradually thicker from edge toback, we ought to expect, in red light, a series of recurrent bands oflight and darkness; the dark bands occurring at thicknesses whichproduce retardations of one, three, five, etc. , half wave-lengths, while the bright bands occur between the dark ones. Experiment provesthe wedge-shaped film to show these bands. They are also beautifullyshown by a circular film, so worked as to be thinnest at the centre, and gradually increasing in thickness from the centre outwards. Asplendid series of rings of light and darkness is thus produced. 

When, instead of employing red light, we employ blue, the rings arealso seen: but as they occur at thinner portions of the film, they aresmaller than the rings obtained with the red light. The consequence ofemploying white light may be now inferred; inasmuch as the red and theblue fall in different places, we have _iris-coloured_ rings producedby the white light. 

Some of the chromatic effects of irregular crystallization arebeautiful in the extreme. Could I introduce between our two Nicols apane of glass covered by those frost-ferns which your cold weatherrenders now so frequent, rich colours would be the result. Thebeautiful effects of the irregular crystallization of tartaric acidand other substances on glass plates now presented to you, illustratewhat you might expect from the frosted window-pane. And not only docrystalline bodies act thus upon light, but almost all bodies thatpossess a definite structure do the same. As a general rule, organicbodies act thus upon light; for their architecture implies anarrangement of the molecules, and of the ether associated with themolecules, which involves double refraction. A film of horn, or thesection of a shell, for example, yields very beautiful colours inpolarized light. In a tree, the ether certainly possesses differentdegrees of elasticity along and across the fibre; and, were woodtransparent, this peculiarity of molecular structure would infalliblyreveal itself by chromatic phenomena like those that you have seen. 

§ 4. _Colours produced by Strain and Pressure. _

Not only do natural bodies behave in this way, but it is possible, asshown by Brewster, to confer, by artificial strain or pressure, atemporary double refracting structure upon non-crystalline bodies suchas common glass. This is a point worthy of illustration. When I placea bar of wood across my knee and seek to break it, what is themechanical condition of the bar? It bends, and its convex surface is_strained_ longitudinally; its concave surface, that next my knee, islongitudinally _pressed_. Both in the strained portion and in thepressed portion of the wood the ether is thrown into a condition whichwould render the wood, were it transparent, double-refracting. For, incases like the present, the drawing of the molecules asunderlongitudinally is always accompanied by their approach to each otherlaterally; while the longitudinal squeezing is accompanied by lateralretreat. Each half of the bar of wood exhibits this antithesis, and istherefore double-refracting. 

Let us now repeat this experiment with a bar of glass. Between thecrossed Nicols I introduce such a bar. By the dim residue of lightlingering upon the screen, you see the image of the glass, but it hasno effect upon the light. I simply bend the glass bar with my fingerand thumb, keeping its length oblique to the directions of vibrationin the Nicols. Instantly light flashes out upon the screen. The twosides of the bar are illuminated, the edges most, for here the strainand pressure are greatest. In passing from longitudinal strain tolongitudinal pressure, we cross a portion of the glass where neitheris exerted. This is the so-called neutral axis of the bar of glass, and along it you see a dark band, indicating that the glass along thisaxis exercises no action upon the light. By employing the force of apress, instead of the force of my finger and thumb, the brilliancy ofthe light is greatly augmented. 

Again, I have here a square of glass which can be inserted into apress of another kind. Introducing the uncompressed square between theprisms, its neutrality is declared; but it can hardly be heldsufficiently loosely in the press to prevent its action frommanifesting itself. Already, though the pressure is infinitesimal, yousee spots of light at the points where the press is in contact withthe glass. On turning a screw, the image of the square of glassflashes out upon the screen. Luminous spaces are seen separated fromeach other by dark bands. 

Every two adjacent spaces are in opposite mechanical conditions. Onone side of the dark band we have strain, on the other side pressure, the band marking the neutral axis between both. I now tighten thevice, and you see colour; tighten still more, and the colours appearas rich as those presented by crystals. Releasing the vice, thecolours suddenly vanish; tightening suddenly, they reappear. From thecolours of a soap-bubble Newton was able to infer the thickness of thebubble, thus uniting by the bond of thought apparently incongruousthings. From the colours here presented to you, the magnitude of thepressure employed might be inferred. Indeed, the late M. Wertheim, ofParis, invented an instrument for the determination of strains andpressures, by the colours of polarized light, which exceeded inaccuracy all previous instruments of the kind. 

And now we have to push these considerations to a final illustration. Polarized light may be turned to account in various ways as ananalyzer of molecular condition. It may, for instance, be applied toreveal the condition of a solid body when it becomes sonorous. A stripof glass six feet long, two inches wide and a quarter of an inchthick, is held at the centre between the finger and thumb. On sweepinga wet woollen rag over one of its halves, you hear an acute sound dueto the vibrations of the glass. What is the condition of the glasswhile the sound is heard? This: its two halves lengthen and shorten inquick succession. Its two ends, therefore, are in a state of quickvibration; but at the centre the pulses from the two ends alternatelymeet and retreat from each other. Between their opposing actions, theglass at the centre is kept motionless: but, on the other hand, it isalternately strained and compressed. In fig. 38, A B may be taken torepresent the glass rectangle with its centre condensed; while A' B'represents the same rectangle with its centre rarefied. The ends ofthe strip suffer neither condensation nor rarefaction. 

[Illustration: Fig. 38]

If we introduce the strip of glass (_s_ _s'_, fig. 39) between thecrossed Nicols, taking care to keep it oblique to the directions ofvibration of the Nicols, and sweep our wet rubber over the glass, thisis what may be expected to occur: At every moment of compression thelight will flash through; at every moment of strain the light willalso flash through; and these states of strain and pressure willfollow each other so rapidly, that we may expect a permanent luminousimpression to be made upon the eye. By pure reasoning, therefore, wereach the conclusion that the light will be revived whenever the glassis sounded. That it is so, experiment testifies: at every sweep of therubber (_h_, fig. 39) a fine luminous disk (O) flashes out upon thescreen. The experiment may be varied in this way: Placing in front ofthe polarizer a plate of unannealed glass, you have a series ofbeautifully coloured rings, intersected by a black cross. Every sweepof the rubber not only abolishes the rings, but introducescomplementary ones, the black cross being, for the moment, supplantedby a white one. This is a modification of a beautiful experiment whichwe owe to Biot. His apparatus, however, confined the observation of itto a single person at a time. 

[Illustration: Fig. 39. ]

§ 5. _Colours of Unannealed Glass_. 

Bodies are usually expanded by heat and contracted by cold. If theheat be applied with perfect uniformity, no local strains or pressurescome into play; but, if one portion of a solid be heated and anotherportion not, the expansion of the heated portion introduces strainsand pressures which reveal themselves under the scrutiny of polarizedlight. When a square of common window-glass is placed between theNicols, you see its dim outline, but it exerts no action on thepolarized light. Held for a moment over the flame of a spirit-lamp, onreintroducing it between the Nicols, light flashes out upon thescreen. Here, as in the case of mechanical action, you have luminousspaces of strain divided by dark neutral axes from spaces of pressure. 

[Illustration: Fig. 40. ]

[Illustration: Fig. 41. ]

Let us apply the heat more symmetrically. A small square of glass isperforated at the centre, and into the orifice a bit of copper wire isintroduced. Placing the square between the prisms, and heating thewire, the heat passes by conduction to the glass, through which itspreads from the centre outwards. You immediately see four luminousquadrants and a dim cross, which becomes gradually blacker, bycomparison with the adjacent brightness. And as, in the case ofpressure, we produced colours, so here also, by the proper applicationof heat, gorgeous chromatic effects may be evoked. The conditionnecessary to the production of these colours may be rendered permanentby first heating the glass sufficiently, and then cooling it, so thatthe chilled mass shall remain in a state of permanent strain andpressure. Two or three examples will illustrate this point. Figs. 40and 41 represent the figures obtained with two pieces of glass thusprepared; two rectangular pieces of unannealed glass, crossed andplaced between the polarizer and analyzer, exhibit the beautiful irisfringes represented in fig. 42. 

[Illustration: Fig. 42. ]

§ 6. _Circular Polarization. _

But we have to follow the ether still further into its hiding-places. Suspended before you is a pendulum, which, when drawn aside andliberated, oscillates to and fro. If, when the pendulum is passing themiddle point of its excursion, I impart a shock to it tending to driveit at right angles to its present course, what occurs? The twoimpulses compound themselves to a vibration oblique in direction tothe former one, but the pendulum still oscillates in _a plane_. But, if the rectangular shock be imparted to the pendulum when it is at thelimit of its swing, then the compounding of the two impulses causesthe suspended ball to describe, not a straight line, but an ellipse;and, if the shock be competent of itself to produce a vibration of thesame amplitude as the first one, the ellipse becomes a circle. 

Why do I dwell upon these things? Simply to make known to you theresemblance of these gross mechanical vibrations to the vibrations oflight. I hold in my hand a plate of quartz cut from the crystalperpendicular to its axis. The crystal thus cut possesses theextraordinary power of twisting the plane of vibration of a polarizedray to an extent dependent on the thickness of the crystal. And themore refrangible the light the greater is the amount of twisting; sothat, when white light is employed, its constituent colours are thusdrawn asunder. Placing the quartz plate between the polarizer andanalyzer, this vivid red appears; and, turning the analyzer in frontfrom right to left, the other colours of the spectrum appear insuccession. Specimens of quartz have been found which require theanalyzer to be turned from left to right to obtain the same successionof colours. Crystals of the first class are therefore calledright-handed, and of the second class, left-handed crystals. 

With profound sagacity, Fresnel, to whose genius we mainly owe theexpansion and final triumph of the undulatory theory of light, reproduced mentally the mechanism of these crystals, and showed theiraction to be due to the circumstance that, in them, the waves ofether so act upon each other as to produce the condition representedby our rotating pendulum. Instead of being plane polarized, the lightin rock crystal is _circularly polarized_. Two such rays, transmittedalong the axis of the crystal, and rotating in opposite directions, when brought to interference by the analyzer, are demonstrablycompetent to produce all the observed phenomena. 

§ 7. _Complementary Colours of Bi-refracting Spar in CircularlyPolarized Light. Proof that Yellow and Blue are Complementary. _

I now remove the analyzer, and put in its place the piece of Icelandspar with which we have already illustrated double refraction. The twoimages of the carbon-points are now before you, produced, as you know, by two beams vibrating at right angles to each other. Introducing aplate of quartz between the polarizer and the spar, the two imagesglow with complementary colours. Employing the image of an apertureinstead of that of the carbon-points, we have two coloured circles. Asthe analyzer is caused to rotate, the colours pass through variouschanges: but they are always complementary. When the one is red, theother is green; when the one is yellow, the other is blue. Here wehave it in our power to demonstrate afresh a statement made in ourfirst lecture, that although the mixture of blue and yellow pigmentsproduces green, the mixture of blue and yellow lights produces white. By enlarging our aperture, the two images produced by the spar arecaused to approach each other, and finally to overlap. The one imageis now a vivid yellow, the other a vivid blue, and you notice thatwhere these colours are superposed we have a pure white. (See fig. 43, where N is the end of the polarizer, Q the quartz plate, L a lens, andB the bi-refracting spar. The two images overlap at O, and producewhite by their mixture. )

[Illustration: Fig. 43. ]

§ 8. _The Magnetization of Light. _

This brings us to a point of our inquiries which, though rarelyillustrated in lectures, is nevertheless so likely to affectprofoundly the future course of scientific thought that I am unwillingto pass it over without reference. I refer to the experiment whichFaraday, its discoverer, called the 'magnetization of light. ' Thearrangement for this celebrated experiment is now before you. We have, first, our electric lamp, then a Nicol prism, to polarize the beamemergent from the lamp; then an electro-magnet, then a second Nicol, and finally our screen. At the present moment the prisms are crossed, and the screen is dark. I place from pole to pole of theelectro-magnet a cylinder of a peculiar kind of glass, first made byFaraday, and called Faraday's heavy glass. Through this glass the beamfrom the polarizer now passes, being intercepted by the Nicol infront. On exciting the magnet light instantly appears upon the screen. By the action of the magnet upon the heavy glass the plane ofvibration is caused to rotate, the light being thus enabled to getthrough the analyzer. 

The two classes into which quartz-crystals are divided have beenalready mentioned. In my hand I hold a compound plate, one half of ittaken from a right-handed, and the other from a left-handed crystal. Placing the plate in front of the polarizer, I turn one of the Nicolsuntil the two halves of the plate show a common puce colour. Thisyields an exceedingly sensitive means of rendering visible the actionof a magnet upon light. By turning either the polarizer or theanalyzer through the smallest angle, the uniformity of the colourdisappears, and the two halves of the quartz show different colours. The magnet produces an effect equivalent to this rotation. Thepuce-coloured circle is now before you on the screen. (See fig. 44, where N is the nozzle of the lamp, H the first Nicol, Q the biquartzplate, L a lens, M the electro-magnet, with the heavy glass across itsperforated poles, and P the second Nicol. ) Exciting the magnet, onehalf of the image becomes suddenly red, the other half green. Interrupting the current, the two colours fade away, and the primitivepuce is restored. 

The action, moreover, depends upon the polarity of the magnet, or, inother words, on the direction of the current which surrounds themagnet. Reversing the current, the red and green reappear, but theyhave changed places. The red was formerly to the right, and the greento the left; the green is now to the right, and the red to the left. With the most exquisite ingenuity, Faraday analyzed all those actionsand stated their laws. This experiment, however, long remained ascientific curiosity rather than a fruitful germ. That it would bearfruit of the highest importance, Faraday felt profoundly convinced, and present researches are on the way to verify his conviction. 

[Illustration: Fig. 44]

§ 9. _Iris-rings surrounding the Axes of Crystals. _

A few more words are necessary to complete our knowledge of thewonderful interaction between ponderable molecules and the etherinterfused among them. Symmetry of molecular arrangement impliessymmetry on the part of the ether; atomic dissymmetry, on the otherhand, involves the dissymmetry of the ether, and, as a consequence, double refraction. In a certain class of crystals the structure ishomogeneous, and such crystals produce no double refraction. Incertain other crystals the molecules are ranged symmetrically round acertain line, and not around others. Along the former, therefore, theray is undivided, while along all the others we have doublerefraction. Ice is a familiar example: its molecules are built withperfect symmetry around the perpendiculars to the planes of freezing, and a ray sent through ice in this direction is not doubly refracted;whereas, in all other directions, it is. Iceland spar is anotherexample of the same kind: its molecules are built symmetrically roundthe line uniting the two blunt angles of the rhomb. In this directiona ray suffers no double refraction, in all others it does. Thisdirection of no double refraction is called the _optic axis_ of thecrystal. 

Hence, if a plate be cut from a crystal of Iceland spar perpendicularto the axis, all rays sent across this plate in the direction of theaxis will produce but one image. But, the moment we deviate from theparallelism with the axis, double refraction sets in. If, therefore, abeam that has been rendered _conical_ by a converging lens be sentthrough the spar so that the central ray of the cone passes along theaxis, this ray only will escape double refraction. Each of the otherswill be divided into an ordinary and an extraordinary ray, the onemoving more slowly through the crystal than the other; the one, therefore, retarded with reference to the other. Here, then, we havethe conditions for interference, when the waves are reduced by theanalyzer to a common plane. 

Placing the plate of Iceland spar between the crossed Nicol prisms, and employing the conical beam, we have upon the screen a beautifulsystem of iris-rings surrounding the end of the optic axis, thecircular bands of colour being intersected by a black cross (fig. 45). The arms of this cross are parallel to the two directions of vibrationin the polarizer and analyzer. It is easy to see that those rays whoseplanes of vibration within the spar coincide with the plane ofvibration of _either_ prism, cannot get through _both_. This completeinterception produces the arms of the cross. 

[Illustration: Fig. 45. ]

With monochromatic light the rings would be simply bright andblack--the bright rings occurring at those thicknesses of the sparwhich cause the rays to conspire; the black rings at those thicknesseswhich cause them to quench each other. Turning the analyzer 90° round, we obtain the complementary phenomena. The black cross gives place toa bright one, and every dark ring is supplanted also by a bright one(fig. 46). Here, as elsewhere, the different lengths of thelight-waves give rise to iris-colours when white light is employed. 

[Illustration: Fig. 46. ]

[Illustration: Fig. 47. ]

Besides the _regular_ crystals which produce double refraction in nodirection, and the _uniaxal_ crystals which produce it in alldirections but one, Brewster discovered that in a large class ofcrystals there are _two_ directions in which double refraction doesnot take place. These are called _biaxal_ crystals. When plates ofthese crystals, suitably cut, are placed between the polarizer andanalyzer, the axes (A A', fig. 47) are seen surrounded, not bycircles, but by curves of another order and of a perfectly definitemathematical character. Each band, as proved experimentally byHerschel, forms a _lemniscata_; but the experimental proof was here, as in numberless other cases, preceded by the deduction which showedthat, according to the undulatory theory, the bands must possess thisspecial character. 

§ 10. _Power of the Wave Theory_. 

I have taken this somewhat wide range over polarization itself, andover the phenomena exhibited by crystals in polarized light, in orderto give you some notion of the firmness and completeness of the theorywhich grasps them all. Starting from the single assumption oftransverse undulations, we first of all determine the wave-lengths, and find that on them all the phenomena of colour are dependent. Thewavelengths may be determined in many independent ways. Newtonvirtually determined them when he measured the periods of his Fits:the length of a fit, in fact, is that of a quarter of an undulation. The wave-lengths may be determined by diffraction at the edges of aslit (as in the Appendix to these Lectures); they may be deduced fromthe interference fringes produced by reflection; from the fringesproduced by refraction; also by lines drawn with a diamond upon glassat measured distances asunder. And when the length determined by theseindependent methods are compared together, the strictest agreement isfound to exist between them. 

With the wave-lengths once at our disposal, we follow the ether intothe most complicated cases of interaction between it and ordinarymatter, 'the theory is equal to them all. It makes not a single newphysical hypothesis; but out of its original stock of principles iteduces the counterparts of all that observation shows. It accountsfor, explains, simplifies the most entangled cases; corrects knownlaws and facts; predicts and discloses unknown ones; becomes the guideof its former teacher Observation; and, enlightened by mechanicalconceptions, acquires an insight which pierces through shape andcolour to force and cause. '[18]

But, while I have thus endeavoured to illustrate before you the powerof the undulatory theory as a solver of all the difficulties ofoptics, do I therefore wish you to close your eyes to any evidencethat may arise against it? By no means. You may urge, and justly urge, that a hundred years ago another theory was held by the most eminentmen, and that, as the theory then held had to yield, the undulatorytheory may have to yield also. This seems reasonable; but let usunderstand the precise value of the argument. In similar language aperson in the time of Newton, or even in our time, might reason thus:Hipparchus and Ptolemy, and numbers of great men after them, believedthat the earth was the centre of the solar system. But this deep-settheoretic notion had to give way, and the helio-centric theory may, inits turn, have to give way also. This is just as reasonable as thefirst argument. Wherein consists the strength of the present theory ofgravitation? Solely in its competence to account for all the phenomenaof the solar system. Wherein consists the strength of the theory ofundulation? Solely in its competence to disentangle and explainphenomena a hundred-fold more complex than those of the solar system. Accept if you will the scepticism of Mr. Mill[19] regarding theundulatory theory; but if your scepticism be philosophical, it willwrap the theory of gravitation in the same or in greater doubt. [20]

§ 11. _The Blue of the Sky_. 

I am unwilling to quit these chromatic phenomena without referring toa source of colour which has often come before me of late in the blueof your skies at noon, and the deep crimson of your horizon after theset of sun. I will here summarize and extend what I have elsewheresaid upon this subject. Proofs of the most cogent description could beadduced to show that the blue light of the firmament is reflectedlight. That light comes to us across the direction of the solar rays, and even against the direction of the solar rays; and this lateral andopposing rush of wave-motion can only be due to the rebound of thewaves from the air itself, or from something suspended in the air. Thesolar light, moreover, is not scattered by the sky in the proportionswhich produce white. The sky is blue, which indicates an excess of thesmaller waves. The blueness of the air has been given as a reason forthe blueness of the sky; but then the question arises, How, if the airbe blue, can the light of sunrise and sunset, which travels throughvast distances of air, be yellow, orange, or even red? The passage ofthe white solar light through a blue medium could by no possibilityredden the light; the hypothesis of a blue atmosphere is thereforeuntenable. In fact, the agent, whatever it be, which sends us thelight of the sky, exercises in so doing a dichroitic action. The lightreflected is blue, the light transmitted is orange or red, A markeddistinction is thus exhibited between reflection from the sky and thatfrom an ordinary cloud, which exercises no such dichroitic action. 

The cloud, in fact, takes no note of size on the part of the waves ofether, but reflects them all alike. Now the cause of this may be thatthe cloud-particles are so large in comparison with the size of thewaves of ether as to scatter them all indifferently. A broad cliffreflects an Atlantic roller as easily as it reflects a ripple producedby a sea-bird's wing; and, in the presence of large reflectingsurfaces, the existing differences of magnitude among the waves ofether may also disappear. But supposing the reflecting particles, instead of being very large, to be very small, in comparison with thesize of the waves. Then, instead of the whole wave being fronted andin great part thrown back, a small portion only is shivered off by theobstacle. Suppose, then, such minute foreign particles to be diffusedin our atmosphere. Waves of all sizes impinge upon them, and at everycollision a portion of the impinging wave is struck off. All the wavesof the spectrum, from the extreme red to the extreme violet, are thusacted upon; but in what proportions will they be scattered? Largenessis a thing of relation; and the smaller the wave, the greater is therelative size of any particle on which the wave impinges, and thegreater also the relative reflection. 

A small pebble, placed in the way of the ring-ripples produced byheavy rain-drops on a tranquil pond, will throw back a large fractionof each ripple incident upon it, while the fractional part of a largerwave thrown back by the same pebble might be infinitesimal. Now topreserve the solar light white, its constituent proportions must notbe altered; but in the scattering of the light by these very smallparticles we see that the proportions _are_ altered. The smaller wavesare in excess, and, as a consequence, in the scattered light blue willbe the predominant colour. The other colours of the spectrum must, tosome extent, be associated with the blue: they are not absent, butdeficient. We ought, in fact, to have them all, but in diminishingproportions, from the violet to the red. 

We have thus reasoned our way to the conclusion, that were particles, small in comparison to the size of the ether waves, sown in ouratmosphere, the light scattered by those particles would be exactlysuch as we observe in our azure skies. And, indeed, when this light isanalyzed, all the colours of the spectrum are found in the proportionsindicated by our conclusion. 

By its successive collisions with the particles the white light ismore and more robbed of its shorter waves; it therefore loses more andmore of its due proportion of blue. The result may be anticipated. Thetransmitted light, where moderate distances are involved, will appearyellowish. But as the sun sinks towards the horizon the atmosphericdistance increases, and consequently the number of the scatteringparticles. They weaken in succession the violet, the indigo, the blue, and even disturb the proportions of green. The transmitted light undersuch circumstances must pass from yellow through orange to red. Thisalso is exactly what we find in nature. Thus, while the reflectedlight gives us, at noon, the deep azure of the Alpine skies, thetransmitted light gives us, at sunset, the warm crimson of the Alpinesnows. 

But can small particles be really proved to act in the mannerindicated? No doubt of it. Each one of you can submit the question toan experimental test. Water will not dissolve resin, but spirit will;and when spirit which holds resin in solution is dropped into water, the resin immediately separates in solid particles, which render thewater milky. The coarseness of this precipitate depends on thequantity of the dissolved resin. Professor Brücke has given us theproportions which produce particles particularly suited to our presentpurpose. One gramme of clean mastic is dissolved in eighty-sevengrammes of absolute alcohol, and the transparent solution is allowedto drop into a beaker containing clear water briskly stirred. Anexceedingly fine precipitate is thus formed, which declares itspresence by its action upon light. Placing a dark surface behind thebeaker, and permitting the light to fall into it from the top orfront, the medium is seen to be of a very fair sky-blue. A trace ofsoap in water gives it a tint of blue. London milk makes anapproximation to the same colour, through the operation of the samecause: and Helmholtz has irreverently disclosed the fact that a blueeye is simply a turbid medium. 

§ 12. _Artificial Sky_. 

But we have it in our power to imitate far more closely the naturalconditions of this problem. We can generate in air artificial skies, and prove their perfect identity with the natural one, as regards theexhibition of a number of wholly unexpected phenomena. It has beenrecently shown in a great number of instances by myself that waves ofether issuing from a strong source, such as the sun or the electriclight, are competent to shake asunder the atoms of gaseous molecules. The apparatus used to illustrate this consists of a glass tube about ayard in length, and from 2½ to 3 inches internal diameter. The gas orvapour to be examined is introduced into this tube, and upon it thecondensed beam of the electric lamp is permitted to act. The vapour isso chosen that one, at least, of its products of decomposition, assoon as it is formed, shall be _precipitated_ to a kind of cloud. Bygraduating the quantity of the vapour, this precipitation may berendered of any degree of fineness, forming particles distinguishableby the naked eye, or particles which are probably far beyond the reachof our highest microscopic powers. I have no reason to doubt thatparticles may be thus obtained whose diameters constitute but a verysmall fraction of the length of a wave of violet light. 

Now, in all such cases when suitable vapours are employed in asufficiently attenuated state, no matter what the vapour may be, thevisible action commences with the formation of a _blue cloud_. Let meguard myself at the outset against all misconception as to the use ofthis term. The blue cloud here referred to is totally invisible inordinary daylight. To be seen, it requires to be surrounded bydarkness, _it only_ being illuminated by a powerful beam of light. This cloud differs in many important particulars from the finestordinary clouds, and might justly have assigned to it an intermediateposition between these clouds and true cloudless vapour. 

It is possible to make the particles of this _actinic cloud_ grow froman infinitesimal and altogether ultra-microscopic size to particles ofsensible magnitude; and by means of these in a certain stage of theirgrowth, we produce a blue which rivals, if it does not transcend, thatof the deepest and purest Italian sky. Introducing into our tube aquantity of mixed air and nitrite of butyl vapour sufficient todepress the mercurial column of an air-pump one-twentieth of an inch, adding a quantity of air and hydrochloric acid sufficient to depressthe mercury half an inch further, and sending through this compoundand highly attenuated atmosphere the beam of the electric light, within the tube arises gradually a splendid azure, which strengthensfor a time, reaches a maximum of depth and purity, and then, as theparticles grow larger, passes into whitish blue. This experiment isrepresentative, and it illustrates a general principle. Various othercolourless substances of the most diverse properties, optical andchemical, might be employed for this experiment. The _incipientcloud_, in every case, would exhibit this superb blue; thus proving todemonstration that particles of infinitesimal size, without any colourof their own, and irrespective of those optical properties exhibitedby the substance in a massive state, are competent to produce the bluecolour of the sky. 

§ 13. _Polarization of Skylight_. 

But there is another subject connected with our firmament, of a moresubtle and recondite character than even its colour. I mean that'mysterious and beautiful phenomenon, ' as Sir John Herschel calls it, the polarization of the light of the sky. Looking at various points ofthe blue firmament through a Nicol prism, and turning the prism roundits axis, we soon notice variations of brightness. In certainpositions of the prism, and from certain points of the firmament, thelight appears to be wholly transmitted, while it is only necessary toturn the prism round its axis through an angle of ninety degrees tomaterially diminish the intensity of the light. Experiments of thiskind prove that the blue light sent to us by the firmament ispolarized, and on close scrutiny it is also found that the directionof most perfect polarization is perpendicular to the solar rays. Werethe heavenly azure like the ordinary light of the sun, the turning ofthe prism would have no effect upon it; it would be transmittedequally during the entire rotation of the prism. The light of the skymay be in great part quenched, because it is in great part polarized. 

The same phenomenon is exhibited in perfection by our actinic clouds, the only condition necessary to its production being the smallness ofthe particles. In all cases, and with all substances, the cloud formedat the commencement, when the precipitated particles are sufficientlyfine, is _blue_. In all cases, moreover, this fine blue cloudpolarizes _perfectly_ the beam which illuminates it, the direction ofpolarization enclosing an angle of 90° with the axis of theilluminating beam. 

It is exceedingly interesting to observe both the growth and the decayof this polarization. For ten or fifteen minutes after its firstappearance, the light from a vividly illuminated incipient cloud, looked at horizontally, is absolutely quenched by a Nicol prism withits longer diagonal vertical. But as the sky-blue is graduallyrendered impure by the introduction of particles of too large a size, in other words, as real clouds begin to be formed, the polarizationbegins to deteriorate, a portion of the light passing through theprism in all its positions, as it does in the case of skylight. It isworthy of note that for some time after the cessation of perfectpolarization the _residual_ light which passes, when the Nicol is inits position of minimum transmission, is of a gorgeous blue, thewhiter light of the cloud being extinguished. When the cloud-texturehas become sufficiently coarse to approximate to that of ordinaryclouds, the rotation of the Nicol ceases to have any sensible effecton the light discharged at right angles to the beam. 

The perfection of the polarization in a direction perpendicular to theilluminating beam may be also illustrated by the following experiment, which has been executed with many vapours. A Nicol prism large enoughto embrace the entire beam of the electric lamp was placed between thelamp and the experimental tube. Sending the beam polarized by theNicol through the tube, I placed myself in front of it, the eyes beingon a level with its axis, my assistant occupying a similar positionbehind the tube. The short diagonal of the large Nicol was in thefirst instance vertical, the plane of vibration of the emergent beambeing therefore also vertical. As the light continued to act, a superbblue cloud visible to both my assistant and myself was slowly formed. But this cloud, so deep and rich when looked at from the positionsmentioned, utterly disappeared when looked at vertically downwards, or vertically upwards. Reflection from the cloud was not possible inthese directions. When the large Nicol was slowly turned round itsaxis, the eye of the observer being on the level of the beam, and theline of vision perpendicular to it, entire extinction of the lightemitted horizontally occurred when the longer diagonal of the largeNicol was vertical. But a vivid blue cloud was seen when looked atdownwards or upwards. This truly fine experiment, which I shouldcertainly have made without suggestion, was, as a matter of fact, first definitely suggested by a remark addressed to me in a letter byProfessor Stokes. 

All the phenomena of colour and of polarization observable in the caseof skylight are manifested by those actinic clouds; and they exhibitadditional phenomena which it would be neither convenient to pursue, nor perhaps possible to detect, in the actual firmament. They enableus, for example, to follow the polarization from its first appearanceon the barely visible blue to its final extinction in the coarsercloud. These changes, as far as it is now necessary to refer to them, may be thus summed up:--

1. The actinic cloud, as long as it continues blue, dischargespolarized light in all directions, but the direction of maximumpolarization, like that of skylight, is at right angles to thedirection of the illuminating beam. 

2. As long as the cloud remains distinctly blue, the light dischargedfrom it at right angles to the illuminating beam is _perfectly_polarized. It may be utterly quenched by a Nicol prism, the cloud fromwhich it issues being caused to disappear. Any deviation from theperpendicular enables a portion of the light to get through the prism. 

3. The direction of vibration of the polarized light is at rightangles to the illuminating beam. Hence a plate of tourmaline, with itsaxis parallel to the beam, stops the light, and with the axisperpendicular to the beam transmits the light. 

4. A plate of selenite placed between the Nicol and the actinic cloudshows the colours of polarized light; in fact, the cloud itself playsthe part of a polarizing Nicol. 

5. The particles of the blue cloud are immeasurably small, but theyincrease gradually in size, and at a certain period of their growthcease to discharge perfectly polarized light. For some time afterwardsthe light that reaches the eye, through the Nicol in its position ofleast transmission, is of a magnificent blue, far exceeding in depthand purity that of the purest sky; thus the waves that first feel theinfluence of size, at both limits of the polarization, are theshortest waves of the spectrum. These are the first to acceptpolarization, and they are the first to escape from it. 

LECTURE V. 

 RANGE OF VISION NOT COMMENSURATE WITH RANGE OF RADIATION THE ULTRA-VIOLET BAYS FLUORESCENCE THE RENDERING OF INVISIBLE RAYS VISIBLE VISION NOT THE ONLY SENSE APPEALED TO BY THE SOLAR AND ELECTRIC BEAM HEAT OF BEAM COMBUSTION BY TOTAL BEAM AT THE FOCI OF MIRRORS AND LENSES COMBUSTION THROUGH ICE-LENS IGNITION OF DIAMOND SEARCH FOR THE RAYS HERE EFFECTIVE SIR WILLIAM HERSCHEL'S DISCOVERY OF DARK SOLAR RAYS INVISIBLE RAYS THE BASIS OF THE VISIBLE DETACHMENT BY A RAY-FILTER OF THE INVISIBLE RAYS FROM THE VISIBLE COMBUSTION AT DARK FOCI CONVERSION OF HEAT-RAYS INTO LIGHT-RAYS CALORESCENCE PART PLAYED IN NATURE BY DARK RAYS IDENTITY OF LIGHT AND RADIANT HEAT INVISIBLE IMAGES REFLECTION, REFRACTION, PLANE POLARIZATION, DEPOLARIZATION, CIRCULAR POLARIZATION, DOUBLE REFRACTION, AND MAGNETIZATION OF RADIANT HEAT. 

§ 1. _Range of Vision and of Radiation_. 

The first question that we have to consider to-night is this: Is theeye, as an organ of vision, commensurate with the whole range of solarradiation--is it capable of receiving visual impressions from all therays emitted by the sun? The answer is negative. If we allowedourselves to accept for a moment that notion of gradual growth, amelioration, and ascension, implied by the term _evolution_, we mightfairly conclude that there are stores of visual impressions awaitingman, far greater than those now in his possession. Ritter discoveredin 1801 that beyond the extreme violet of the spectrum there is a vastefflux of rays which are totally useless as regards our present powersof vision. These ultra-violet waves, however, though incompetent toawaken the optic nerve, can shake asunder the molecules of certaincompound substances on which they impinge, thus producing chemicaldecomposition. 

But though the blue, violet, and ultra-violet rays can act thus uponcertain substances, the fact is hardly sufficient to entitle them tothe name of 'chemical rays, ' which is usually applied to distinguishthem from the other constituents of the spectrum. As regards theiraction upon the salts of silver, and many other substances, they mayperhaps merit this title; but in the case of the grandest example ofthe chemical action of light--the decomposition of carbonic acid inthe leaves of plants, with which my eminent friend Dr. Draper (now nomore) has so indissolubly associated his name--the yellow rays arefound to be the most active. 

There are substances, however, on which the violet and ultra-violetwaves exert a special decomposing power; and, by permitting theinvisible spectrum to fall upon surfaces prepared with suchsubstances, we reveal both the existence and the extent of theultraviolet spectrum. 

§ 2. _Ultra-violet Rays: Fluorescence_. 

The method of exhibiting the action of the ultraviolet rays by theirchemical action has been long known; indeed, Thomas Young photographedthe ultra-violet rings of Newton. We have now to demonstrate theirpresence in another way. As a general rule, bodies either transmitlight or absorb it; but there is a third case in which the lightfalling upon the body is neither transmitted nor absorbed, butconverted into light of another kind. Professor Stokes, the occupantof the chair of Newton in the University of Cambridge, hasdemonstrated this change of one kind of light into another, and haspushed his experiments so far as to render the invisible rays visible. 

A large number of substances examined by Stokes, when excited by theinvisible ultra-violet waves, have been proved to emit light. You knowthe rate of vibration corresponding to the extreme violet of thespectrum; you are aware that to produce the impression of this colour, the retina is struck 789 millions of millions of times in a second. Atthis point, the retina ceases to be useful as an organ of vision; for, though struck by waves of more rapid recurrence, they are incompetentto awaken the sensation of light. But when such non-visual waves arecaused to impinge upon the molecules of certain substances--on thoseof sulphate of quinine, for example--they compel those molecules, ortheir constituent atoms, to vibrate; and the peculiarity is, that thevibrations thus set up are _of slower period_ than those of theexciting waves. By this lowering of the rate of vibration through theintermediation of the sulphate of quinine, the invisible rays arebrought within the range of vision. We shall subsequently haveabundant opportunity for learning that transparency to the visible byno means involves transparency to the invisible rays. Our bisulphideof carbon, for example, which, employed in prisms, is so eminentlysuitable for experiments on the visual rays, is by no means sosuitable for these ultra-violet rays. Flint glass is better, and rockcrystal is better than flint glass. A glass prism, however, will suitour present purpose. 

Casting by means of such a prism a spectrum, not upon the whitesurface of our screen, but upon a sheet of paper which has been wettedwith a saturated solution of the sulphate of quinine and afterwardsdried, an obvious extension of the spectrum is revealed. We have, inthe first instance, a portion of the violet rendered whiter and morebrilliant; but, besides this, we have the gleaming of the colourwhere, in the case of unprepared paper, nothing is seen. Othersubstances produce a similar effect. A substance, for example, recently discovered by President Morton, and named by him _Thallene_, produces a very striking elongation of the spectrum, the new lightgenerated being of peculiar brilliancy. 

Fluor spar, and some other substances, when raised to a temperaturestill under redness, emit light. During the ages which have elapsedsince their formation, this capacity of shaking the ether into visualtremors appears to have been enjoyed by these substances. Light hasbeen potential within them all this time; and, as well explained byDraper, the heat, though not itself of visual intensity, can unlockthe molecules so as to enable them to exert their long-latent power ofvibration. This deportment of fluor spar determined Stokes in hischoice of a name for his great discovery: he called this renderingvisible of the ultra-violet rays _Fluorescence_. 

By means of a deeply coloured violet glass, we cut off almost thewhole of the light of our electric beam; but this glass is peculiarlytransparent to the violet and ultra-violet rays. The violet beam nowcrosses a large jar filled with water, into which I pour a solution ofsulphate of quinine. Clouds, to all appearance opaque, instantlytumble downwards. Fragments of horse-chestnut bark thrown upon thewater also send down beautiful cloud-like strife. But these are notclouds: there is nothing precipitated here: the observed action is anaction of _molecules_, not of _particles_. The medium before you isnot a turbid medium, for when you look through it at a luminoussurface it is perfectly clear. 

If we paint upon a piece of paper a flower or a bouquet with thesulphate of quinine, and expose it to the full beam, scarcely anythingis seen. But on interposing the violet glass, the design instantlyflashes forth in strong contrast with the deep surrounding violet. President Morton has prepared for me a most beautiful example of sucha design which, when placed in the violet light, exhibits a peculiarlybrilliant fluorescence. From the experiments of Drs. Bence Jones andDupré, it would seem that there is some substance in the human bodyresembling the sulphate of quinine, which causes all the tissues ofthe body to be more or less fluorescent. All animal infusions showthis fluorescence. The crystalline lens of the eye exhibits the effectin a very striking manner. When, for example, I plunge my eye intothis violet beam, I am conscious of a whitish-blue shimmer filling thespace before me. This is caused by fluorescent light generated in theeye itself. Looked at from without, the crystalline lens at the sametime is seen to gleam vividly. 

Long before its physical origin was understood this fluorescent lightattracted attention. Boyle describes it with great fulness andexactness. 'We have sometimes, ' he says, 'found in the shops of ourdruggists certain wood which is there called _Lignum Nephriticum, _because the inhabitants of the country where it grows are wont to usethe infusion of it, made in fair water, against the stone in thekidneys. This wood may afford us an experiment which, besides thesingularity of it, may give no small assistance to an attentiveconsiderer towards the detection of the nature of colours. Take_Lignum, Nephriticum_, and with a knife cut it into thin slices: putabout a handful of these slices into two or three or four pounds ofthe purest spring water. Decant this impregnated water into a glassphial; and if you hold it directly between the light and your eye, youshall see it wholly tinted with an almost golden colour. But if youhold this phial from the light, so that your eye be placed betwixt thewindow and the phial, the liquid will appear of a deep and lovelyceruleous colour. '

'These, ' he continues, 'and other phenomena which I have observed inthis delightful experiment, divers of my friends have looked upon, notwithout some wonder; and I remember an excellent oculist, finding byaccident in a friend's chamber a phial full of this liquor, which Ihad given that friend, and having never heard anything of theexperiment, nor having anybody near him who could tell him what thisstrange liquor might be, was a great while apprehensive, as hepresently afterwards told me, that some strange new distemper wasinvading his eyes. And I confess that the unusualness of thephenomenon made me very solicitous to find out the cause of thisexperiment; and though I am far from pretending to have found it, yetmy enquiries have, I suppose, enabled me to give such hints as maylead your greater sagacity to the discovery of the cause of thiswonder. '[21]

Goethe in his 'Farbenlehre' thus describes the fluorescence ofhorse-chestnut bark:--'Let a strip of fresh horse-chestnut bark betaken and clipped into a glass of water; the most perfect sky-bluewill be immediately produced. '[22] Sir John Herschel first noticed anddescribed the fluorescence of the sulphate of quinine, and showed thatthe light proceeded from a thin stratum of the solution adjacent tothe surface where the light enters it. He showed, moreover, that theincident beam, although not sensibly weakened in luminous intensity, lost, in its transmission through the solution of sulphate of quinine, the power of producing the blue fluorescent light. Sir David Brewsteralso worked at the subject; but to Professor Stokes we are indebtednot only for its expansion, but for its full and final explanation. 

§ 3. _The Heat of the Electric Beam. Ignition through a Lens of Ice. Possible Cometary Temperature_. 

But the waves from our incandescent carbon-points appeal to anothersense than that of vision. They not only produce light, but heat, as asensation. The magnified image of the carbon-points is now upon thescreen; and with a suitable instrument the heating power of the rayswhich form that image might be readily demonstrated. In this case, however, the heat is spread over too large an area to be very intense. Drawing out the camera lens, and causing a movable screen to approachthe lamp, the image is seen to become smaller and smaller; the rays atthe same time becoming more and more concentrated, until finally theyare able to pierce black paper with a burning ring. Pushing back thelens so as to render the rays parallel, and receiving them upon aconcave mirror, they are brought to a focus; paper placed at thatfocus is caused to smoke and burn. Heat of this intensity may beobtained with our ordinary camera and lens, and a concave mirror ofvery moderate power. 

[Illustration: Fig. 48. ]

We will now adopt stronger measures with the radiation. In this largercamera of blackened tin is placed a lamp, in all particulars similarto those already employed. But instead of gathering up the rays fromthe carbon-points by a condensing lens, we gather them up by a concavemirror (_m_ _m'_, fig. 48), silvered in front and placed behind thecarbons (P). By this mirror we can cause the rays to issue through theorifice in front of the camera, either parallel or convergent. Theyare now parallel, and therefore to a certain extent diffused. We placea convex lens (L) in the path of the beam; the light is converged to afocus (C), and at that focus paper is not only pierced, but it isinstantly set ablaze. 

Many metals may be burned up in the same way. In our first lecturethe combustibility of zinc was mentioned. Placing a strip ofsheet-zinc at this focus, it is instantly ignited, burning with itscharacteristic purple flame. And now I will substitute for our glasslens (L) one of a more novel character. In a smooth iron mould a lensof pellucid ice has been formed. Placing it in the position occupied amoment ago by the glass lens, I can see the beam brought to a sharpfocus. At the focus I place, a bit of black paper, with a littlegun-cotton folded up within it. The paper immediately ignites and thecotton explodes. Strange, is it not, that the beam should possess suchheating power after having passed through so cold a substance? In hisarctic expeditions Dr. Scoresby succeeded in exploding gunpowder bythe sun's rays, converged by large lenses of ice; here we havesucceeded in producing the effect with a small lens, and with aterrestrial source of heat. 

In this experiment, you observe that, before the beam reaches theice-lens, it has passed through a glass cell containing water. Thebeam is thus sifted of constituents, which, if permitted to fall uponthe lens, would injure its surface, and blur the focus. And this leadsme to say an anticipatory word regarding transparency. In our firstlecture we entered fully into the production of colours by absorption, and we spoke repeatedly of the quenching of the rays of light. Didthis mean that the light was altogether annihilated? By no means. Itwas simply so lowered in refrangibility as to escape the visual range. It was converted into heat. Our red ribbon in the green of thespectrum quenched the green, but if suitably examined its temperaturewould have been found raised. Our green ribbon in the red of thespectrum quenched the red, but its temperature at the same time wasaugmented to a degree exactly equivalent to the light extinguished. Our black ribbon, when passed through the spectrum, was foundcompetent to quench all its colours; but at every stage of itsprogress an amount of heat was generated in the ribbon exactlyequivalent to the light lost. It is only when _absorption_ takes placethat heat is thus produced: and heat is always a result of absorption. 

Examine the water, then, in front of the lamp after the beam haspassed through it: it is sensibly warm, and, if permitted to remainthere long enough, it might be made to boil. This is due to theabsorption, by the water, of a certain portion of the electric beam. But a portion passes through unabsorbed, and does not at allcontribute to the heating of the water. Now, ice is also in great parttransparent to these latter rays, and therefore is but little meltedby them. Hence, by employing the portion of the beam transmitted bywater, we are able to keep our lens intact, and to produce by means ofit a sharply defined focus. Placed at that focus, white paper is notignited, because it fails to absorb the rays emergent from theice-lens. At the same place, however, black paper instantly burns, because it absorbs the transmitted light. 

And here it may be useful to refer to an estimate by Newton, basedupon doubtful data, but repeated by various astronomers of eminencesince his time. The comet of 1680, when nearest to the sun, was only asixth of the sun's diameter from his surface. Newton estimated itstemperature, in this position, to be more than two thousand times thatof molted iron. Now it is clear from the foregoing experiments thatthe temperature of the comet could not be inferred from its nearnessto the sun. If its power of absorption were sufficiently low, thecomet might carry into the sun's neighbourhood the chill of stellarspace. 

§ 4. _Combustion of a Diamond by Radiant Heat_. 

The experiment of burning a diamond in oxygen by the concentrated raysof the sun was repeated at Florence, in presence of Sir Humphry Davy, on Tuesday, the 27th of March, 1814. It is thus described byFaraday:--'To-day we made the grand experiment of burning the diamond, and certainly the phenomena presented were extremely beautiful andinteresting. A glass globe containing about 22 cubical inches wasexhausted of air, and filled with pure oxygen. The diamond wassupported in the centre of this globe. The Duke's burning-glass wasthe instrument used to apply heat to the diamond. It consists of twodouble convex lenses, distant from each other about 3½ feet; the largelens is about 14 or 15 inches in diameter, the smaller one about 3inches in diameter. By means of the second lens the focus is very muchreduced, and the heat, when the sun shines brightly, rendered veryintense. The diamond was placed in the focus and anxiously watched. Ona sudden Sir H. Davy observed the diamond to burn visibly, and whenremoved from the focus it was found to be in a state of active andrapid combustion. '

The combustion of the diamond had never been effected by radiant heatfrom a terrestrial source. I tried to accomplish this before crossingthe Atlantic, and succeeded in doing so. The small diamond now in myhand is held by a loop of platinum wire. To protect it as far aspossible from air currents, and also to concentrate the heat upon it, it is surrounded by a hood of sheet platinum. Bringing a jar of oxygenunderneath, I cause the focus of the electric beam to fall upon thediamond. A small fraction of the time expended in the experimentdescribed by Faraday suffices to raise the diamond to a brilliant red. Plunging it then into the oxygen, it glows like a little white star;and it would continue to burn and glow until wholly consumed. Thefocus can also be made to fall upon the diamond in oxygen, as in theFlorentine experiment: the result is the same. It was simply to securemore complete mastery over the position of the focus, so as to causeit to fall accurately upon the diamond, that the mode of experimenthere described was resorted to. 

§ 5. _Ultra-red Rays: Calorescence_. 

In the path of the beam issuing from our lamp I now place a cell withglass sides containing a solution of alum. All the _light_ of the beampasses through this solution. This light is received on a powerfullyconverging mirror silvered in front, and brought to a focus by themirror. You can see the conical beam of reflected light trackingitself through the dust of the room. A scrap of white paper placed atthe focus shines there with dazzling brightness, but it is not evencharred. On removing the alum cell, however, the paper instantlyinflames. There must, therefore, be something in this beam besides itslight. The _light_ is not absorbed by the white paper, and thereforedoes not burn the paper; but there is something over and above thelight which _is_ absorbed, and which provokes combustion. What is thissomething?

In the year 1800 Sir William Herschel passed a thermometer throughthe various colours of the solar spectrum, and marked the rise oftemperature corresponding to each colour. He found the heating effectto augment from the violet to the red; he did not, however, stop atthe red, but pushed his thermometer into the dark space beyond it. Here he found the temperature actually higher than in any part of thevisible spectrum. By this important observation, he proved that thesun emitted heat-rays which are entirely unfit for the purposes ofvision. The subject was subsequently taken up by Seebeck, Melloni, Müller, and others, and within the last few years it has been foundcapable of unexpected expansions and applications. I have devised amethod whereby the solar or electric beam can be so _filtered_ as todetach from it, and preserve intact, this invisible ultra-redemission, while the visible and ultra-violet emissions are whollyintercepted. We are thus enabled to operate at will upon the purelyultra-red waves. 

In the heating of solid bodies to incandescence, this non-visualemission is the necessary basis of the visual. A platinum wire isstretched in front of the table, and through it an electric currentflows. It is warmed by the current, and may be felt to be warm by thehand. It emits waves of heat, but no light. Augmenting the strength ofthe current, the wire becomes hotter; it finally glows with a soberred light. At this point Dr. Draper many years ago began aninteresting investigation. He employed a voltaic current to heat hisplatinum, and he studied, by means of a prism, the successiveintroduction of the colours of the spectrum. His first colour, ashere, was red; then came orange, then yellow, then green, and lastlyall the shades of blue. As the temperature of the platinum wasgradually augmented, the atoms were caused to vibrate more rapidly;shorter waves were thus introduced, until finally waves were obtainedcorresponding to the entire spectrum. As each successive colour wasintroduced, the colours preceding it became more vivid. Now thevividness or intensity of light, like that of sound, depends not uponthe length of the wave, but on the amplitude of the vibration. Hence, as the less refrangible colours grew more intense when the morerefrangible ones were introduced, we are forced to conclude that sideby side with the introduction of the shorter waves we had anaugmentation of the amplitude of the longer ones. 

These remarks apply not only to the visible emission examined by Dr. Draper, but to the invisible emission which precedes the appearance ofany light. In the emission from the white-hot platinum wire now beforeyou, the lightless waves exist with which we started, only theirintensity has been increased a thousand-fold by the augmentation oftemperature necessary to the production of this white light. Botheffects are bound up together: in an incandescent solid, or in amolten solid, you cannot have the shorter waves without thisintensification of the longer ones. A sun is possible only on theseconditions; hence Sir William Herschel's discovery of the invisibleultra-red solar emission. 

The invisible heat, emitted both by dark bodies and by luminous ones, flies through space with the velosity of light, and is called _radiantheat_. Now, radiant heat may be made a subtle and powerful explorer ofmolecular condition, and, of late years, it has given a newsignificance to the act of chemical combination. Take, for example, the air we breathe. It is a mixture of oxygen and nitrogen; and itbehaves towards radiant heat like a vacuum, being incompetent toabsorb it in any sensible degree. But permit the same two gases tounite chemically; then, without any augmentation of the quantity ofmatter, without altering the gaseous condition, without interfering inany way with the transparency of the gas, the act of chemical union isaccompanied by an enormous diminution of its _diathermancy_, orperviousness to radiant heat. 

The researches which established this result also proved theelementary gases, generally, to be highly transparent to radiant heat. This, again, led to the proof of the diathermancy of elementaryliquids, like bromine, and of solutions of the solid elements sulphur, phosphorus, and iodine. A spectrum is now before you, and you noticethat the transparent bisulphide of carbon has no effect upon thecolours. Dropping into the liquid a few flakes of iodine, you see themiddle of the spectrum cut away. By augmenting the quantity of iodine, we invade the entire spectrum, and finally cut it off altogether. Now, the iodine, which proves itself thus hostile to the light, isperfectly transparent to the ultra-red emission with which we have nowto deal. It, therefore, is to be our ray-filter. 

Placing the alum-cell again in front of the electric lamp, we assureourselves, as before, of the utter inability of the concentrated lightto fire white paper-Introducing a cell containing the solution ofiodine, the light is entirely cut off; and then, on removing thealum-cell, the white paper at the dark focus is instantly set on fire. Black paper is more absorbent than white for these rays; and theconsequence is, that with it the suddenness and vigour of thecombustion are augmented. Zinc is burnt up at the same place, magnesium bursts into vivid combustion, while a sheet of platinizedplatinum, placed at the focus, is heated to whiteness. 

Looked at through a prism, the white-hot platinum yields all thecolours of the spectrum. Before impinging upon the platinum, the waveswere of too slow recurrence to awaken vision; by the atoms of theplatinum, these long and sluggish waves are broken up into shorterones, being thus brought within the visual range. At the other end ofthe spectrum, by the interposition of suitable substances, ProfessorStokes _lowered_ the refrangibility, so as to render the non-visualrays visual, and to this change he gave the name of _Fluorescence_. Here, by the intervention of the platinum, the refrangibility is_raised_, so as to render the non-visual visual, and to this change Ihave given the name of _Calorescence_. 

At the perfectly invisible focus where these effects are produced, theair may be as cold as ice. Air, as already stated, does not absorbradiant heat, and is therefore not warmed by it. Nothing could moreforcibly illustrate the isolation, if I may use the term, of theluminiferous ether from the air. The wave-motion of the one is heapedup to an extraordinary degree of intensity, without producing anysensible effect upon the other. I may add that, with suitableprecautions, the eye may be placed in a focus competent to heatplatinum to vivid redness, without experiencing any damage, or theslightest sensation either of light or heat. 

The important part played by these ultra-red rays in Nature may bethus illustrated: I remove the iodine filter, and concentrate thetotal beam upon a test tube containing water. It immediately begins tosplutter, and in a minute or two it _boils_. What boils it? Placingthe alum solution in front of the lamp, the boiling instantly ceases. Now, the alum is pervious to all the luminous rays; hence it cannot bethese rays that caused the boiling. I now introduce the iodine, andremove the alum: vigorous ebullition immediately recommences at theinvisible focus. So that we here fix upon the invisible ultra-red raysthe heating of the water. 

We are thus enabled to understand the momentous part played by theserays in Nature. It is to them that we owe the warming and theconsequent evaporation of the tropical ocean; it is to them, therefore, that we owe our rains and snows. They are absorbed close tothe surface of the ocean, and warm the superficial water, while theluminous rays plunge to great depths without producing any sensibleeffect. But we can proceed further than this. Here is a large flaskcontaining a freezing mixture, which has so chilled the flask, thatthe aqueous vapour of the air of this room has been condensed andfrozen upon it to a white fur. Introducing the alum-cell, and placingthe coating of hoar-frost at the intensely luminous focus of theelectric lamp, not a spicula of the dazzling frost is melted. Introducing the iodine-cell, and removing the alum, a broad space ofthe frozen coating is instantly melted away. Hence we infer that thesnow and ice, which feed the Rhone, the Rhine, and other rivers withglaciers for their sources, are released from their imprisonment uponthe mountains by the invisible ultra-red rays of the sun. 

§ 6. _Identity of Light and Radiant Heat. Reflection from Plane andCurved Surfaces. Total Reflection of Heat_. 

The growth of science is organic. That which today is an _end_ becomesto-morrow a _means_ to a remoter end. Every new discovery in scienceis immediately made the basis of other discoveries, or of new methodsof investigation. Thus about fifty years ago OErsted, of Copenhagen, discovered the deflection of a magnetic needle by an electric current;and about the same time Thomas Seebeck, of Berlin, discoveredthermoelectricity. These great discoveries were soon afterwards turnedto account, by Nobili and Melloni, in the construction of aninstrument which has vastly augmented our knowledge of radiant heat. This instrument, which is called a _thermo-electric pile_, or morebriefly a thermo-pile, consists of thin bars of bismuth and antimony, soldered alternately together at their ends, but separated from eachother elsewhere. From the ends of this 'thermo-pile' wires pass to agalvanometer, which consists of a coil of covered wire, within andabove which are suspended two magnetic needles, joined to a rigidsystem, and carefully defended from currents of air. 

The action of the arrangement is this: the heat, falling on the pile, produces an electric current; the current, passing through the coil, deflects the needles, and the magnitude of the deflection may be madea measure of the heat. The upper needle moves over a graduated dialfar too small to be directly seen. It is now, however, stronglyilluminated; and above it is a lens which, if permitted, would form animage of the needle and dial upon the ceiling. There, however, itcould not be conveniently viewed. The beam is therefore received upona looking-glass, placed at the proper angle, which throws the imageupon a screen. In this way the motions of this small needle may bemade visible to you all. 

The delicacy of this apparatus is such that in a room filled, as thisroom now is, with an audience physically warm, it is exceedinglydifficult to work with it. My assistant stands several feet off. Iturn the pile towards him: the heat radiated from his face, even atthis distance, produces a deflection of 90°. I turn the instrumenttowards a distant wall, a little below the average temperature of theroom. The needle descends and passes to the other side of zero, declaring by this negative deflection that the pile has lost itswarmth by radiation against the cold wall. Possessed of thisinstrument, of our ray-filter, and of our large Nicol prisms, we arein a condition to investigate a subject of great philosophicalinterest; one which long engaged the attention of some of our foremostscientific workers--the substantial _identity of light and radiantheat_. 

That they are identical in _all_ respects cannot of course be thecase, for if they were they would act in the same manner upon allinstruments, the _eye_ included. The identity meant is such assubsists between one colour and another, causing them to behave alikeas regards reflection, refraction, double refraction, andpolarization. Let us here run rapidly over the resemblances of lightand heat. As regards reflection from plane surfaces, we may employ alooking-glass to reflect the light. Marking any point in the track ofthe reflected beam, cutting off the light by the dissolved iodine, and placing the pile at the marked point, the needle immediatelystarts aside, showing that the heat is reflected in the same directionas the light. This is true for every position of the mirror. Recurring, for example, to the simple apparatus employed in our firstlecture (fig. 3, p. 11); moving the index attached to the mirror alongthe divisions of our graduated arc (_m_ _n_), and determining by thepile the positions of the invisible reflected beam, we prove that theangular velocity of the heat-beam, like that of the light-beam, istwice that of the mirror. 

[Illustration: Fig. 49. ]

As regards reflection from curved surfaces, the identity also holdsgood. Receiving the beam from our electric lamp on a concave mirror(_m_ _m_, fig. 49), it is gathered up into a cone of reflected lightrendered visible by the floating dust of the air; marking the apex ofthe cone by a pointer, and cutting off the light by the iodinesolution (T), a moment's exposure of the pile (P) at the marked pointproduces a violent deflection of the needle. 

The common reflection and the total reflection of a beam of radiantheat may be simultaneously demonstrated. From the nozzle of the lamp(L, fig. 50) a beam impinges upon a plane mirror (M N), is reflectedupwards, and enters a right-angled prism, of which _a_ _b_ _c_ is thesection. It meets the hypothenuse at an obliquity greater than thelimiting angle, [23] and is therefore totally reflected. Quenching thelight by the ray-filter at F, and placing the pile at P, the totallyreflected heat-beam is immediately felt by the pile, and declared bythe galvanometric deflection. 

[Illustration: Fig. 50. ]

§ 7. _Invisible Images formed by Radiant Heat. _

Perhaps no experiment proves more conclusively the substantialidentity of light and radiant heat, than the formation of invisibleheat-images. Employing the mirror already used to raise the beam toits highest state of concentration, we obtain, as is well known, aninverted image of the carbon points, formed by the light rays at thefocus. Cutting off the light by the ray-filter, and placing at thefocus a thin sheet of platinized platinum, the invisible rays declaretheir presence and distribution, by stamping upon the platinum awhite-hot image of the carbons. (See fig. 51. )

[Illustration: Fig. 51. ]

§ 8. _Polarization of Heat_. 

Whether radiant heat be capable of polarization or not was for a longtime a subject of discussion. Bérard had announced affirmativeresults, but Powell and Lloyd failed to verify them. The doubts thusthrown upon the question were removed by the experiments of Forbes, who first established the polarization and 'depolarization' of heat. The subject was subsequently followed up by Melloni, an investigatorof consummate ability, who sagaciously turned to account his owndiscovery, that the obscure rays of luminous sources are in parttransmitted by black glass. Intercepting by a plate of this glass thelight from an oil flame, and operating upon the transmitted invisibleheat, he obtained effects of polarization, far exceeding in magnitudethose which could be obtained with non-luminous sources. At presentthe possession of our more perfect ray-filter, and more powerfulsource of heat, enables us to pursue this identity question to itsutmost practical limits. 

[Illustration: Fig. 52. ]

Mounting our two Nicols (B and C, fig. 52) in front of the electriclamp, with their principal sections crossed, no light reaches thescreen. Placing our thermo-electric pile (D) behind the prisms, withits face turned towards the source, no deflection of the galvanometeris observed. Interposing between the lamp (A) and the first prism (B)our ray-filter, the light previously transmitted through the firstNicol is quenched; and now the slightest turning of either Nicol opensa way for the transmission of the heat, a very small rotationsufficing to send the needle up to 90°. When the Nicol is turned backto its first position, the needle again sinks to zero, thusdemonstrating, in the plainest manner, the polarization of the heat. 

When the Nicols are crossed and the field is dark, you have seen, inthe case of light, the effect of introducing a plate of mica betweenthe polarizer and analyzer. In two positions the mica exerts nosensible influence; in all others it does. A precisely analogousdeportment is observed as regards radiant heat. Introducing ourray-filter, the thermo-pile, playing the part of an eye as regards theinvisible radiation, receives no heat when the eye receives no light;but when the mica is so turned as to make its planes of vibrationoblique to those of the polarizer and analyzer, the heat immediatelypasses through. So strong does the action become, that the momentaryplunging of the film of mica into the dark space between the Nicolssuffices to send the needle up to 90°. This is the effect to which theterm 'depolarization' has been applied; the experiment really provingthat with both light and heat we have the same resolution by the plateof mica, and recompounding by the analyzer, of the etherealvibrations. 

Removing the mica and restoring the needle once more to 0°, Iintroduce between the Nicols a plate of quartz cut perpendicular tothe axis; the immediate deflection of the needle declares thetransmission of the heat, and when the transmitted beam is properlyexamined, it is found to be circularly polarized, exactly as a beam oflight is polarized under the same conditions. 

§ 9. _Double Refraction of Heat_. 

I will now abandon the Nicols, and send through the piece of Icelandspar (B, fig. 53), already employed (in Lecture III. ) to illustratethe double refraction of light, our sifted beam of invisible heat. Todetermine the positions of the two images, let us first operate uponthe luminous beam. Marking the places of the light-images, weintroduce between N and L our ray-filter (not in the figure) andquench the light. Causing the pile to approach one of the markedplaces, the needle remains unmoved until the place has been attained;here the pile at once detects the heat. Pushing the pile across theinterval separating the two marks, the needle first falls to 0°, andthen rises again to 90° in the second position. This proves the doublerefraction of the heat. 

[Illustration: Fig. 53. ]

I now turn the Iceland spar: the needle remains fixed; there is noalteration of the deflection. Passing the pile rapidly across to theother mark, the deflection is maintained. Once more I turn the spar, but now the needle falls to 0°, rising, however, again to 90° after arotation of 360°. We know that in the case of light the extraordinarybeam rotates round the ordinary one; and we have here been operatingon the extraordinary heat-beam, which, as regards double refraction, behaves exactly like a beam of light. 

§ 10. _Magnetization of Heat_. 

To render our series of comparisons complete, we must demonstrate themagnetization of heat. But here a slight modification of ourarrangement will be necessary. In repeating Faraday's experiment onthe magnetization of light, we had, in the first instance, our Nicolscrossed and the field rendered dark, a flash of light appearing uponthe screen when the magnet was excited. Now the quantity of lighttransmitted in this case is really very small, its effect beingrendered striking through contrast with the preceding darkness. Whenwe so place the Nicols that their principal sections enclose an angleof 45°, the excitement of the magnet causes a far greater positiveaugmentation of the light, though the augmentation is not so well_seen_ through lack of contrast, because here, at starting, the fieldis illuminated. 

In trying to magnetize our beam of heat, we will adopt thisarrangement. Here, however, at the outset, a considerable amount ofheat falls upon one face of the pile. This it is necessary toneutralize, by permitting rays from another source to fall upon theopposite face of the pile. The needle is thus brought to zero. Cuttingoff the light by our ray-filter, and exciting the magnet, the needleis instantly deflected, proving that the magnet has opened a door forthe heat, exactly as in Faraday's experiment it opened a door for thelight. Thus, in every case brought under our notice, the substantialidentity of light and radiant heat has been demonstrated. 

By the refined experiments of Knoblauch, who worked long andsuccessfully at this question, the double refraction of heat, byIceland spar, was first demonstrated; but, though he employed theluminous heat of the sun, the observed deflections were exceedinglysmall. So, likewise, those eminent investigators De la Povostaye andDesains succeeded in magnetizing a beam of heat; but though, in theircase also, the luminous solar heat was employed, the deflectionobtained did not amount to more than two or three degrees. With_obscure_ radiant heat the effect, prior to the experiments nowbrought before you, had not been obtained; but, with the arrangementhere described, we obtain deflections from purely invisible heat, equal to 150 of the lower degrees of the galvanometer. 

§ 11. _Distribution of Heat in the Electric Spectrum_. 

We have finally to determine the position and magnitude of theinvisible radiation which produces these results. For this purpose weemploy a particular form of the thermo-pile. Its face is a rectangle, which by movable side-pieces can be rendered as narrow as desirable. Throwing a small and concentrated spectrum upon a screen, by means ofan endless screw we move the rectangular pile through the entirespectrum, and determine in succession the thermal power of all itscolours. 

[Illustration: SPECTRUM OF ELECTRIC LIGHT. ]

When this instrument is brought to the violet end of the spectrum, the heat is found to be almost insensible. As the pile gradually movesfrom the violet towards the red, it encounters a gradually augmentingheat. The red itself possesses the highest heating power of all thecolours of the spectrum. Pushing the pile into the dark space beyondthe red, the heat rises suddenly in intensity, and at some distancebeyond the red it attains a maximum. From this point the heat fallssomewhat more rapidly than it rose, and afterwards gradually fadesaway. 

Drawing a horizontal line to represent the length of the spectrum, anderecting along it, at various points, perpendiculars proportional inlength to the heat existing at those points, we obtain a curve whichexhibits the distribution of heat in the prismatic spectrum. It isrepresented in the adjacent figure. Beginning at the blue, the curverises, at first very gradually; towards the red it rises more rapidly, the line C D (fig. 54, opposite page) representing the strength of theextreme red radiation. Beyond the red it shoots upwards in a steep andmassive peak to B; whence it falls, rapidly for a time, and afterwardsgradually fades from the perception of the pile. This figure is theresult of more than twelve careful series of measurements, from eachof which the curve was constructed. On superposing all these curves, asatisfactory agreement was found to exist between them. So that it maysafely be concluded that the areas of the dark and white spaces, respectively, represent the relative energies of the visible andinvisible radiation. The one is 7. 7 times the other. 

But in verification, as already stated, consists the strength ofscience. Determining in the first place the total emission from theelectric lamp, and then, by means of the iodine filter, determiningthe ultra-red emission; the difference between both gives the luminousemission. In this way, it is found that the energy of the invisibleemission is eight times that of the visible. No two methods could bemore opposed to each other, and hardly any two results could betterharmonize. I think, therefore, you may rely upon the accuracy of thedistribution of heat here assigned to the prismatic spectrum of theelectric light. There is nothing vague in the mode of investigation, or doubtful in its conclusions. Spectra are, however, formed by_diffraction_, wherein the distribution of both heat and light isdifferent from that produced by the prism. These diffractive spectrahave been examined with great skill by Draper and Langley. In theprismatic spectrum the less refrangible rays are compressed into amuch smaller space than in the diffraction spectrum. 

LECTURE VI. 

PRINCIPLES OF SPECTRUM ANALYSISPRISMATIC ANALYSIS OF THE LIGHT OF INCANDESCENT VAPOURSDISCONTINUOUS SPECTRASPECTRUM BANDS PROVED BY BUNSEN AND KIRCHHOFF TO BE CHARACTERISTIC OF THE VAPOURDISCOVERY OF RUBIDIUM, CÆSIUM, AND THALLIUMRELATION OF EMISSION TO ABSORPTIONTHE LINES OF FRAUNHOFERTHEIR EXPLANATION BY KIRCHHOFFSOLAR CHEMISTRY INVOLVED IN THIS EXPLANATIONFOUCAULT'S EXPERIMENTPRINCIPLES OF ABSORPTIONANALOGY OF SOUND AND LIGHTEXPERIMENTAL DEMONSTRATION OF THIS ANALOGYRECENT APPLICATIONS OF THE SPECTROSCOPESUMMARY AND CONCLUSION. 

We have employed as our source of light in these lectures the ends oftwo rods of coke rendered incandescent by electricity. Coke isparticularly suitable for this purpose, because it can bear intenseheat without fusion or vaporization. It is also black, which helps thelight; for, other circumstances being equal, as shown experimentallyby Professor Balfour Stewart, the blacker the body the brighter willbe its light when incandescent. Still, refractory as carbon is, if weclosely examined our voltaic arc, or stream of light between thecarbon-points, we should find there incandescent carbon-vapour. And ifwe could detach the light of this vapour from the more dazzling lightof the solid points, we should find its spectrum not only lessbrilliant, but of a totally different character from the spectra thatwe have already seen. Instead of being an unbroken succession ofcolours from red to violet, the carbon-vapour would yield a few bandsof colour with spaces of darkness between them. 

What is true of the carbon is true in a still more striking degree ofthe metals, the most refractory of which can be fused, boiled, andreduced to vapour by the electric current. From the incandescentvapour the light, as a general rule, flashes in groups of rays ofdefinite degrees of refrangibility, spaces existing between group andgroup, which are unfilled by rays of any kind. But the contemplationof the facts will render this subject more intelligible than words canmake it. Within the camera is now placed a cylinder of carbon hollowedout at the top; in the hollow is placed a fragment of the metalthallium. Down upon this we bring the upper carbon-point, and thenseparate the one from the other. A stream of incandescentthallium-vapour passes between them, the magnified image of which isnow seen upon the screen. It is of a beautiful green colour. What isthe meaning of that green? We answer the question by subjecting thelight to prismatic analysis. Sent through the prism, its spectrum isseen to consist of a single refracted band. Light of one degree ofrefrangibility--that corresponding to this particular green--isemitted by the thallium-vapour. 

We will now remove the thallium and put a bit of silver in its place. The are of silver is not to be distinguished from that of thallium; itis not only green, but the same shade of green. Are they then alike?Prismatic analysis enables us to answer the question. Howeverimpossible it is to distinguish the one _colour_ from the other, it isequally impossible to confound the _spectrum_ of incandescentsilver-vapour with that of thallium. In the case of silver, we havetwo green bands instead of one. 

If we add to the silver in our camera a bit of thallium, we shallobtain the light of both metals. After waiting a little, we see thatthe green of the thallium lies midway between the two greens of thesilver. Hence this similarity of colour. 

But why have we to 'wait a little' before we see this effect? Thethallium band at first almost masks the silver bands by its superiorbrightness. Indeed, the silver bands have wonderfully degeneratedsince the bit of thallium was put in, and for a reason worth knowing. It is the _resistance_ offered to the passage of the electric currentfrom carbon to carbon, that calls forth the power of the current toproduce heat. If the resistance were materially lessened, the heatwould be materially lessened; and if all resistance were abolished, there would be no heat at all. Now, thallium is a much more fusibleand vaporizable metal than silver; and its vapour facilitates thepassage of the electricity to such a degree, as to render the currentalmost incompetent to vaporize the more refractory silver. But thethallium is gradually consumed; its vapour diminishes, the resistancerises, until finally you see the two silver bands as brilliant as theywere at first. [24]

We have in these bands a perfectly unalterable characteristic of thetwo metals. You never get other bands than these two green ones fromthe silver, never other than the single green band from the thallium, never other than the three green bands from the mixture of bothmetals. Every known metal has its own particular bands, and in noknown case are the bands of two different metals alike inrefrangibility. It follows, therefore, that these spectra may be madea sure test for the presence or absence of any particular metal. If wepass from the metals to their alloys, we find no confusion. Coppergives green bands; zinc gives blue and red bands; brass--an alloy ofcopper and zinc--gives the bands of both metals, perfectly unalteredin position or character. 

But we are not confined to the metals themselves; the _salts_ of thesemetals yield the bands of the metals. Chemical union is ruptured by asufficiently high heat; the vapour of the metal is set free, and ityields its characteristic bands. The chlorides of the metals areparticularly suitable for experiments of this character. Common salt, for example, is a compound of chlorine and sodium; in the electriclamp it yields the spectrum of the metal sodium. The chlorides ofcopper, lithium, and strontium yield, in like manner, the bands ofthese metals. 

When, therefore, Bunsen and Kirchhoff, the illustrious founders of_spectrum analysis_, after having established by an exhaustiveexamination the spectra of all known substances, discovered a spectrumcontaining bands different from any known bands, they immediatelyinferred the existence of a new metal. They were operating at the timeupon a residue, obtained by evaporating one of the mineral waters ofGermany. In that water they knew the unknown metal was concealed, butvast quantities of it had to be evaporated before a residue could beobtained sufficiently large to enable ordinary chemistry to grapplewith the metal. They, however, hunted it down, and it now standsamong chemical substances as the metal _Rubidium_. They subsequentlydiscovered a second metal, which they called _Cæsium_. Thus, havingfirst placed spectrum analysis on a sure foundation, they demonstratedits capacity as an agent of discovery. Soon afterwards Mr. Crookes, pursuing the same method, discovered the bright green band of_Thallium_, and obtained the salts of the metal which yielded it. Themetal itself was first isolated in ingots by M. Lamy, a Frenchchemist. 

All this relates to chemical discovery upon earth, where the materialsare in our own hands. But it was soon shown how spectrum analysismight be applied to the investigation of the sun and stars; and thisresult was reached through the solution of a problem which had beenlong an enigma to natural philosophers. The scope and conquest of thisproblem we must now endeavour to comprehend. A spectrum is _pure_ inwhich the colours do not overlap each other. We purify the spectrum bymaking our beam narrow, and by augmenting the number of our prisms. When a pure spectrum of the sun has been obtained in this way, it isfound to be furrowed by innumerable dark lines. Four of them werefirst seen by Dr. Wollaston, but they were afterwards multiplied andmeasured by Fraunhofer with such masterly skill, that they are nowuniversally known as Fraunhofer's lines. To give an explanation ofthese lines was, as I have said, a problem which long challenged theattention of philosophers, and to Professor Kirchhoff belongs thehonour of having first conquered this problem. 

(The positions of the principal lines, lettered according toFraunhofer, are shown in the annexed sketch (fig. 55) of the solarspectrum. A is supposed to stand near the extreme red, and J near theextreme violet. )

[Illustration: Fig. 55. ]

The brief memoir of two pages, in which this immortal discovery isrecorded, was communicated to the Berlin Academy on October 27, 1859. Fraunhofer had remarked in the spectrum of a candle flame two brightlines, which coincide accurately, as to position, with the double darkline D of the solar spectrum. These bright lines are produced withparticular intensity by the yellow flame derived from a mixture ofsalt and alcohol. They are in fact the lines of sodium vapour. Kirchhoff produced a spectrum by permitting the sunlight to enter histelescope by a slit and prism, and in front of the slit he placed theyellow sodium flame. As long as the spectrum remained feeble, therealways appeared two bright lines, derived from the flame, in the placeof the two dark lines D of the spectrum. In this case, such absorptionas the flame exerted upon the sunlight was more than atoned for by theradiation from the flame. When, however, the solar spectrum wasrendered sufficiently intense, the bright bands vanished, and the twodark Fraunhofer lines appeared with much greater sharpness anddistinctness than when the flame was not employed. 

This result, be it noted, was not due to any real quenching of thebright lines of the flame, but to the augmentation of the intensity ofthe adjacent spectrum. The experiment proved to demonstration, thatwhen the white light sent through the flame was sufficiently intense, the quantity which the flame absorbed was far in excess of that whichit radiated. 

Here then is a result of the utmost significance. Kirchhoffimmediately inferred from it that the salt flame, which couldintensify so remarkably the dark lines of Fraunhofer, ought also to beable to _produce_ them. The spectrum of the Drummond light is known toexhibit the two bright lines of sodium, which, however, graduallydisappear as the modicum of sodium, contained as an impurity in theincandescent lime, is exhausted. Kirchhoff formed a spectrum of thelimelight, and after the two bright lines had vanished, he placed hissalt flame in front of the slit. The two dark lines immediatelystarted forth. Thus, in the continuous spectrum of the lime-light, heevoked, artificially, the lines D of Fraunhofer. 

Kirchhoff knew that this was an action not peculiar to the sodiumflame, and he immediately extended his generalisation to all colouredflames which yield sharply defined bright bands in their spectra. White light, with all its constituents complete, sent through suchflames, would, he inferred, have those precise constituents absorbed, whose refrangibilities are the same as those of the bright bands; sothat after passing through such flames, the white light, ifsufficiently intense, would have its spectrum furrowed by bands ofdarkness. On the occasion here referred to Kirchhoff also succeeded inreversing a bright band of lithium. 

The long-standing difficulty of Fraunhofer's lines fell to pieces inthe presence of facts and reflections like these, which also carriedwith them an immeasurable extension of the chemist's power. Kirchhoffsaw that from the agreement of the lines in the spectra of terrestrialsubstances with Fraunhofer's lines, the presence of these substancesin the sun and fixed stars might be immediately inferred. Thus thedark lines D in the solar spectrum proved the existence of sodium inthe solar atmosphere; while the bright lines discovered by Brewster ina nitre flame, which had been proved to coincide exactly with certaindark lines between A and B in the solar spectrum, proved the existenceof potassium in the sun. 

All subsequent research verified the accuracy of these first daringconclusions. In his second paper, communicated to the Berlin Academybefore the close of 1859, Kirchhoff proved the existence of iron inthe sun. The bright lines of the spectrum of iron vapour areexceedingly numerous, and 65 of them were subsequently proved byKirchhoff to be absolutely identical in position with 65 darkFraunhofer's lines. Ångström and Thalén pushed the coincidences to 450for iron, while, according to the same excellent investigators, thefollowing numbers express the coincidences, in the case of therespective metals to which they are attached:--

Calcium 75Barium 11Magnesium 4Manganese 57Titanium 118Chromium 18Nickel 33Cobalt 19Hydrogen 4Aluminium 2Zinc 2Copper 7

The probability is overwhelming that all these substances exist in theatmosphere of the sun. 

Kirchhoff's discovery profoundly modified the conceptions previouslyentertained regarding the constitution of the sun, leading him toviews which, though they may be modified in detail, will, I believe, remain substantially valid to the end of time. The sun, according toKirchhoff, consists of a molten nucleus which is surrounded by aflaming atmosphere of lower temperature. The nucleus may, in part, be_clouds_, mixed with, or underlying true vapour. The light of thenucleus would give us a continuous spectrum, like that of the Drummondlight; but having to pass through the photosphere, as Kirchhoff's beampassed through the sodium flame, those rays of the nucleus which thephotosphere emit are absorbed, and shaded lines, corresponding to therays absorbed, occur in the spectrum. Abolish the solar nucleus, andwe should have a spectrum showing a bright line in the place of everydark line of Fraunhofer, just as, in the case of Kirchhoff's secondexperiment, we should have the bright sodium lines of the flame if thelime-light were withdrawn. These lines of Fraunhofer are therefore notabsolutely dark, but dark by an amount corresponding to the differencebetween the light intercepted and the light emitted by thephotosphere. 

Almost every great scientific discovery is approachedcontemporaneously by many minds, the fact that one mind usuallyconfers upon it the distinctness of demonstration being anillustration, not of genius isolated, but of genius in advance. ThusFoucault, in 1849, came to the verge of Kirchhoff's discovery. Byconverging an image of the sun upon a voltaic arc, and thus obtainingthe spectra of both sun and arc superposed, he found that the twobright lines which, owing to the presence of a little sodium in thecarbons or in the air, are seen in the spectrum of the arc, coincidewith the dark lines D of the solar spectrum. The lines D he found tohe considerably strengthened by the passage of the solar light throughthe voltaic arc. 

Instead of the image of the sun, Foucault then projected upon the arcthe image of one of the solid incandescent carbon points, which ofitself would give a continuous spectrum; and he found that the lines Dwere thus _generated_ in that spectrum. Foucault's conclusion fromthis admirable experiment was 'that the arc is a medium which emitsthe rays D on its own account, and at the same time absorbs them whenthey come from another quarter. ' Here he stopped. He did not extendhis observations beyond the voltaic arc; he did not offer anyexplanation of the lines of Fraunhofer; he did not arrive at anyconception of solar chemistry, or of the constitution of the sun. Hisbeautiful experiment remained a germ without fruit, until thediscernment, ten years subsequently, of the whole class of phenomenato which it belongs, enabled Kirchhoff to solve these great problems. 

Soon after the publication of Kirchhoff's discovery, Professor Stokes, who also, ten years prior to the discovery, had nearly anticipated it, borrowed an illustration from sound, to explain the reciprocity ofradiation and absorption. A stretched string responds to aërialvibrations which synchronize with its own. A great number of suchstrings stretched in space would roughly represent a medium; and ifthe note common to them all were sounded at a distance they would takeup or absorb its vibrations. 

When a violin-bow is drawn across this tuning-fork, the room isimmediately filled with a musical sound, which may be regarded as the_radiation_ or _emission_ of sound from the fork. A few days ago, onsounding this fork, I noticed that when its vibrations were quenched, the sound seemed to be continued, though more feebly. It appeared, moreover, to come from under a distant table, where stood a number oftuning-forks of different sizes and rates of vibration. One of these, and one only, had been started by the sounding fork, and it was theone whose rate of vibration was the same as that of the fork whichstarted it. This is an instance of the _absorption_ of the sound ofone fork by another. Placing two unisonant forks near each other, sweeping the bow over one of them, and then quenching the agitatedfork, the other continues to sound; this other can re-excite theformer, and several transfers of sound between the two forks can bethus effected. Placing a cent-piece on each prong of one of the forks, we destroy its perfect synchronism with the other, and no suchcommunication of sound from the one to the other is then possible. 

I have now to bring before you, on a suitable scale, the demonstrationthat we can do with _light_ what has been here done with sound. Forseveral days in 1861 I endeavoured to accomplish this, with onlypartial success. In iron dishes a mixture of dilute alcohol and saltwas placed, and warmed so as to promote vaporization. The vapour wasignited, and through the yellow flame thus produced the beam from theelectric lamp was sent; but a faint darkening only of the yellow bandof a projected spectrum could be obtained. A trough was then madewhich, when fed with the salt and alcohol, yielded a flame ten feetthick; but the result of sending the light through this depth of flamewas still unsatisfactory. Remembering that the direct combustion ofsodium in a Bunsen's flame produces a yellow far more intense thanthat of the salt flame, and inferring that the intensity of the colourindicated the copiousness of the incandescent vapour, I sent throughthe flame from metallic sodium the beam of the electric lamp. Thesuccess was complete; and this experiment I wish now to repeat in yourpresence. [25]

Firstly then you notice, when a fragment of sodium is placed in aplatinum spoon and introduced into a Bunsen's flame, an intenselyyellow light is produced. It corresponds in refrangibility with theyellow band of the spectrum. Like our tuning-fork, it emits waves of aspecial period. When the white light from the electric lamp is sentthrough that flame, you will have ocular proof that the yellow flameintercepts the yellow of the spectrum; in other words, that it absorbswaves of the same period as its own, thus producing, to all intentsand purposes, a dark Fraunhofer's band in the place of the yellow. 

In front of the slit (at L, fig. 56) through which the beam issues isplaced a Bunsen's burner (_b_) protected by a chimney (C). This beam, after passing through a lens, traverses the prism (P) (in the realexperiment there was a pair of prisms), is there decomposed, and formsa vivid continuous spectrum (S S) upon the screen. Introducing aplatinum spoon with its pellet of sodium into the Bunsen's flame, thepellet first fuses, colours the flame intensely yellow, and at lengthbursts into violent combustion. At the same moment the spectrum isfurrowed by an intensely dark band (D), two inches wide and two feetlong. Introducing and withdrawing the sodium flame in rapidsuccession, the sudden appearance and disappearance of the band ofdarkness is shown in a most striking manner. In contrast with theadjacent brightness this band appears absolutely black, so vigorous isthe absorption. The blackness, however, is but relative, for upon thedark space falls a portion of the light of the sodium flame. 

[Illustration: Fig. 56. ]

I have already referred to the experiment of Foucault; but otherworkers also had been engaged on the borders of this subject before itwas taken up by Bunsen and Kirchhoff. With some modification I have ona former occasion used the following words regarding the precursors ofthe discovery of spectrum analysis, and solar chemistry:--'Mr. Talbothad observed the bright lines in the spectra of coloured flames, andboth he and Sir John Herschel pointed out the possibility of makingprismatic analysis a chemical test of exceeding delicacy, though notof entire certainty. More than a quarter of a century ago Dr. Millergave drawings and descriptions of the spectra of various colouredflames. Wheatstone, with his accustomed acuteness, analyzed the lightof the electric spark, and proved that the metals between which thespark passed determined the bright bands in its spectrum. In aninvestigation described by Kirchhoff as "classical, " Swan had shownthat 1/2, 500, 000 of a grain of sodium in a Bunsen's flame could bedetected by its spectrum. He also proved the constancy of the brightlines in the spectra of hydrocarbon flames. Masson published a prizeessay on the bands of the induction spark; while Van der Willigen, andmore recently Plücker, have also given us beautiful drawings ofspectra obtained from the same source. 

'But none of these distinguished men betrayed the least knowledge ofthe connexion between the bright bands of the metals and the darklines of the solar spectrum; nor could spectrum analysis be said to beplaced upon anything like a safe foundation prior to the researches ofBunsen and Kirchhoff. The man who, in a published paper, came nearestto the philosophy of the subject was Ångström. In that paper, translated by myself, and published in the "Philosophical Magazine"for 1855, he indicates that the rays which a body absorbs areprecisely those which, when luminous, it can emit. In another place, he speaks of one of his spectra giving the general impression of the_reversal_ of the solar spectrum. But his memoir, philosophical as itis, is distinctly marked by the uncertainty of his time. Foucault, Thomson, and Balfour Stewart have all been near the discovery, while, as already stated, it was almost hit by the acute but unpublishedconjecture of Stokes. '

Mentally, as well as physically, every year of the world's age is theoutgrowth and offspring of all preceding years. Science proves itselfto be a genuine product of Nature by growing according to this law. Wehave no solution of continuity here. All great discoveries are dulyprepared for in two ways; first, by other discoveries which form theirprelude; and, secondly, by the sharpening of the inquiring intellect. Thus Ptolemy grew out of Hipparchus, Copernicus out of both, Keplerout of all three, and Newton out of all the four. Newton did not risesuddenly from the sea-level of the intellect to his amazing elevation. At the time that he appeared, the table-land of knowledge was alreadyhigh. He juts, it is true, above the table-land, as a massive peak;still he is supported by the plateau, and a great part of his absoluteheight is the height of humanity in his time. It is thus with thediscoveries of Kirchhoff. Much had been previously accomplished; thishe mastered, and then by the force of individual genius went beyondit. He replaced uncertainty by certainty, vagueness by definiteness, confusion by order; and I do not think that Newton has a surer claimto the discoveries that have made his name immortal, than Kirchhoffhas to the credit of gathering up the fragmentary knowledge of histime, of vastly extending it, and of infusing into it the life ofgreat principles. 

With one additional point we will wind up our illustrations of theprinciples of solar chemistry. Owing to the scattering of light bymatter floating mechanically in the earth's atmosphere, the sun isseen not sharply defined, but surrounded by a luminous glare. Now, aloud noise will drown a whisper, an intense light will overpower afeeble one, and so this circumsolar glare prevents us from seeing manystriking appearances round the border of the sun. The glare isabolished in total eclipses, when the moon comes between the earth andthe sun, and there are then seen a series of rose-colouredprotuberances, stretching sometimes tens of thousands of miles beyondthe dark edge of the moon. They are described by Vassenius in the'Philosophical Transactions' for 1733; and were probably observed evenearlier than this. In 1842 they attracted great attention, and werethen compared to Alpine snow-peaks reddened by the evening sun. Thatthese prominences are flaming gas, and principally hydrogen gas, wasfirst proved by M. Janssen during an eclipse observed in India, on the18th of August, 1868. 

But the prominences may be rendered visible in sunshine; and for areason easily understood. You have seen in these lectures a singleprism employed to produce a spectrum, and you have seen a pair ofprisms employed. In the latter case, the dispersed white light, beingdiffused over about twice the area, had all its coloursproportionately diluted. You have also seen one prism and a pair ofprisms employed to produce the bands of incandescent vapours; but herethe light of each band, being absolutely monochromatic, was incapableof further dispersion by the second prism, and could not therefore beweakened by such dispersion. 

Apply these considerations to the circumsolar region. The glare ofwhite light round the sun can be dispersed and weakened to any extent, by augmenting the number of prisms; while a monochromatic light, mixed with this glare, and masked by it, would retain its intensityunenfeebled by dispersion. Upon this consideration has been founded amethod of observation, applied independently by M. Janssen in Indiaand by Mr. Lockyer in England, by which the monochromatic bands of theprominences are caused to obtain the mastery, and to appear in broaddaylight. By searching carefully and skilfully round the sun's rim, Mr. Lockyer has proved these prominences to be mere local juttingsfrom a fiery envelope which entirely clasps the sun, and which he hascalled the _Chromosphere_. 

It would lead us far beyond the object of these lectures to dwell uponthe numerous interesting and important results obtained by Secchi, Respighi, Young, and other distinguished men who have worked at thechemistry of the sun and its appendages. Nor can I do more at presentthan make a passing reference to the excellent labours of Dr. Hugginsin connexion with the fixed stars, nebulae, and comets. They, morethan any others, illustrate the literal truth of the statement, thatthe establishment of spectrum analysis, and the explanation ofFraunhofer's lines, carried with them an immeasurable extension of thechemist's range. The truly powerful experiments of Professor Dewar aredaily adding to our knowledge, while the refined researches of Capt. Abney and others are opening new fields of inquiry. But my object hereis to make principles plain, rather than to follow out the details oftheir illustration. 

SUMMARY AND CONCLUSION. 

My desire in these lectures has been to show you, with as littlebreach of continuity as possible, something of the past growth andpresent aspect of a department of science, in which have laboured someof the greatest intellects the world has ever seen. I have sought toconfer upon each experiment a distinct intellectual value, forexperiments ought to be the representatives and expositors ofthought--a language addressed to the eye as spoken words are to theear. In association with its context, nothing is more impressive orinstructive than a fit experiment; but, apart from its context, itrather suits the conjurer's purpose of surprise, than the purpose ofeducation which ought to be the ruling motive of the scientific man. 

And now a brief summary of our work will not be out of place. Ourpresent mastery over the laws and phenomena of light has its origin inthe desire of man to _know_. We have seen the ancients busy with thisproblem, but, like a child who uses his arms aimlessly, for want ofthe necessary muscular training, so these early men speculated vaguelyand confusedly regarding natural phenomena, not having had thediscipline needed to give clearness to their insight, and firmness totheir grasp of principles. They assured themselves of the rectilinealpropagation of light, and that the angle of incidence was equal to theangle of reflection. For more than a thousand years--I might say, indeed, for more than fifteen hundred years--the scientific intellectappears as if smitten with paralysis, the fact being that, during thistime, the mental force, which might have run in the direction ofscience, was diverted into other directions. 

The course of investigation, as regards light, was resumed in 1100 byan Arabian philosopher named Alhazen. Then it was taken up insuccession by Roger Bacon, Vitellio, and Kepler. These men, thoughfailing to detect the principles which ruled the facts, kept the fireof investigation constantly burning. Then came the fundamentaldiscovery of Snell, that cornerstone of optics, as I have alreadycalled it, and immediately afterwards we have the application, byDescartes, of Snell's discovery to the explanation of the rainbow. Following this we have the overthrow, by Roemer, of the notion ofDescartes, that light was transmitted instantaneously through space. Then came Newton's crowning experiments on the analysis and synthesisof white light, by which it was proved to be compounded of variouskinds of light of different degrees of refrangibility. 

Up to his demonstration of the composition of white light, Newton hadbeen everywhere triumphant--triumphant in the heavens, triumphant onthe earth, and his subsequent experimental work is, for the most part, of immortal value. But infallibility is not an attribute of man, and, soon after his discovery of the nature of white light, Newton provedhimself human. He supposed that refraction and chromatic dispersionwent hand in hand, and that you could not abolish the one without atthe same time abolishing the other. Here Dollond corrected him. 

But Newton committed a graver error than this. Science, as I sought tomake clear to you in our second lecture, is only in part a thing ofthe senses. The roots of phenomena are embedded in a region beyond thereach of the senses, and less than the root of the matter will neversatisfy the scientific mind. We find, accordingly, in this career ofoptics the greatest minds constantly yearning to break the bounds ofthe senses, and to trace phenomena to their subsensible foundation. Thus impelled, they entered the region of theory, and here Newton, though drawn from time to time towards truth, was drawn still morestrongly towards error; and he made error his substantial choice. Hisexperiments are imperishable, but his theory has passed away. For acentury it stood like a dam across the course of discovery; but, aswith all barriers that rest upon authority, and not upon truth, thepressure from behind increased, and eventually swept the barrier away. 

In 1808 Malus, looking through Iceland spar at the sun, reflected fromthe window of the Luxembourg Palace in Paris, discovered thepolarization of light by reflection. As stated at the time, thisdiscovery ushered in the darkest hour in the fortunes of the wavetheory. But the darkness did not continue. In 1811 Arago discoveredthe splendid chromatic phenomena which we have had illustrated by thedeportment of plates of gypsum in polarized light; he also discoveredthe rotation of the plane of polarization by quartz-crystals. In 1813Seebeck discovered the polarization of light by tourmaline. That sameyear Brewster discovered those magnificent bands of colour thatsurround the axes of biaxal crystals. In 1814 Wollaston discovered therings of Iceland spar. All these effects, which, without a theoreticclue, would leave the human mind in a jungle of phenomena withoutharmony or relation, were organically connected by the theory ofundulation. 

The wave theory was applied and verified in all directions, Airy beingespecially conspicuous for the severity and conclusiveness of hisproofs. A most remarkable verification fell to the lot of the late SirWilliam Hamilton, of Dublin, who, taking up the theory where Fresnelhad left it, arrived at the conclusion that at four special points ofthe 'wave-surface' in double-refracting crystals, the ray was divided, not into two parts but into an infinite number of parts; forming atthese points a continuous conical envelope instead of two images. Nohuman eye had ever seen this envelope when Sir William Hamiltoninferred its existence. He asked Dr. Lloyd to test experimentally thetruth of his theoretic conclusion. Lloyd, taking a crystal ofarragonite, and following with the most scrupulous exactness theindications of theory, cutting the crystal where theory said it oughtto be cut, observing it where theory said it ought to be observed, discovered the luminous envelope which had previously been a mere ideain the mind of the mathematician. 

Nevertheless this great theory of undulation, like many another truth, which in the long run has proved a blessing to humanity, had toestablish, by hot conflict, its right to existence. Illustrious nameswere arrayed against it. It had been enunciated by Hooke, it had beenexpounded and applied by Huyghens, it had been defended by Euler. Butthey made no impression. And, indeed, the theory in their hands lackedthe strength of a demonstration. It first took the form of ademonstrated verity in the hands of Thomas Young. He brought the wavesof light to bear upon each other, causing them to support each other, and to extinguish each other at will. From their mutual actions hedetermined their lengths, and applied his knowledge in all directions. He finally showed that the difficulty of polarization yielded to thegrasp of theory. 

After him came Fresnel, whose transcendent mathematical abilitiesenabled him to give the theory a generality unattained by Young. Heseized it in its entirety; followed the ether into the hearts ofcrystals of the most complicated structure, and into bodies subjectedto strain and pressure. He showed that the facts discovered by Malus, Arago, Brewster, and Biot were so many ganglia, so to speak, of histheoretic organism, deriving from it sustenance and explanation. Witha mind too strong for the body with which it was associated, that bodybecame a wreck long before it had become old, and Fresnel died, leaving, however, behind him a name immortal in the annals of science. 

One word more I should like to say regarding Fresnel. There are thingsbetter even than science. Character is higher than Intellect, but itis especially pleasant to those who wish to think well of human naturewhen high intellect and upright character are found combined. Theywere combined in this young Frenchman. In those hot conflicts of theundulatory theory, he stood forth as a man of integrity, claiming nomore than his right, and ready to concede their rights to others. Heat once recognized and acknowledged the merits of Thomas Young. Indeed, it was he, and his fellow-countryman Arago, who first startledEngland into the consciousness of the injustice done to Young in the'Edinburgh Review. '

I should like to read to you a brief extract from a letter written byFresnel to Young in 1824, as it throws a pleasant light upon thecharacter of the French philosopher. 'For a long time, ' says Fresnel, 'that sensibility, or that vanity, which people call love of glory hasbeen much blunted in me. I labour much less to catch the suffrages ofthe public, than to obtain that inward approval which has always beenthe sweetest reward of my efforts. Without doubt, in moments ofdisgust and discouragement, I have often needed the spur of vanity toexcite me to pursue my researches. But all the compliments I havereceived from Arago, De la Place, and Biot never gave me so muchpleasure as the discovery of a theoretic truth or the confirmation ofa calculation by experiment. '

 * * * * *

This, then, is the core of the whole matter as regards science. Itmust be cultivated for its own sake, for the pure love of truth, rather than for the applause or profit that it brings. And now myoccupation in America is well-nigh gone. Still I will bespeak yourtolerance for a few concluding remarks, in reference to the men whohave bequeathed to us the vast body of knowledge of which I havesought to give you some faint idea in these lectures. What was themotive that spurred them on? What urged them to those battles andthose victories over reticent Nature, which have become the heritageof the human race? It is never to be forgotten that not one of thosegreat investigators, from Aristotle down to Stokes and Kirchhoff, hadany practical end in view, according to the ordinary definition of theword 'practical. ' They did not propose to themselves money as an end, and knowledge as a means of obtaining it. For the most part, theynobly reversed this process, made knowledge their end, and such moneyas they possessed the means of obtaining it. 

We see to-day the issues of their work in a thousand practical forms, and this may be thought sufficient to justify, if not ennoble, theirefforts. But they did not work for such issues; their reward was of atotally different kind. In what way different? We love clothes, welove luxuries, we love fine equipages, we love money, and any man whocan point to these as the result of his efforts in life, justifiesthese results before all the world. In America and England, moreespecially, he is a 'practical' man. But I would appeal confidently tothis assembly whether such things exhaust the demands of human nature?The very presence here for six inclement nights of this greataudience, embodying so much of the mental force and refinement of thisvast city, [26] is an answer to my question. I need not tell such anassembly that there are joys of the intellect as well as joys of thebody, or that these pleasures of the spirit constituted the reward ofour great investigators. Led on by the whisperings of natural truth, through pain and self-denial, they often pursued their work. With theruling passion strong in death, some of them, when no longer able tohold a pen, dictated to their friends the last results of theirlabours, and then rested from them for ever. 

Could we have seen these men at work, without any knowledge of theconsequences of their work, what should we have thought of them? Tothe uninitiated, in their day, they might often appear as big childrenplaying with soap-bubbles and other trifles. It is so to this hour. Could you watch the true investigator--your Henry or your Draper, forexample--in his laboratory, unless animated by his spirit, you couldhardly understand what keeps him there. Many of the objects whichrivet his attention might appear to you utterly trivial; and if youwere to ask him what is the _use_ of his work, the chances are thatyou would confound him. He might not be able to express the use of itin intelligible terms. He might not be able to assure you that it willput a dollar into the pocket of any human being present or to come. That scientific discovery _may_ put not only dollars into the pocketsof individuals, but millions into the exchequers of nations, thehistory of science amply proves; but the hope of its doing so neverwas, and it never can be, the motive power of the investigator. 

I know that some risk is run in speaking thus before practical men. Iknow what De Tocqueville says of you. 'The man of the North, ' he says, 'has not only experience, but knowledge. He, however, does not carefor science as a pleasure, and only embraces it with avidity when itleads to useful applications. ' But what, I would ask, are the hopes ofuseful applications which have caused you so many times to fill thisplace, in spite of snow-drifts and biting cold? What, I may ask, isthe origin of that kindness which drew me from my work in London toaddress you here, and which, if I permitted it, would send me home amillionaire? Not because I had taught you to make a single cent byscience am I here to-night, but because I tried to the best of myability to present science to the world as an intellectual good. Surely no two terms were ever so distorted and misapplied withreference to man, in his higher relations, as these terms useful andpractical. Let us expand our definitions until they embrace all theneeds of man, his highest intellectual needs inclusive. It isspecially on this ground of its administering to the higher needs ofthe intellect; it is mainly because I believe it to be wholesome, notonly as a source of knowledge but as a means of discipline, that Iurge the claims of science upon your attention. 

But with reference to material needs and joys, surely pure science hasalso a word to say. People sometimes speak as if steam had not beenstudied before James Watt, or electricity before Wheatstone and Morse;whereas, in point of fact, Watt and Wheatstone and Morse, with alltheir practicality, were the mere outcome of antecedent forces, whichacted without reference to practical ends. This also, I think, meritsa moment's attention. You are delighted, and with good reason, withyour electric telegraphs, proud of your steam-engines and yourfactories, and charmed with the productions of photography. You seedaily, with just elation, the creation of new forms of industry--newpowers of adding to the wealth and comfort of society. IndustrialEngland is heaving with forces tending to this end; and the pulse ofindustry beats still stronger in the United States. And yet, whenanalyzed, what are industrial America and industrial England?

If you can tolerate freedom of speech on my part, I will answer thisquestion by an illustration. Strip a strong arm, and regard theknotted muscles when the hand is clenched and the arm bent. Is thisexhibition of energy the work of the muscle alone? By no means. Themuscle is the channel of an influence, without which it would be aspowerless as a lump of plastic dough. It is the delicate unseen nervethat unlocks the power of the muscle. And without those filaments ofgenius, which have been shot like nerves through the body of societyby the original discoverer, industrial America, and industrialEngland, would be very much in the condition of that plastic dough. 

At the present time there is a cry in England for technical education, and it is a cry in which the most commonplace intellect can join, itsnecessity is so obvious. But there is no such cry for originalinvestigation. Still, without this, as surely as the stream dwindleswhen the spring dies, so surely will 'technical education' lose allforce of growth, all power of reproduction. Our great investigatorshave given us sufficient work for a time; but if their spirit die out, we shall find ourselves eventually in the condition of those Chinesementioned by De Tocqueville, who, having forgotten the scientificorigin of what they did, were at length compelled to copy withoutvariation the inventions of an ancestry wiser than themselves, who haddrawn their inspiration direct from Nature. 

Both England and America have reason to bear those things in mind, forthe largeness and nearness of material results are only too likely tocause both countries to forget the small spiritual beginnings of suchresults, in the mind of the scientific discoverer. You multiply, buthe creates. And if you starve him, or otherwise kill him--nay, if youfail to secure for him free scope and encouragement--you not only losethe motive power of intellectual progress, but infallibly severyourselves from the springs of industrial life. 

What has been said of technical operations holds equally good foreducation, for here also the original investigator constitutes thefountain-head of knowledge. It belongs to the teacher to give thisknowledge the requisite form; an honourable and often a difficulttask. But it is a task which receives its final sanctification, whenthe teacher himself honestly tries to add a rill to the great streamof scientific discovery. Indeed, it may be doubted whether the reallife of science can be fully felt and communicated by the man who hasnot himself been taught by direct communion with Nature. We may, it istrue, have good and instructive lectures from men of ability, thewhole of whose knowledge is second-hand, just as we may have good andinstructive sermons from intellectually able and unregenerate men. Butfor that power of science, which corresponds to what the Puritanfathers would call experimental religion in the heart, you must ascendto the original investigator. 

To keep society as regards science in healthy play, three classes ofworkers are necessary: Firstly, the investigator of natural truth, whose vocation it is to pursue that truth, and extend the field ofdiscovery for the truth's own sake and without reference to practicalends. Secondly, the teacher of natural truth, whose vocation it is togive public diffusion to the knowledge already won by the discoverer. Thirdly, the applier of natural truth, whose vocation it is to makescientific knowledge available for the needs, comforts, and luxuriesof civilized life. These three classes ought to co-exist and interact. Now, the popular notion of science, both in this country and inEngland, often relates not to science strictly so called, but to theapplications of science. Such applications, especially on thiscontinent, are so astounding--they spread themselves so largely andumbrageously before the public eye--that they often shut out from viewthose workers who are engaged in the quieter and profounder businessof original investigation. 

Take the electric telegraph as an example, which has been repeatedlyforced upon my attention of late. I am not here to attenuate in theslightest degree the services of those who, in England and America, have given the telegraph a form so wonderfully fitted for public use. They earned a great reward, and they have received it. But I should beuntrue to you and to myself if I failed to tell you that, however highin particular respects their claims and qualities may be, yourpractical men did not discover the electric telegraph. The discoveryof the electric telegraph implies the discovery of electricity itself, and the development of its laws and phenomena. Such discoveries arenot made by practical men, and they never will be made by them, because their minds are beset by ideas which, though of the highestvalue from one point of view, are not those which stimulate theoriginal discoverer. 

The ancients discovered the electricity of amber; and Gilbert, in theyear 1600, extended the discovery to other bodies. Then followedBoyle, Von Guericke, Gray, Canton, Du Fay, Kleist, Cunæus, and yourown Franklin. But their form of electricity, though tried, did notcome into use for telegraphic purposes. Then appeared the greatItalian Volta, who discovered the source of electricity which bearshis name, and applied the most profound insight, and the most delicateexperimental skill to its development. Then arose the man who added tothe powers of his intellect all the graces of the human heart, MichaelFaraday, the discoverer of the great domain of magneto-electricity. OErsted discovered the deflection of the magnetic needle, and Arago andSturgeon the magnetization of iron by the electric current. Thevoltaic circuit finally found its theoretic Newton in Ohm; whileHenry, of Princeton, who had the sagacity to recognize the merits ofOhm while they were still decried in his own country, was at this timein the van of experimental inquiry. 

In the works of these men you have all the materials employed at thishour, in all the forms of the electric telegraph. Nay, more; Gauss, the illustrious astronomer, and Weber, the illustrious naturalphilosopher, both professors in the University of Göttingen, wishingto establish a rapid mode of communication between the observatory andthe physical cabinet of the university, did this by means of anelectric telegraph. Thus, before your practical men appeared upon thescene, the force had been discovered, its laws investigated and madesure, the most complete mastery of its phenomena had beenattained--nay, its applicability to telegraphic purposesdemonstrated--by men whose sole reward for their labours was the nobleexcitement of research, and the joy attendant on the discovery ofnatural truth. 

Are we to ignore all this? We do so at our peril. For I say againthat, behind all our practical applications, there is a region ofintellectual action to which practical men have rarely contributed, but from which they draw all their supplies. Cut them off from thisregion, and they become eventually helpless. In no case is the adagetruer, 'Other men laboured, but ye are entered into their labours, 'than in the case of the discoverer and applier of natural truth. Butnow a word on the other side. While practical men are not the men tomake the necessary antecedent discoveries, the cases are rare, though, in our day, not absent, in which the discoverer knows how to turn hislabours to practical account. Different qualities of mind and habitsof thought are usually needed in the two cases; and while I wish togive emphatic utterance to the claims of those whose position, owingto the simple fact of their intellectual elevation, is oftenmisunderstood, I am not here to exalt the one class of workers at theexpense of the other. They are the necessary complements of eachother. But remember that one class is sure to be taken care of. Allthe material rewards of society are already within their reach, whilethat same society habitually ascribes to them intellectualachievements which were never theirs. This cannot but act to thedetriment of those studies out of which, not only our knowledge ofnature, but our present industrial arts themselves, have sprung, andfrom which the rising genius of the country is incessantly temptedaway. 

Pasteur, one of the most illustrious members of the Institute ofFrance, in accounting for the disastrous overthrow of his country, and the predominance of Germany in the late war, expresses himselfthus: 'Few persons comprehend the real origin of the marvels ofindustry and the wealth of nations. I need no further proof of thisthan the employment, more and more frequent, in official language, andin writings of all sorts, of the erroneous expression _appliedscience_. The abandonment of scientific careers by men capable ofpursuing them with distinction, was recently deplored in the presenceof a minister of the greatest talent. The statesman endeavoured toshow that we ought not to be surprised at this result, because _in ourday the reign of theoretic science yielded place to that of appliedscience_. Nothing could be more erroneous than this opinion, nothing, I venture to say, more dangerous, even to practical life, than theconsequences which might flow from these words. They have rested in mymind as a proof of the imperious necessity of reform in our superioreducation. There exists no category of the sciences, to which the nameof applied science could be rightly given. _We have science, and theapplications of science_, which are united together as the tree andits fruit. '

And Cuvier, the great comparative anatomist, writes thus upon the sametheme: 'These grand practical innovations are the mere applications oftruths of a higher order, not sought with a practical intent, butpursued for their own sake, and solely through an ardour forknowledge. Those who applied them could not have discovered them; butthose who discovered them had no inclination to pursue them to apractical end. Engaged in the high regions whither their thoughts hadcarried them, they hardly perceived these practical issues thoughborn of their own deeds. These rising workshops, these peopledcolonies, those ships which furrow the seas--this abundance, thisluxury, this tumult--all this comes from discoveries in science, andit all remains strange to the discoverers. At the point where sciencemerges into practice they abandon it; it concerns them no more. '

When the Pilgrim Fathers landed at Plymouth Rock, and when Penn madehis treaty with the Indians, the new-comers had to build their houses, to cultivate the earth, and to take care of their souls. In such acommunity science, in its more abstract forms, was not to be thoughtof. And at the present hour, when your hardy Western pioneers standface to face with stubborn Nature, piercing the mountains and subduingthe forest and the prairie, the pursuit of science, for its own sake, is not to be expected. The first need of man is food and shelter; buta vast portion of this continent is already raised far beyond thisneed. The gentlemen of New York, Brooklyn, Boston, Philadelphia, Baltimore, and Washington have already built their houses, and verybeautiful they are; they have also secured their dinners, to theexcellence of which I can also bear testimony. They have, in fact, reached that precise condition of well-being and independence when aculture, as high as humanity has yet reached, may be justly demandedat their hands. They have reached that maturity, as possessors ofwealth and leisure, when the investigator of natural truth, for thetruth's own sake, ought to find among them promoters and protectors. 

Among the many problems before them they have this to solve, whethera republic is able to foster the highest forms of genius. You arefamiliar with the writings of De Tocqueville, and must be aware of theintense sympathy which he felt for your institutions; and thissympathy is all the more valuable from the philosophic candour withwhich he points out not only your merits, but your defects anddangers. Now if I come here to speak of science in America in acritical and captious spirit, an invisible radiation from my words andmanner will enable you to find me out, and will guide your treatmentof me to-night. But if I in no unfriendly spirit--in a spirit, indeed, the reverse of unfriendly--venture to repeat before you what thisgreat historian and analyst of democratic institutions said ofAmerica, I am persuaded that you will hear me out. He wrote some threeand twenty years ago, and, perhaps, would not write the same to-day;but it will do nobody any harm to have his words repeated, and, ifnecessary, laid to heart. 

In a work published in 1850, De Tocqueville says: 'It must beconfessed that, among the civilized peoples of our age, there are fewin which the highest sciences have made so little progress as in theUnited States. '[27] He declares his conviction that, had you beenalone in the universe, you would soon have discovered that you cannotlong make progress in practical science without cultivating theoreticscience at the same time. But, according to De Tocqueville, you arenot thus alone. He refuses to separate America from its ancestralhome; and it is there, he contends, that you collect the treasures ofthe intellect, without taking the trouble to create them. 

De Tocqueville evidently doubts the capacity of a democracy to fostergenius as it was fostered in the ancient aristocracies. 'The future, 'he says, 'will prove whether the passion for profound knowledge, sorare and so fruitful, can be born and developed as readily indemocratic societies as in aristocracies. For my part, ' he continues, 'I can hardly believe it. ' He speaks of the unquiet feverishness ofdemocratic communities, not in times of great excitement, for suchtimes may give an extraordinary impetus to ideas, but in times ofpeace. There is then, he says, 'a small and uncomfortable agitation, asort of incessant attrition of man against man, which troubles anddistracts the mind without imparting to it either loftiness oranimation. ' It rests with you to prove whether these things arenecessarily so--whether scientific genius cannot find, in the midst ofyou, a tranquil home. 

I should be loth to gainsay so keen an observer and so profound apolitical writer, but, since my arrival in this country, I have beenunable to see anything in the constitution of society, to prevent astudent, with the root of the matter in him, from bestowing the moststeadfast devotion on pure science. If great scientific results arenot achieved in America, it is not to the small agitations of societythat I should be disposed to ascribe the defect, but to the fact thatthe men among you who possess the endowments necessary for profoundscientific inquiry, are laden with duties of administration, ortuition, so heavy as to be utterly incompatible with the continuousand tranquil meditation which original investigation demands. It maywell be asked whether Henry would have been transformed into anadministrator, or whether Draper would have forsaken science to writehistory, if the original investigator had been honoured as he ought tobe in this land. I hardly think they would. Still I do not imaginethis state of things likely to last. In America there is a willingnesson the part of individuals to devote their fortunes, in the matter ofeducation, to the service of the commonwealth, which is probablywithout a parallel elsewhere; and this willingness requires but wisedirection to enable you effectually to wipe away the reproach of DeTocqueville. 

Your most difficult problem will be, not to build institutions, but todiscover men. You may erect laboratories and endow them; you mayfurnish them with all the appliances needed for inquiry; in so doingyou are but creating opportunity for the exercise of powers which comefrom sources entirely beyond your reach. You cannot create genius bybidding for it. In biblical language, it is the gift of God; and themost you could do, were your wealth, and your willingness to apply it, a million-fold what they are, would be to make sure that this gloriousplant shall have the freedom, light, and warmth necessary for itsdevelopment. We see from time to time a noble tree dragged down byparasitic runners. These the gardener can remove, though the vitalforce of the tree itself may lie beyond him: and so, in many a caseyou men of wealth can liberate genius from the hampering toils whichthe struggle for existence often casts around it. 

Drawn by your kindness, I have come here to give these lectures, andnow that my visit to America has become almost a thing of the past, Ilook back upon it as a memory without a single stain. No lecturer wasever rewarded as I have been. From this vantage-ground, however, letme remind you that the work of the lecturer is not the highest work;that in science, the lecturer is usually the distributor ofintellectual wealth amassed by better men. And though lecturing andteaching, in moderation, will in general promote their moral health, it is not solely or even chiefly, as lecturers, but as investigators, that your highest men ought to be employed. You have scientific geniusamongst you--not sown broadcast, believe me, it is sown thusnowhere--but still scattered here and there. Take all unnecessaryimpediments out of its way. Keep your sympathetic eye upon theoriginator of knowledge. Give him the freedom necessary for hisresearches, not overloading him, either with the duties of tuition orof administration, nor demanding from him so-called practicalresults--above all things, avoiding that question which ignorance sooften addresses to genius: 'What is the use of your work?' Let himmake truth his object, however unpractical for the time being it mayappear. If you cast your bread thus upon the waters, be assured itwill return to you, though it be after many days. 

APPENDIX. 

ON THE SPECTRA OF POLARIZED LIGHT. 

Mr. William Spottiswoode introduced some years ago to the members ofthe Royal Institution, in a very striking form, a series ofexperiments on the spectra of polarized light. With his large Nicolprisms he in the first place repeated and explained the experiments ofFoucault and Fizeau, and subsequently enriched the subject by verybeautiful additions of his own. I here append a portion of theabstract of his discourse:--

 'It is well known that if a plate of selenite sufficiently thin be placed between two Nicol's prisms, or, more technically speaking, between a polarizer and analyzer, colour will be produced. And the question proposed is, What is the nature of that colour? is it simply a pure colour of the spectrum, or is it a compound, and if so, what are its component parts? The answer given by the wave theory is in brief this: In its passage through the selenite plate the rays have been so separated in the direction of their vibrations and in the velocity of their transmission, that, when re-compounded by means of the analyzer, they have in some instances neutralized one another. If this be the case, the fact ought to be visible when the beam emerging from the analyzer is dispersed by the prism; for then we have the rays of all the different colours ranged side by side, and, if any be wanting, their absence will be shown by the appearance of a dark band in their place in the spectrum. But not only so; the spectrum ought also to give an account of the other phenomena exhibited by the selenite when the analyzer is turned round, viz. That when the angle of turning amounts to 45°, all trace of colour disappears; and also that when the angle amounts to 90°, colour reappears, not, however, the original colour, but one complementary to it. 

 'You see in the spectrum of the reddish light produced by the selenite a broad but dark band in the blue; when the analyzer is turned round the band becomes less and less dark, until when the angle of turning amounts to 45° it has entirely disappeared. At this stage each part of the spectrum has its own proportional intensity, and the whole produces the colourless image seen without the spectroscope. Lastly, as the turning of the analyzer is continued, a dark band appears in the red, the part of the spectrum complementary to that occupied by the first band; and the darkness is most complete when the turning amounts to 90°. Thus we have from the spectroscope a complete account of what has taken place to produce the original colour and its changes. 

 'It is further well known that the colour produced by a selenite, or other crystal plate, is dependent upon the thickness of the plate. And, in fact, if a series of plates be taken, giving different colours, their spectra are found to show bands arranged in different positions. The thinner plates show bands in the parts of the spectrum nearest to the violet, where the waves are shorter, and consequently give rise to redder colours; while the thicker show bands nearer to the red, where the waves are longer and consequently supply bluer tints. 

 'When the thickness of the plate is continually increased, so that the colour produced has gone through the complete cycle of the spectrum, a further increase of thickness causes a reproduction of the colours in the same order; but it will be noticed that at each recurrence of the cycle the tints become paler, until when a number of cycles have been performed, and the thickness of the plate is considerable, all trace of colour is lost. Let us now take a series of plates, the first two of which, as you see, give colours; with the others which are successively of greater thickness the tints are so feeble that they can scarcely be distinguished. The spectrum of the first shows a single band; that of the second, two; showing that the second series of tints is not identical with the first, but that it is produced by the extinction of two colours from the components of white light. The spectra of the others show series of bands more and more numerous in proportion to the thickness of the plate, an array which may be increased indefinitely. The total light, then, of which the spectrum is deprived by the thicker plates is taken from a greater number of its parts; or, in other words, the light which still remains is distributed more and more evenly over the spectrum; and in the same proportion the sum total of it approaches more and more nearly to white light. 

 'These experiments were made more than thirty years ago by the French philosophers, MM. Foucault and Fizeau. 

 'If instead of selenite, Iceland spar, or other ordinary crystals, we use plates of quartz cut perpendicularly to the axis, and turn the analyzer round as before, the light, instead of exhibiting only one colour and its complementary with an intermediate stage in which colour is absent, changes continuously in tint; and the order of the colour depends partly upon the direction in which the analyzer is turned, and partly upon the character of the crystal, _i. E. _ whether it is right-handed or left-handed. If we examine the spectrum in this case we find that the dark band never disappears, but marches from one end of the spectrum to another, or _vice versâ_, precisely in such a direction as to give rise to the tints seen by direct projection. 

 'The kind of polarization effected by the quartz plates is called circular, while that effected by the other class of crystals is called plane, on account of the form of the vibrations executed by the molecules of æther; and this leads us to examine a little more closely the nature of the polarization of different parts of these spectra of polarized light. 

 'Now, two things are clear: first, that if the light be plane-polarized--that is, if all the vibrations throughout the entire ray are rectilinear and in one plane--they must in all their bearings have reference to a particular direction in space, so that they will be differently affected by different positions of the analyzer. Secondly, that if the vibrations be circular, they will be affected in precisely the same way (whatever that may be) in all positions of the analyzer. This statement merely recapitulates a fundamental point in polarization. In fact, plane-polarized light is alternately transmitted and extinguished by the analyzer as it is turned through 90°; while circularly polarized light [if we could get a single ray] remains to all appearance unchanged. And if we examine carefully the spectrum of light which has passed through a selenite, or other ordinary crystal, we shall find that, commencing with two consecutive bands in position, the parts occupied by the bands and those midway between them are plane-polarized, for they become alternately dark and bright; while the intermediate parts, _i. E. _ the parts at one-fourth of the distance from one band to the next, remain permanently bright. These are, in fact, circularly polarized. But it would be incorrect to conclude from this experiment alone that such is really the case, because the same appearance would be seen if those parts were unpolarized, _i. E. _ in the condition of ordinary lights. And on such a supposition we should conclude with equal justice that the parts on either side of the parts last mentioned (e. G. The parts separated by eighth parts of the interval between two bands) were partially polarized. But there is an instrument of very simple construction, called a "quarter-undulation plate, " a plate usually of mica, whose thickness is an odd multiple of a quarter of a wave-length, which enables us to discriminate between light unpolarized and circularly polarized. The exact mechanical effect produced upon the ray could hardly be explained in detail within our present limits of time; but suffice it for the present to say that, when placed in a proper position, the plate transforms plane into circular and circular into plane polarization. That being so, the parts which were originally banded ought to remain bright, and those which originally remained bright ought to become banded during the rotation of the analyzer. The general effect to the eye will consequently be a general shifting of the bands through one-fourth of the space which separates each pair. 

 'Circular polarization, like circular motion generally, may of course be of two kinds, which differ only in the direction of the motion. And, in fact, to convert the circular polarization produced by this plate from one of these kinds to the other (say from right-handed to left-handed, or _vice versâ_), we have only to turn the plate round through 90°. Conversely, right-handed circular polarization will be changed by the plate into plane-polarization in one direction, while left-handed will be changed into plane at right angles to the first. Hence if the plate be turned round through 90° we shall see that the bands are shifted in a direction opposite to that in which they were moved at first. In this therefore we have evidence not only that the polarization immediately on either side of a band is circular; but also that that immediately on the one side is right-handed, while that immediately on the other is left-handed[28]. 

 'If time permitted, I might enter still further into detail, and show that the polarization between the plane and the circular is elliptical, and even the positions of the longer and shorter axes and the direction of motion in each case. But sufficient has, perhaps, been said for our present purpose. 

 'Before proceeding to the more varied forms of spectral bands, which I hope presently to bring under your notice, I should like to ask your attention for a few minutes to the peculiar phenomena exhibited when two plates of selenite giving complementary colours are used. The appearance of the spectrum varies with the relative position of the plates. If they are similarly placed--that is, as if they were one plate of crystal--they will behave as a single plate, whose thickness is the sum of the thicknesses of each, and will produce double the number of bands which one alone would give; and when the analyzer is turned, the bands will disappear and re-appear in their complementary positions, as usual in the case of plane-polarization. If one of them be turned round through 45°, a single band will be seen at a particular position in the spectrum. This breaks into two, which recede from one another towards the red and violet ends respectively, or advance towards one another according to the direction in which the analyzer is turned. If the plate be turned through 45° in the opposite direction, the effects will be reversed. The darkness of the bands is, however, not equally complete during their whole passage. Lastly, if one of the plates be turned through 90°, no bands will be seen, and the spectrum will be alternately bright and dark, as if no plates were used, except only that the polarization is itself turned through 90°. 

 'If a wedge-shaped crystal be used, the bands, instead of being straight, will cross the spectrum diagonally, the direction of the diagonal (dexter or sinister) being determined by the position of the thicker end of the wedge. If two similar wedges be used with their thickest ends together, they will act as a wedge whose angle and whose thickness is double of the first. If they be placed in the reverse position they will act as a flat plate, and the bands will again cross the spectrum in straight lines at right angles to its length. 

 'If a concave plate be used the bands will dispose themselves in a fanlike arrangement, their divergence depending upon the distance of the slit from the centre of concavity. 

 'If two quartz wedges, one of which has the optic axis parallel to the edge of the refractory angle, and the other perpendicular to it, but in one of the planes containing the angle (Babinet's Compensator), the appearances of the bands are very various. 

 'The diagonal bands, besides sometimes doubling themselves as with ordinary wedges, sometimes combine so as to form longitudinal (instead of transverse) bands; and sometimes cross one another so as to form a diaper pattern with bright compartments in a dark framework, and _vice versâ_, according to the position of the plates. 

 'The effects of different dispositions of the interposed crystals might be varied indefinitely; but enough has perhaps been said to show the delicacy of the method of spectrum analysis as applied to the examination of polarized light. '

 * * * * *

The singular and beautiful effect obtained with a circular plate ofselenite, thin at the centre, and gradually thickening towards thecircumference, is easily connected with a similar effect obtained withNewton's rings. Let a thin slice of light fall upon the glasses whichshow the rings, so as to cover a narrow central vertical zone passingthrough them all. The image of this zone upon the screen is crossed byportions of the iris-rings. Subjecting the reflected beam to prismaticanalysis, the resultant spectrum may be regarded as an indefinitenumber of images of the zone placed side by side. In the image beforedispersion we have _iris-rings_, the extinction of the light beingnowhere complete; but when the different colours are separated bydispersion, each colour is crossed transversely by its own system ofdark interference bands, which become gradually closer with theincreasing refrangibility of the light. The complete spectrum, therefore, appears furrowed by a system of continuous dark bands, crossing the colours transversely, and approaching each other as theypass from red to blue. 

In the case of the plate of selenite, a slit is placed in front of thepolarizer, and the film of selenite is held close to the slit, so thatthe light passes through the central zone of the film. As in the caseof Newton's rings, the image of the zone is crossed by iris-colouredbands; but when subjected to prismatic dispersion, the light of thezone yields a spectrum furrowed by bands of complete darkness exactlyas in the case of Newton's rings and for a similar reason. This is thebeautiful effect described by Mr. Spottiswoode as the fanlikearrangement of the bands--the fan opening out at the red end of thespectrum. 

 * * * * *

_MEASUREMENT OF THE WAVES OF LIGHT. _

The diffraction fringes described in Lecture II. , instead of beingformed on the retina, may be formed on a screen, or upon ground glass, when they can be looked at through a magnifying lens from behind, orthey can be observed in the air when the ground glass is removed. Instead of permitting them to form on the retina, we will suppose themformed on a screen. This places us in a condition to understand, evenwithout trigonometry, the solution of the important problem ofmeasuring _the length_ of a wave of light. 

We will suppose the screen so distant that the rays falling upon itfrom the two margins of the slit are sensibly parallel. We havelearned in Lecture II. That the first of the dark bands corresponds toa difference of marginal path of one undulation; the second dark bandto a difference of path of two undulations; the third dark band to adifference of three undulations, and so on. Now the angular distanceof the bands from the centre is capable of exact measurement; thisdistance depending, as already stated, on the width of the slit. Witha slit 1. 35 millimeter wide, [29] Schwerd found the angular distance ofthe first dark band from the centre of the field to be 1'38"; theangular distances of the second, third, fourth dark bands being twice, three times, four times this quantity. 

[Illustration: Fig. 57. ]

Let A B, fig. 57, be the plate in which the slit is cut, and C D thegrossly exaggerated width of the slit, with the beam of red lightproceeding from it at the obliquity corresponding to the first darkband. Let fall a perpendicular from one edge, D, of the slit on themarginal ray of the other edge at _d_. The distance, C _d_, betweenthe foot of this perpendicular and the other edge is the length of awave of the light. The angle C D _d_, moreover, being equal to R C R', is, in the case now under consideration, 1'38". From the centre D, with the width D C as radius, describe a semicircle; its radius D Cbeing 1. 35 millimeter, the length of this semicircle is found by aneasy calculation to be 4. 248 millimeters. The length C _d_ is so smallthat it sensibly coincides with the arc of the circle. Hence thelength of the semicircle is to the length C _d_ of the wave as 180° to1'38", or, reducing all to seconds, as 648, 000" to 98". Thus, we havethe proportion--

 648, 000 : 98 :: 4. 248 to the wave-length C _d_. 

Making the calculation, we find the wave-length for this particularkind of light to be 0. 000643 of a millimeter, or 0. 000026 of an inch. 

FOOTNOTES:

[Footnote 1: Among whom may be especially mentioned the late SirEdmund Head, Bart. , with whom I had many conversations on thissubject. ]

[Footnote 2: At whose hands it gives me pleasure to state I havealways experienced honourable and liberal treatment. ]

[Footnote 3: One of the earliest of these came from Mr. John AmoryLowell of Boston. ]

[Footnote 4: It will be subsequently shown how this simple apparatusmay be employed to determine the 'polarizing angle' of a liquid. ]

[Footnote 5: From this principle Sir John Herschel deduces in a simpleand elegant manner the fundamental law of reflection. --See _FamiliarLectures_, p. 236. ]

[Footnote 6: The low dispersive power of water masks, as Helmholtz hasremarked, the imperfect achromatism of the eye. With the naked eye Ican see a distant blue disk sharply defined, but not a red one. I canalso see the lines which mark the upper and lower boundaries of ahorizontally refracted spectrum sharp at the blue end, but ill-definedat the red end. Projecting a luminous disk upon a screen, and coveringone semicircle of the aperture with a red and the other with a blue orgreen glass, the difference between the apparent sizes of the twosemicircles is in my case, and in numerous other cases, extraordinary. Many persons, however, see the apparent sizes of the two semicirclesreversed. If with a spectacle glass I correct the dispersion of thered light over the retina, then the blue ceases to give a sharplydefined image. Thus examined, the departure of the eye fromachromatism appears very gross indeed. ]

[Footnote 7: Both in foliage and in flowers there are strikingdifferences of absorption. The copper beech and the green beech, forexample, take in different rays. But the very growth of the tree isdue to some of the rays thus taken in. Are the chemical rays, then, the same in the copper and the green beech? In two such flowers as theprimrose and the violet, where the absorptions, to judge by thecolours, are almost complementary, are the chemically active rays thesame? The general relation of colour to chemical action is worthy ofthe application of the method by which Dr. Draper proved soconclusively the chemical potency of the yellow rays of the sun. ]

[Footnote 8: Young, Helmholtz, and Maxwell reduce all differences ofhue to combinations in different proportions of three primary colours. It is demonstrable by experiment that from the red, green, and violet_all_ the other colours of the spectrum may be obtained. 

Some years ago Sir Charles Wheatstone drew my attention to a work byChristian Ernst Wünsch, Leipzig 1792, in which the author announcesthe proposition that there are neither five nor seven, but only threesimple colours in white light. Wünsch produced five spectra, with fiveprisms and five small apertures, and he mixed the colours first inpairs, and afterwards in other ways and proportions. His result isthat red is a _simple_ colour incapable of being decomposed; thatorange is compounded of intense red and weak green; that yellow is amixture of intense red and intense green; that green is a _simple_colour; that blue is compounded of saturated green and saturatedviolet; that indigo is a mixture of saturated violet and weak green;while violet is a pure _simple_ colour. He also finds that yellow andindigo blue produce _white_ by their mixture. Yellow mixed with brightblue (Hochblau) also produces white, which seems, however, to have atinge of green, while the pigments of these two colours when mixedalways give a more or less beautiful green, Wünsch very emphaticallydistinguishes the mixture of pigments from that of lights. Speaking ofthe generation of yellow, he says, 'I say expressly _red and greenlight_, because I am speaking about light-colours (Lichtfarben), andnot about pigments. ' However faulty his theories may be, Wünsch'sexperiments appear in the main to be precise and conclusive. Nearlyten years subsequently, Young adopted red, green, and violet as thethree primary colours, each of them capable of producing threesensations, one of which, however, predominates over the two others. Helmholtz adopts, elucidates, and enriches this notion. (_PopularLectures_, p. 249. The paper of Helmholtz on the mixture of colours, translated by myself, is published in the _Philosophical Magazine_ for1852. Maxwell's memoir on the Theory of Compound Colours is publishedin the _Philosophical Transactions_, vol. 150, p. 67. )]

[Footnote 9: The following charming extract, bearing upon this point, was discovered and written out for me by my deeply lamented friend Dr. Bence Jones, when Hon. Secretary to the Royal Institution:--

 'In every kind of magnitude there is a degree or sort to which our sense is proportioned, the perception and knowledge of which is of the greatest use to mankind. The same is the groundwork of philosophy; for, though all sorts and degrees are equally the object of philosophical speculation, yet it is from those which are proportioned to sense that a philosopher must set out in his inquiries, ascending or descending afterwards as his pursuits may require. He does well indeed to take his views from many points of sight, and supply the defects of sense by a well-regulated imagination; nor is he to be confined by any limit in space or time; but, as his knowledge of Nature is founded on the observation of sensible things, he must begin with these, and must often return to them to examine his progress by them. Here is his secure hold: and as he sets out from thence, so if he likewise trace not often his steps backwards with caution, he will be in hazard of losing his way in the labyrinths of Nature. '--(_Maclaurin: An Account of Sir I. Newton's Philosophical Discoveries. Written 1728; second edition_, 1750; pp. 18, 19. )]

[Footnote 10: I do not wish to encumber the conception here with thedetails of the motion, but I may draw attention to the beautiful modelof Prof. Lyman, wherein waves are shown to be produced by the_circular_ motion of the particles. This, as proved by the brothersWeber, is the real motion in the case of water-waves. ]

[Footnote 11: Copied from Weber's _Wellenlehre_. ]

[Footnote 12: See _Lectures on Sound_, 1st and 2nd ed. , Lecture VII. ;and 3rd ed. , Chap. VIII. Longmans. ]

[Footnote 13: _Boyle's Works_, Birch's edition, p. 675. ]

[Footnote 14: Page 743. ]

[Footnote 15: The beautiful plumes produced by water-crystallizationhave been successfully photographed by Professor Lockett. ]

[Footnote 16: In a little volume entitled 'Forms of Water, ' I havementioned that cold iron floats upon molten iron. In company with myfriend Sir William Armstrong, I had repeated opportunities ofwitnessing this fact in his works at Elswick, 1863. Faraday, Iremember, spoke to me subsequently of the perfection of iron castingsas probably due to the swelling of the metal on solidification. Beyondthis, I have given the subject no special attention; and I know thatmany intelligent iron-founders doubt the fact of expansion. It isquite possible that the solid floats because it is not _wetted_ by themolten iron, its volume being virtually augmented by capillaryrepulsion. Certain flies walk freely upon water in virtue of an actionof this kind. With bismuth, however, it is easy to burst iron bottlesby the force of solidification. ]

[Footnote 17: This beautiful law is usually thus expressed: _The indexof refraction of any substance is the tangent of its polarizingangle_. With the aid of this law and an apparatus similar to thatfigured at page 15, we can readily determine the index of refractionof any liquid. The refracted and reflected beams being visible, theycan readily be caused to inclose a right angle. The polarizing angleof the liquid may be thus found with the sharpest precision. It isthen only necessary to seek out its natural tangent to obtain theindex of refraction. ]

[Footnote 18: Whewell. ]

[Footnote 19: Removed from us since these words were written. ]

[Footnote 20: The only essay known to me on the Undulatory Theory, from the pen of an American writer, is an excellent one by PresidentBarnard, published in the Smithsonian Report for 1862. ]

[Footnote 21: _Boyle's Works_, Birch's edition, vol. I. Pp, 729 and730. ]

[Footnote 22: _Werke_, B. Xxix. P. 24. ]

[Footnote 23: Defined in Lecture I. ]

[Footnote 24: This circumstance ought not to be lost sight of in theexamination of compound spectra. Other similar instances might becited. ]

[Footnote 25: The dark band produced when the sodium is placed withinthe lamp was observed on the same occasion. Then was also observed forthe first time the magnificent blue band of lithium which the Bunsen'sflame fails to bring out. ]

[Footnote 26: New York: for more than a decade no such weather hadbeen experienced. The snow was so deep that the ordinary means oflocomotion were for a time suspended. ]

[Footnote 27: 'Il faut reconnaître que parmi les peuples civilisés denos jours il en est pen chez qui les hautes sciences aient fait moinsde progrès qu'aux États-Unis, ou qui aient fourni moins de grandsartistes, de poëtes illustres et de célèbres écrivains. ' (_De laDémocratie en Amérique_, etc. Tome ii. P. 36. )]

[Footnote 28: At these points the two rectangular vibrations intowhich the original polarized ray is resolved by the plates of gypsum, act upon each other like the two rectangular impulses imparted to ourpendulum in Lecture IV. , one being given when the pendulum is at thelimit of its swing. Vibration is thus converted into rotation. ]

[Footnote 29: The millimeter is about 1/25th of an inch. ]

INDEX. 

Absorption, principles of, 199

Airy, Sir George, severity and conclusiveness of his proofs, 209

Alhazen, his inquiry respecting light, 14, 207

Analyzer, polarizer and, 127----recompounding of the two systems of waves by the analyzer, 129

Ångström, his paper on spectrum analysis, 202

Arago, François, and Dr. Young, 50----his discoveries respecting light, 208

Atomic polarity, 93-96

Bacon, Roger, his inquiry respecting light, 14, 207

Bartholinus, Erasmus, on Iceland spar, 112

Bérard on polarization of heat, 180

Blackness, meaning of, 32

Boyle, Robert, his observations on colours, 65, 66----his remarks on fluorescence, 163, 164

Bradley, James, discovers the aberration of light, 21, 22

Brewster, Sir David, his chief objection to the undulatory theory oflight, 47

Brewster, Sir David, his discovery in biaxal crystals, 209

Brougham, Mr. (afterwards Lord), ridicules Dr. T. Young'sspeculations, 50, 51

Cæsium, discovery of, 193

Calorescence, 174

Clouds, actinic, 152-154----polarization of, 155

Colours of thin plates, 64----Boyle's observations on, 65, 66----Hooke on the colours of thin plates, 67----of striated surfaces, 89, 90

Comet of 1680, Newton's estimate of the temperature of, 168

Crookes, Mr. , his discovery of thallium, 193

Crystals, action of, upon light, 98----built by polar force, 98----illustrations of crystallization, 99----architecture of, considered as an introduction to their action upon light, 98----bearings of crystallization upon optical phenomena, 106

Crystals, rings surrounding the axes of, uniaxal and biaxal, 145

Cuvier on ardour for knowledge, 220

De Tocqueville, writings of, 215, 222, 223

Descartes, his explanation of the rainbow, 24, 25----his ideas respecting the transmission of light, 43----his notion of light, 207

Diamond, ignition of a, in oxygen, 169

Diathermancy, 173

Diffraction of light, phenomena of, 78----bands, 78, 79----explanation of, 80----colours produced by, 89

Dollond, his experiments on achromatism, 28

Draper, Dr. , his investigation on heat, 172

Drummond light, spectrum of, 195

Earth, daily orbit of, 74

Electric beam, heat of the, 168

Electricity, discoveries in, 217, 218

Emission theory of light, bases of the, 45----Newton espouses the theory, and the results of this espousal, 77

Ether, Huyghens and Euler advocate and defend the conception of an, 48, 58----objected to by Newton, 58

Euler espouses and defends the conception of an ether, 48, 58

Eusebius on the natural philosophers of his time, 13

Expansion by cold, 104

Experiment, uses of, 3

Eye, the, its imperfections, grown for ages towards perfection, 8----imperfect achromatism of the, 29, _note_

Faraday, Michael, his discovery of magneto-electricity, 218

'Fits, ' theory of, 73----its explanation of Newton's rings, 74----overthrow of the theory, 77

Fizeau determines the velocity of light, 22

Fluorescence, Stokes's discovery of, 161----the name, 174

Forbes, Professor, polarizes and depolarizes heat, 180

Foucault, determines the velocity of light, 22----his experiments on absorption, 197, 198

Fraunhofer, his theoretical calculations respecting diffraction, 87----his lines, 193------their explanation by Kirchhoff, 193

Fresnel, and Dr. Young, 50----his theoretical calculations respecting diffraction, 87----his mathematical abilities and immortal name, 210

Goethe on fluorescence, 165

Gravitation, origin of the notion of the attraction of, 92----strength of the theory of, 148

Grimaldi, his discovery with respect to light, 56----Young's generalizations of, 56

Hamilton, Sir William, of Dublin, his discovery of conical refraction, 209

Heat, generation of, 6----Dr. Draper's investigation respecting, 171

Helmholtz, his estimate of the genius of Young, 50----on the imperfect achromatism of the eye, 29 _note_, 31----reveals the cause of green in the case of pigments, 37

Henry, Professor Joseph, his invitation, 2

Herschel, Sir John, his theoretical calculations respectingdiffraction, 87----first notices and describes the fluorescence of sulphate of quinine, 165----his experiments on spectra, 201

Herschel, Sir William, his experiments on the heat of the variouscolours of the solar spectrum, 171

Hooke, Robert, on the colours of thin plates, 67----his remarks on the idea that light and heat are modes of motion, 68

Horse-chestnut bark, fluorescence of, 165

Huggins, Dr. , his labours, 205

Huyghens advocates the conception of ether, 48, 58----his celebrated principle, 83

Huyghens on the double refraction of Iceland spar, 112

Iceland spar, 109----double refraction caused by, 110----this double refraction first treated by Erasmus Bartholinus, 112----character of the beams emergent from, 114----tested by tourmaline, 116----Knoblauch's demonstration of the double refraction of, 185

Ice-lens, combustion through, 167

Imagination, scope of the, 42----note by Maclaurin on this point, 43 _note_

Janssen, M. , on the rose-coloured solar prominences, 204

Jupiter, Roemer's observations of the moons of, 20

Jupiter's distance from the sun, 20

Kepler, his investigations on the refraction of light, 14, 207

Kirchhoff, Professor, his explanation of Fraunhofer's lines, 193----his precursors, 201----his claims, 203

Knoblauch, his demonstration of the double refraction of heat ofIceland spar, 185

Lactantius, on the natural philosophers of his time, 13

Lamy, M. , isolates thallium in ingots, 193

Lesley, Professor, his invitation, 2

Light familiar to the ancients, 5----generation of, 6, 7----spherical aberration of, 8----the rectilineal propagation of, and mode of producing it, 9----illustration showing that the angle of incidence is equal to the angle of reflection, 10, 11----sterility of the Middle Ages, 13----history of refraction, 14----demonstration of the fact of refraction, 14----partial and total reflection of, 16-20----velocity of, 20----Bradley's discovery of the aberration of light, 21, 22----principle of least time, 23----Descartes and the rainbow, 24----Newton's analysis of, 26, 27----synthesis of white light, 30----complementary colours, 31----yellow and blue lights produce white by their mixture, 31----what is the meaning of blackness? 32----analysis of the action of pigments upon, 33----absorption, 34----mixture of pigments contrasted with mixture of lights, 37----Wünsch on three simple colours in white light, 39 _note_----Newton arrives at the emission theory, 45----Young's discovery of the undulatory theory, 49----illustrations of wave-motion, 58----interference of sound-waves, 58----velocity of, 60----principle of interference of waves of, 61----phenomena which first suggested the undulatory theory 62-69----soap-bubbles and their colours, 62-65----Newton's rings, 69-77----his espousal of the emission theory, and the results of this espousal, 77----transmitted light, 77----diffraction, 77, 89----origin of the notion of the attraction of gravitation, 92----polarity, how generated, 93----action of crystals upon, 98----refraction of, 106----elasticity and density, 108----double refraction, 109----chromatic phenomena produced by crystals in polarized, 121----the Nicol prism, 122----mechanism of, 125----vibrations, 125----composition and resolution of vibrations, 128----polarizer and analyzer, 127----recompounding the two systems of waves by the analyzer, 129----interference thus rendered possible, 131----chromatic phenomena produced by quartz, 139----magnetization, of, 141----rings surrounding the axes of crystals, 143----colour and polarization of sky, 149, 154----range of vision incommensurate with range of radiation, 159----effect of thallene on the spectrum, 162----fluorescence, 162----transparency, 167----the ultra-red rays, 170----part played in Nature by these rays, 175----conversion of heat-rays into light-rays, 176----identity of radiant heat and, 177----polarization of heat, 180----principles of spectrum analysis, 189----spectra of incandescent vapours, 190----Fraunhofer's lines, and Kirchhoff's explanation of them, 193----solar chemistry, 195-197----demonstration of analogy between sound and, 198, 199----Kirchhoff and his precursors, 201----rose-coloured solar prominences, 204----results obtained by various workers, 205----summary and conclusion, 206----polarized, the spectra of, 227----measurement of the waves of, 234

Lignum Nephriticum, fluorescence of, 164

Lloyd, Dr. , on polarization of heat, 180, 209

Lockyer, Mr. , on the rose-coloured solar prominences, 205

Lycopodium, diffraction effects caused by the spores of, 88

Magnetization of light, 141

Malus, his discovery respecting reflected light through Iceland spar, 115----discovers the polarization of light by reflection, 208

Masson, his essay on the bands of the induction spark, 202

Melloni, on the polarization of heat, 180

Metals, combustion of, 5, 6----spectrum analysis of, 190----spectrum bands proved by Bunsen and Kirchhoff to be characteristicof the vapour of, 192

Mill, John Stuart, his scepticism regarding the undulatory theory, 149

Miller, Dr. , his drawings and descriptions of the spectra of variouscoloured flames, 201

Morton, Professor, his discovery of thallene, 162

Mother-of-pearl, colours of, 90

Nature, a savage's interpretation of, 4

Newton, Sir Isaac, his experiments on the composition of solar light, 26----his spectrum, 27----dispersion, 27----arrives at the emission theory of light, 45----his objection to the conception of an ether espoused and defended by Huyghens and Euler, 58----his optical career, 70----his rings, 69-77----his rings explained by the theory of 'fits, ' 73----espouses the emission theory, 77----effects of this espousal, 77----his idea of gravitation, 92----his errors, 208

Nicol prism, the, 122

Ocean, colour of the, 35

OErsted, discovers the deflection of a magnetic needle by an electriccurrent, 176

Optics, science of, 4

Pasteur referred to, 219

Physical theories, origin of, 41-44

Pigments, analysis of the action of, upon light, 33----mixture of, contrasted with mixture of lights, 37----Helmholtz reveals the cause of the green in the case of mixed blue and yellow pigments, 37----impurity of natural colours, 37

Pitch of sound, 59

Plücker, his drawings of spectra, 202

Polariscope, stained glass in the, 130, 131----unannealed glass in the, 136

Polarity, notion of, how generated, 93----atomic, 93-96----structural arrangements due to, 96----polarization of light, 112----tested by tourmaline, 116----and by reflection and refraction, 119----depolarization, 120

Polarization of light, 112----circular, 140----sky-light, 149, 157----of artificial sky, 156----of radiant heat, 180

Polarizer and analyzer, 127

Poles of a magnet, 93

Powell, Professor, on polarization of heat, 180

Prism, the Nicol, 122

Quartz, chromatic phenomena produced by, 139

Radiant heat, 172----diathermancy, or perviousness to radiant heat, 173----conversion of heat-rays into light rays, 174----formation of invisible heat-images, 179----polarization of, 180----double refraction, 182----magnetization of, 184

Rainbow, Descartes' explanation of the, 24

Refraction, demonstration of, 14

Refraction of light, 106----double, 109

Reflection, partial and total, 16-20

Respighi, results obtained by, 205

Ritter, his discovery of the ultraviolet rays of the sun, 159

Roemer, Olav, his observations of Jupiter's moons, 20----his determination of the velocity of light, 21

Rubidium, discovery of, 193

Rusting of iron, what it is, 5

Schwerd, his observations respecting diffraction, 87

Science, growth of, 176, 203

Scoresby, Dr. , succeeds in exploding gunpowder by the sun's raysconveyed by large lenses of ice, 167

Secchi, results obtained by, 205

Seebeck, Thomas, discovers thermo-electricity, 176----discovers the polarization of light by tourmaline, 208

Selenite, experiments with thick and thin plates of, 124

Silver spectrum, analysis of, 190, 191

Sky-light, colour and polarization of, 149, 154----generation of artificial skies, 152

Snell, Willebrord, his discovery, 14----his law, 15, 24

Soap-bubbles and their colours, 63, 65

Sound, early notions of the ancients respecting, 51----interference of waves of, 58----pitch of, 59----analogies of light and, 56----demonstration of analogy between, and light, 198, 199

Sonorous vibrations, action of, 134

Spectrum analysis, principles of, 189

Spectra of incandescent vapours, 190----discontinuous, 191, 192----of polarized light, 227

Spectrum bands proved by Bunsen and Kirchhoff to be characteristic ofthe vapour, 192----its capacity as an agent of discovery, 193----analysis of the sun and stars, 193

Spottiswoode, Mr. William, 123, 227

Stewart, Professor Balfour, 202

Stokes, Professor, results of his examination of substances excited bythe ultra-violet waves, 161----his discovery of fluorescence, 162----on fluorescence, 165----nearly anticipates Kirchhoff's discovery, 198, 202

Striated surfaces, colours of, 89

Sulphate of quinine first noticed and described by Sir John Herschel, 165

Sun, chemistry of the, 195

Sun, rose-coloured solar prominences, 204

Talbot, Mr. , his experiments, 201

Tartaric acid, irregular crystallization of, and its effects, 131

Thallene, its effect on the spectrum, 162

Thallium, spectrum analysis of, 190, 191----discovery of, 193----isolated in ingots by M. Lamy, 193

Theory, relation of, to experience, 91

Thermo-electric pile, 176

Thermo-electricity, discovery of, 176

Tombeline, Mont, inverted image of, 19

Tourmaline, polarization of light by means of, 112

Transmitted light, reason for, 77

Transparency, remarks on, 167

Ultra-violet sun-rays, discovered by Ritter, 159----effects of, 160

Ultra-red rays of the solar spectrum, 171----part played by the, 173

Undulatory theory of light, bases of the, 47----Sir David Brewster's chief objection to the, 47

Undulatory theory of light, Young's foundation of the, 49----phenomena which first suggested the, 62, 69----Mr. Mill's scepticism regarding the, 143----a demonstrated verity in the hands of Young, 210

Vassenius describes the rose-coloured solar prominences in 1733, 204

Vitellio, his skill and conscientiousness, 14----his investigations respecting light, 207

Voltaic battery, use of, and its production of heat, 6, 7

Water, deportment of, considered and explained, 105, 106

Waves of water, 51----length of a wave, 52----interference of waves, 53-55

Wertheim, M. , his instrument for the determination of strains andpressures by the colours of polarized light, 134

Wheatstone, Sir Charles, his analysis of the light of the electricspark, 202

Whirlpool Rapids, illustration of the principle of the interference ofwaves at the, 55

Willigen, Van der, his drawings of spectra, 202

Wollaston, Dr. , first observes lines in solar spectrum, 193----discovers the rings of Iceland spar, 209

Woodbury, Mr. , on the impurity of natural colours, 37

Wünsch, Christian Ernst, on the three simple colours in whitelights, 39 _note_----his experiments, 39 _note_

Young, Dr. Thomas, his discovery of Egyptian hieroglyphics, 49;----and the undulatory theory of light, 49----Helmholtz's estimate of him, 50----ridiculed by Brougham in the 'Edinburgh Review, ' 50----generalizes Grimaldi's observation on light, 56, 57----photographs the ultra-violet rings of Newton, 160