_THE ROMANCE OF SCIENCE_ THE SPLASH OF A DROP BY PROF. A. M. WORTHINGTON, M. A. , F. R. S. _Being the reprint of a Discourse delivered at the Royal Institution of Great Britain, May 18, 1894. _ PUBLISHED UNDER THE DIRECTION OF THE GENERAL LITERATURE COMMITTEE. LONDON: SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE, NORTHUMBERLAND AVENUE, CHARING CROSS, W. C. ; 43, QUEEN VICTORIA STREET, E. C. BRIGHTON: 129, NORTH STREET. NEW YORK: E. & J. B. YOUNG & CO. 1895. THE SPLASH OF A DROP INSTANTANEOUS PHOTOGRAPHS OF THE SPLASH OF A WATER-DROP FALLING ABOUT 16INCHES INTO MILK. [Illustration: Time after contact = ·0262 sec. ] [Illustration: Time after contact = ·0391 sec. ] [Illustration: Time after contact = ·101 sec. ] THE SPLASH OF A DROP The splash of a drop is a transaction which is accomplished in thetwinkling of an eye, and it may seem to some that a man who proposes todiscourse on the matter for an hour must have lost all sense ofproportion. If that opinion exists, I hope this evening to be able toremove it, and to convince you that we have to deal with an exquisitelyregulated phenomenon, and one which very happily illustrates some of thefundamental properties of fluids. It may be mentioned also that therecent researches of Lenard in Germany and J. J. Thomson at Cambridge, onthe curious development of electrical charges that accompanies certainkinds of splashes, have invested with a new interest any examination ofthe mechanics of the phenomenon. It is to the mechanical and not to theelectrical side of the question that I shall call your attention thisevening. The first well-directed and deliberate observations on the subject thatI am acquainted with were made by a school-boy at Rugby some twentyyears ago, and were reported by him to the Rugby Natural HistorySociety. He had observed that the marks of accidental splashes ofink-drops that had fallen on some smoked glasses with which he wasexperimenting, presented an appearance not easy to account for. Drops ofthe same size falling from the same height had made always the samekind of mark, which, when carefully examined with a lens, showed thatthe smoke had been swept away in a system of minute concentric rings andfine striæ. Specimens of such patterns, obtained by letting drops ofmercury, alcohol, and water fall on to smoked glass, are thrown on thescreen, and the main characteristics are easily recognized. Such apattern corresponds to the footprints of the dance that has beenperformed on the surface, and though the drop may be lying unbroken onthe plate, it has evidently been taking violent exercise, and were ourvision acute enough we might observe that it was still palpitating afterits exertions. A careful examination of a large number of such footprints showed thatany opinion that could be formed therefrom of the nature of the motionof the drop must be largely conjectural, and it occurred to me abouteighteen years ago to endeavour by means of the illumination of asuitably-timed electric spark to watch a drop through its variouschanges on impact. The reason that with ordinary continuous light nothing can besatisfactorily seen of the splash, is not that the phenomenon is of suchshort duration, but because the changes are so rapid that before theimage of one stage has faded from the eye the image of a later and quitedifferent stage is superposed upon it. Thus the resulting impression isa confused assemblage of all the stages, as in the photograph of aperson who has not sat still while the camera was looking at him. Theproblem to be solved experimentally was therefore this: to let a drop ofdefinite size fall from a definite height in comparative darkness on toa surface, and to illuminate it by a flash of exceedingly short durationat any desired stage, so as to exclude all the stages previous andsubsequent to the one thus picked out. The flash must be bright enoughfor the image of what is seen to remain long enough on the eye for theobserver to be able to attend to it, and even to shift his attentionfrom one part to another, and thus to make a drawing of what is seen. Ifnecessary the experiment must be capable of repetition, with an exactlysimilar drop falling from exactly the same height, and illuminated atexactly the same stage. Then, when this stage has been sufficientlystudied, we must be able to arrange with another similar drop toilluminate it at a rather later stage, say 1/1000 second later, and inthis way to follow step by step the whole course of the phenomenon. The apparatus by which this has been accomplished is on the table beforeyou. Time will not suffice to explain how it grew out of earlierarrangements very different in appearance, but its action is very simpleand easy to follow by reference to the diagram (Fig. 1). AA´ is a light wooden rod rather longer and thicker than an ordinarylead pencil, and pivoted on a horizontal axle O. The rod bears at theend A a small deep watch-glass, or segment of a watch-glass, whosesurface has been smoked, so that a drop even of water will lie on itwithout adhesion. The end A´ carries a small strip of tinned iron, whichcan be pressed against and held down by an electro-magnet CC´. When thecurrent of the electro-magnet is cut off the iron is released, and theend A´ of the rod is tossed up by the action of a piece of india-rubberstretched catapult-wise across two pegs at E, and by this means the dropresting on the watch-glass is left in mid-air free to fall from rest. [Illustration: FIG. 1. ] BB´ is a precisely similar rod worked in just the same way, but carryingat B a small horizontal metal ring, on which an ivory timing sphere ofthe size of a child's marble can be supported. On cutting off thecurrent of the electro-magnet the ends A´ and B´ of the two levers aresimultaneously tossed up by the catapults, and thus drop and spherebegin to fall at the same moment. Before, however, the drop reaches thesurface on which it is to impinge, the timing sphere strikes a plate Dattached to one end of a third lever pivoted at Q, and thus breaks thecontact between a platinum wire bound to the underside of this lever andanother wire crossing the first at right angles. This action breaks anelectric current which has traversed a second electro-magnet F (Fig. 2), and releases the iron armature N of the lever NP, pivoted at P, thusenabling a strong spiral spring G to lift a stout brass wire L out ofmercury, and to break at the surface of the mercury a strong currentthat has circulated round the primary circuit of a Ruhmkorff's inductioncoil; this produces at the surface of the mercury a brightself-induction spark in the neighbourhood of the splash, and it is bythis flash that the splash is viewed. The illumination is greatly helpedby surrounding the place where the splash and flash are produced by awhite cardboard enclosure, seen in Fig. 2, from whose walls the light isdiffused. [Illustration: FIG. 2. ] It will be observed that the time at which the spark is made will dependupon the distance that the sphere has to fall before striking the plateD, for the subsequent action of demagnetizing F and pulling the wire Lout of the mercury in the cup H is the same on each occasion. The modusoperandi is consequently as follows:--The observer, sitting incomparative but by no means complete darkness, faces the apparatus as itappears in Fig. 2, presses down the ends A´B´ of the levers firstdescribed, so that they are held by the electro-magnet C (Fig. 1); thenhe presses the lever NP down on the electro-magnet F, sets the timingsphere and drop in place, and then by means of a bridge between twomercury cups, short-circuits and thus cuts off the current of theelectro-magnet C. This lets off drop and sphere, and produces the flash. The stage of the phenomenon that is thus revealed having beensufficiently studied by repetition of the experiment as often as may benecessary, he lowers the plate D a fraction of an inch and thus obtainsa later stage. Not only is any desired stage of the phenomenon thuseasily brought under examination, but the apparatus also affords themeans of measuring the time interval between any two stages. All thatis necessary is to know the distance that the timing sphere falls in thetwo cases. Elementary dynamics then give us the interval required. Thus, if the sphere falls one foot and we then lower D 1/4 inch, the intervalbetween the corresponding stages will be about ·0026 second. Having thus described the apparatus, which I hope shortly to show you inaction, I pass to the information that has been obtained by it. This is contained in a long series of drawings, of which a selectionwill be presented on the screen. The First Series that I have to showrepresents the splash of a drop of mercury 0·15 inch in diameter thathas fallen 3 inches on to a smooth glass plate. It will be noticed thatvery soon after the first moment of impact, minute rays are shot out inall directions on the surface. These are afterwards overflowed orunited, until, as in Fig. 8, the outline is only slightly rippled. Then(Fig. 9) main rays shoot out, from the ends of which in some casesminute droplets of liquid would split off, to be left lying in a circleon the plate, and visible in all subsequent stages. By counting thesedroplets when they were thus left, the number of rays was ascertained tohave been generally about 24. This exquisite shell-like configuration, shown in Fig. 9, marks about the maximum spread of the liquid, which, subsiding in the middle, afterwards flows into an annulus or rim with avery thin central film, so thin, in fact, as often to tear more or lessirregularly. This annular rim then divides or segments (Figs. 14, 15, 16) in such a manner as to join up the rays in pairs, and thus passesinto the 12-lobed annulus of Fig. 16. Then the whole contracts, butcontracts most rapidly between the lobes, the liquid then being driveninto and feeding the arms, which follow more slowly. In Fig. 21 the endof this stage is reached, and now the arms continuing to come in, theliquid rises in the centre; this is, in fact, the beginning of therebound of the drop from the plate. In the case before us the drops atthe ends of the arms now break off (Fig. 25), while the central massrises in a column which just fails itself to break up into drops, andfalls back into the middle of the circle of satellites which, it will beunderstood, may in some cases again be surrounded by a second circle ofthe still smaller and more numerous droplets that split off the ends ofthe rays in Fig. 9. The whole of the 30 stages described areaccomplished in about 1/20 second, so that the average interval betweenthem is about 1/600 second. FIRST SERIES. [Illustration: 1] [Illustration: 2] [Illustration: 3] [Illustration: 4] [Illustration: 5] [Illustration: 6] [Illustration: 7] [Illustration: 8] [Illustration: 9] [Illustration: 10] [Illustration: 11] [Illustration: 12] [Illustration: 13] [Illustration: 14] [Illustration: 15] [Illustration: 16] [Illustration: 17] [Illustration: 18] [Illustration: 19] [Illustration: 20] [Illustration: 21] [Illustration: 22] [Illustration: 23] [Illustration: 24] [Illustration: 25] [Illustration: 26] [Illustration: 27] [Illustration: 28] [Illustration: 29] [Illustration: 30] It should be mentioned that it is only in rare cases that thesubordinate drops seen in the last six figures, are found lying in avery complete circle after all is over, for there is generally someslight disturbing lateral velocity which causes many to mingle againwith the central drop, or with each other. But even if only half or aquarter of the circle is left, it is easy to estimate how many drops, and therefore how many arms there have been. It may be mentioned thatsometimes the surface of the central lake of liquid (Figs. 14, 15, 16, 17) was seen to be covered with beautiful concentric ripples, not shownin the figures. The question now naturally presents itself, Why should the drop behavein this manner? In seeking the answer it will be useful to ask ourselvesanother question. What should we have expected the drop to do? Well, tothis I suppose most people would be inclined, arguing from analogy witha solid, to reply that it would be reasonable to expect the drop toflatten itself, and even very considerably flatten itself, and then, collecting itself together again, to rebound, perhaps as a column suchas we have seen, but not to form this regular system of rays and armsand subordinate drops. Now this argument from analogy with a solid is rather misleading, forthe forces that operate in the case of a solid sphere that flattensitself and rebounds, are due to the bodily elasticity which enables itnot only to resist, but also to recover from any distortion of shape orshearing of its internal parts past each other. But a liquid has nopower of recovering from such internal shear, and the only force thatchecks the spread, and ultimately causes the recovery of shape, is the_surface tension_, which arises from the fact that the surface layersare always in a state of extension and always endeavouring to contract. Thus we are at liberty when dealing with the motions of the drop tothink of the interior liquid as not coherent, provided we furnish itwith a suitable elastic skin. Where the surface skin is sharply curvedoutwards, as it is at the sharp edge of the flattened disc, there theinterior liquid will be strongly pressed back. In fact the process offlattening and recoil is one in which energy of motion is first expendedin creating fresh liquid surface, and subsequently recovered as thesurface contracts. The transformation is, however, at all momentsaccompanied by a great loss of energy as heat. Moreover, it must beremembered that the energy expended in creating the surface of thesatellite drops is not restored if these remain permanently separate. Thus the surface tension explains the recoil, and it is also closelyconnected with the formation of the subordinate rays and arms. Toexplain this it is only necessary to remind you that a liquid cylinderis an unstable configuration. As you know, any fine jet becomes beadedand breaks into drops, but it is not necessary that there should be anyflow of liquid along the jet; if, for example, we could realize a rod ofliquid of the shape and size of this cylindrical ruler that I hold in myhand, and liberate it in the air, it would not retain its cylindricalshape, but would segment or divide itself up into a row of dropsregularly disposed according to a definite and very simple numericallaw, viz. That the distances between the centres of contiguous dropswould be equal to the circumference of the cylinder. This can be shownby calculation to be a consequence of the surface tension, and thecalculation has been closely verified by experiment. If the liquidcylinder were liberated on a plate, it would still topple into a regularrow of drops, but they would be further apart; this was shown byPlateau. Now imagine the cylinder bent into an annulus. It will stillfollow the same law, [1] _i. E. _ it will topple into drops just as if itwere straight. This I can show you by a direct experiment. I have here asmall thick disc of iron, with an accurately planed face and a handle atthe back. In the face is cut a circular groove, whose cross section is asemi-circle. I now lay this disc face downwards on the horizontal faceof the lantern condenser, and through one of two small holes boredthrough to the back of the disc I fill the groove with quicksilver. Now, suddenly lifting the disc from the plate, I release an annulus ofliquid, which splits into the circle of very equal drops which you seeprojected on the screen. You will notice that the main drops havebetween them still smaller ones, which have come from the splitting upof the thin cylindrical necks of liquid which connected the larger dropsat the last moment. Now this tendency to segment or topple into drops, whether of a straightcylinder or of an annulus, is the key to the formation of the arms andsatellites, and indeed to much that happens in all the splashes that weshall examine. Thus in Fig. 12 we have an annular rim, which in Figs. 13and 14 is seen to topple into lobes by which the rays are united inpairs, and even the special rays that are seen in Fig. 9 owe theirorigin to the segmentation of the rim of the thin disc into which theliquid has spread. The proceeding is probably exactly analogous to whattakes place in a sea wave that curls over in calm weather on a slightlysloping shore. Any one may notice how, as it curls over, the wavepresents a long smooth edge, from which at a given instant a multitudeof jets suddenly shoot out, and at once the back of the wave, hithertosmooth, is seen to be furrowed or "combed. " There can be no doubt thatthe cylindrical edge topples into alternate convexities and concavities;at the former the flow is helped, at the latter hindered, and thus thejets begin, and special lines of flow are determined. In precisely thesame way the previously smooth circular edge of Fig. 8 topples, anddetermines the rays and lines of flow of Fig. 9. Before going on to other splashes I will now endeavour to reproduce amercury splash of the kind I have described, in a manner that shall bevisible to all. For this purpose I have reduplicated the apparatus whichyou have seen, and have it here so arranged that I can let the drop fallon to the horizontal condenser plate of the lantern, through which thelight passes upwards, to be afterwards thrown upon this screen. Theilluminating flash will be made inside the lantern, where the arc lightwould ordinarily be placed. I have now set a drop of mercury inreadiness and put the timing sphere in place, and now if you will lookintently at the middle of the screen I will darken the room and let offthe splash. (The experiment was repeated four or five times, and thefigures seen were like those of Series X. ) Of course all that can beshown in this way is the outline, or rather a horizontal section of thesplash; but you are able to recognize some of the configurations alreadydescribed, and will be the more willing to believe that a momentary viewis after all sufficient to give much information if one is on the alertand has acquired skill by practice. The general features of the splash that we have examined are not merelycharacteristic of the liquid mercury, but belong to all splashes of aliquid falling on to a surface which it does not wet, provided theheight of fall or size of the drop are not so great as to cause completedisruption, [2] in which case there is no recovery and rebound. Thus adrop of milk falling on to smoked glass will, if the height of fall andsize of drop are properly adjusted, give forms very similar to thosepresented by a drop of mercury. The whole course of the phenomenondepends, in fact, mainly on four quantities only: (1) the size of thedrop; (2) the height of fall; (3) the value of the surface tension; (4)the viscosity of the liquid. The next series of drawings illustrates the splash of a drop of waterfalling into water. In order the better to distinguish the liquid of the original drop fromthat into which it falls, the latter was coloured with ink or with ananiline dye, and the drop itself was of water rendered turbid withfinely-divided matter in suspension. Finally drops of milk were found tobe very suitable for the purpose, the substitution of milk for water notproducing any observable change in the phenomenon. In Series II. The drop fell 3 inches, and was 1/5 inch in diameter. [In most of the figures of this and of succeeding series the centralwhite patch represents the original drop, and the white parts round itrepresent those raised portions of the liquid which catch the light. Thenumbers under each figure give the time interval in seconds from theoccurrence of the first figure, or of the figure marked [Tau] = 0. ] SERIES II. _The Splash of a Drop, followed in detail by InstantaneousIllumination. _ Diameter of Drop, 1/5 inch. Height of Fall, 3-1/5 inches. [Illustration: 1 [Tau] = 0 sec. ] [Illustration: 2 [Tau] = 0 sec. ] [Illustration: 3 [Tau] = ·0097 sec. ] [Illustration: 4 [Tau] = ·0392 sec. ] [Illustration: 5 [Tau] = ·0392 sec. ] [Illustration: 6] [Illustration: 7 [Tau] = ·0979 sec. ] [Illustration: 8 [Tau] = ·1095 sec. ] [Illustration: 9 [Tau] = ·167 sec. ] It will be observed that the drop flattens itself out somewhat, anddescends at the bottom of a hollow with a raised beaded edge (Fig. 2). This edge would be smooth and circular but for the instability whichcauses it to topple into drops. As the drop descends the hollow becomeswider and deeper, and finally closes over the drop (Fig. 3), which, however, soon again emerges as the hollow flattens out, appearing firstnear, but still below the surface (Fig. 4), in a flattened, lobed form, afterwards rising as a column somewhat mixed with adherent water, inwhich traces of the lobes are at first very visible. The rising column, which is nearly cylindrical, breaks up into dropsbefore or during its subsequent descent into the liquid. As itdisappears below the surface the outward and downward flow causes ahollow to be again formed, up the sides of which an annulus of milk iscarried, while the remainder descends to be torn again a second timeinto a vortex ring, which, however, is liable to disturbance from thefalling in of the drops which once formed the upper part of therebounding column. It is not difficult to recognize some features of this splash withoutany apparatus beyond a cup of tea and a spoonful of milk. Any drinker ofafternoon tea, after the tea is poured out and before the milk is putin, may let the milk fall into it drop by drop from one or two inchesabove it. The rebounding column will be seen to consist almost entirelyof milk, and to break up into drops in the manner described, while thevortex ring, whose core is of milk, may be seen to shoot down into theliquid. But this is better observed by dropping ink into a tumbler ofclear water. Let us now increase the height of fall to 17 inches. Series III. Exhibits the result. All the characteristics of the last splash aremore strongly marked. In Fig. 1 we have caught sight of the littleraised rim of the hollow before it was headed, but in Fig. 2 specialchannels of easiest flow have been already determined. The number ofribs and rays in this basket-shaped hollow seemed to vary a good dealwith different drops, as also did the number of arms and lobes seen inlater figures, in a somewhat puzzling manner, and I made no attempt toselect drawings which are in agreement in this respect. It will beunderstood that these rays contain little or none of the liquid of thedrop, which remains collected together in the middle. Drops from theserays or from the larger arms and lobes of subsequent figures are oftenthrown off high into the air. In Figs. 3 and 4 the drop is clean gonebelow the surface of the hollow, which is now deeper and larger thanbefore. The beautiful beaded annular edge then subsides, and in Fig. 5we see the drop again, and in Fig. 6 it begins to emerge. But althoughthe drop has fallen from a greater height than in the previous splash, the energy of the impact, instead of being expended in raising the sameamount of liquid to a greater height, is now spent in lifting a muchthicker adherent column to about the same height as in the last splash. There was sometimes noticed, as seen in Fig. 9, a tendency in the waterto flow up past the milk, which, still comparatively unmixed with water, rides triumphant on the top of the emergent column. The greater relativethickness of this column prevents it splitting into drops, and Figs. 10and 11 show it descending below the surface to form the hollow of Fig. 12, up the sides of which an annular film of milk is carried (Figs. 12and 13), having been detached from the central mass, which descends tobe torn again, this time centrally into a well-marked vortex ring. SERIES III. _The Splash of a Drop, followed in detail by InstantaneousIllumination. _ Diameter of Drop, 1/5 inch. Height of Fall, 1 ft. 5 in. [Illustration: 1 [Tau] = 0 sec. ] [Illustration: 2 [Tau] = ·0314 sec. ] [Illustration: 3 [Tau] = ·0317 sec. ] [Illustration: 4 [Tau] = ·0389 sec. ] [Illustration: 5 [Tau] = ·0498 sec. ] [Illustration: 6 [Tau] = ·0551 sec. ] [Illustration: 7 [Tau] = ·0759 sec. ] [Illustration: 8 [Tau] = ·0901 sec. ] [Illustration: 9] [Illustration: 10] [Illustration: 11] [Illustration: 12 [Tau] = ·295 sec. ] [Illustration: 13] [Illustration: 14] If we keep to the same size of drop and increase the fall to somethingover a yard, no great change occurs in the nature of the splash, but theemergent column is rather higher and thinner and shows a tendency tosplit into drops. When, however, we double the volume of the drop and raise the height offall to 52 inches, the splash of Series IV. Is obtained, which isbeginning to assume quite a different character. The raised rim of theprevious series is now developed into a hollow shell of considerableheight, which tends to close over the drop. This shell or dome is acharacteristic feature of all splashes made by large drops falling froma considerable height, and is extremely beautiful. In the splash atpresent under consideration it does not always succeed in closingpermanently, but opens out as it subsides, and is followed by theemergence of the drop (Fig. 8). In Fig. 9 the return wave overwhelms thedrop for an instant, but it is again seen at the summit of the column inFig. 10. SERIES IV. _The Splash of a Drop, followed in detail by InstantaneousIllumination. _ Diameter of Drop, 1/4 inch. Height of Fall, 4 ft. 4 in. [Illustration: 1 [Tau] = 0 sec. ] [Illustration: 2 [Tau] = ·0021 sec. ] [Illustration: 3 [Tau] = ·0042 sec. ] [Illustration: 4 [Tau] = ·0165 sec. ] [Illustration: 5 [Tau] = ·0206 sec. ] [Illustration: 6 [Tau] = ·0443 sec. ] [Illustration: 7 [Tau] = ·0482 sec. ] [Illustration: 8 [Tau] = ·0595 sec. ] [Illustration: 9 [Tau] = ·0707 sec. ] [Illustration: 10] [Illustration: 11] But on other occasions the shell or dome of Figs. 4 and 5 closespermanently over the imprisoned air, the liquid then flowing down thesides, which become thinner and thinner, till at length we are left witha large bubble floating on the water (see Series V. ). It will beobserved that the flow of liquid down the sides is chiefly alongdefinite channels, which are probably determined by the arms thrown upat an earlier stage. The bubble is generally creased by the weight ofthe liquid along these channels. It must be remembered that the base ofthe bubble is in a state of oscillation, and that the whole is liable toburst at any moment, when such figures as 6 and 7 of the previous serieswill be seen. [Illustration: SERIES V. _The Splash of a Drop, followed in detail by InstantaneousIllumination. _ The Size of Drop and Height of Fall are the same as before, but thehollow shell (see figs. 4 and 5 of the previous Series) does not succeedin opening, but is left as a bubble on the surface. This explains theformation of bubbles when _big_ rain-drops fall into a pool of water. ] Such is the history of the building of the bubbles which big rain-dropsleave on the smooth water of a lake, or pond, or puddle. Only the biggerdrops can do it, and reference to the number at the side of Fig. 5 ofSeries IV. Shows that the dome is raised in about two-hundredths of asecond. Should the domes fail to close, or should they open again, wehave the emergent columns which any attentive observer will readilyrecognize, and which have never been better described than by Mr. R. L. Stevenson, who, in his delightful _Inland Voyage_, speaks of the surfaceof the Belgian canals along which he was canoeing, as thrown up by therain into "an infinity of little crystal fountains. " Very beautiful forms of the same type indeed, but different in detail, are those produced by a drop of water falling into the lighter and moremobile liquid, petroleum. It will now be interesting to turn to the splash that is produced when asolid sphere, such as a child's marble, falls into water. I found to my great surprise that the character of the splash, at anyrate up to a height of 4 or 5 feet, depends entirely on the state of thesurface of the sphere. A polished sphere of marble about 0·6 of an inchin diameter, rubbed very dry with a cloth just beforehand and droppedfrom a height of 2 feet into water, gave the figures of Series VI. , inwhich it is seen that the water spreads over the sphere so rapidly, thatit is sheathed with the liquid even before it has passed below thegeneral level of the surface. The splash is insignificantly small and ofvery short duration. [3] If the drying and polishing be not so perfect, the configurations of Series VII. Are produced; while if the sphere beroughened with sandpaper, or _left wet_, Series VIII. Is obtained, inwhich it will be perceived that, as was the case with the liquid drop, the water is driven away laterally, forming the ribbed basket-shapedhollow, which, however, is now prolonged to a great depth, the dropbeing followed by a cone of air, while the water seems to find greatdifficulty in wetting the surface completely. Part of this column of airwas carried down at least 16 inches, and then only detached when thesphere struck the bottom of the vessel. SERIES VI. , VII. _Splash of a Solid Sphere (a marble 1/2 inch in diameter falling 2 feetinto water). _ [Illustration: SERIES VI. When the sphere is _dry_ and _polished_. ] [Illustration: SERIES VII. When the sphere is _not_ well _dried_ and _polished_. ] [Illustration: SERIES VIII. _The Splash of a Solid Sphere_--(continued. ) When the sphere is _rough_ or _wet_. ] [Illustration: SERIES IX. _The Splash of a Solid Sphere_--(continued. ) When the sphere is rough or wet, and falls above 5 feet. ] Figs. 6 and 7 show the crater falling in, but this did not alwayshappen, for the walls often closed over the hollow exactly as in Figs. 4and 5 of Series IV. Meanwhile the long and nearly cylindrical portionbelow breaks up into bubbles which rise quickly to the surface. By increasing the fall to 5 feet we obtain the figures of Series IX. Thetube of Fig. 1 corresponds to the dome of Series IV. And V. , and is notonly elevated to a surprising height, but is also in the act of cleaving(the outline being approximately that of the unduloid of M. Plateau). Figs. 2 and 3 show the bubble formed by the closing up of this tube, weighed down in the centre as in Figs. 5 and 6 of Series V. Similarresults were obtained with other liquids, such as petroleum and alcohol. It is easy to show in a very striking manner the paramount influence ofthe condition of the solid surface. I have here a number of similarmarbles; this set has been well polished by rubbing with wash leather. Idrop them one by one through a space of about 1 foot into this deep, wide, cylindrical glass vessel, lighted up by a lamp placed behind it. You see each marble enters noiselessly and with hardly a visible traceof splash. Now I pick them out and drop them in again (or to savetrouble, I drop in the place of these other wet ones), everything ischanged. You see how the air is carried to the very bottom of thevessel, and you hear the "phloisbos" of the bubbles as theyrise to the surface and burst. These dry but rough marbles behave inmuch the same way. Such are the main features of the Natural History of Splashes, as I madeit out between thirteen and eighteen years ago. Before passing on to thephotographs that I have since obtained, I desire to add a few words ofcomment. I have not till now alluded to any imperfections in the timingapparatus. But no apparatus of the kind can be absolutely perfect, and, as a matter of fact, when everything is adjusted so as to display aparticular stage, it will happen that in a succession of observationsthere is a certain variation in what is seen. Thus the configurationviewed may be said to oscillate slightly about the mean for which theapparatus is adjusted. Now this is due both to small imperfections inthe timing apparatus and to the fact that the splashes themselves doactually vary within certain limits. The reasons are not very far toseek. In the first place the rate of demagnetization of theelectro-magnets varies slightly, being partly dependent on the varyingresistance of the contacts of crossed wires, partly on the temperatureof the magnet, which is affected by the length of time for which thecurrent has been running. But a much more important reason is thevariation of the slight adhesion of the drop to the smoked watch-glassthat has supported it, and consequently of the oscillations to which, aswe shall see, the drop is subjected as it descends. Thus the drop willsometimes strike the surface in a flattened form, at others in anelongated form, and there will be a difference, not only in the time ofimpact, but in the nature of the ensuing splash; consequently somejudgment is required in selecting a consecutive series of drawings. Theonly way is to make a considerable number of drawings of each stage, andthen to pick out a consecutive series. Now, whenever judgment has to beused, there is room for error of judgment, and moreover, it isimpossible to put together the drawings so as to tell a consecutivestory, without being guided by some theory, such as I have alreadysketched, as to the nature of the motion and the conditions that governit. You will therefore be good enough to remember that this chronicle ofthe events of a tenth of a second is not a mechanical record but ispresented by a fallible human historian, whose account, like that ofany other contemporary observer, will be none the worse for independentconfirmation. That confirmation is fortunately obtainable. In an attemptmade eighteen years ago to photograph the splash of a drop of mercury, Iwas unable to procure plates sufficiently sensitive to respond to thevery short exposures that were required, and consequently abandoned theendeavour. But in recent years plates of exquisite sensitiveness havebeen produced, and such photographs as those taken by Mr. Boys of aflying rifle bullet have shown that difficulties on the score ofsensitiveness have been practically overcome. Within the last few weeks, with the valuable assistance of my colleague at Devonport, Mr. R. S. Cole, I have succeeded in obtaining photographs of various splashes. Following Prof. Boys' suggestion, we employed Thomas's cyclist plates, or occasionally the less sensitive "extra-rapid" plates of the samemakers, and as a developer, Eikonogen solution of triple strength, inwhich the plates were kept for about 40 minutes, the development beingconducted in complete darkness. A few preliminary trials with the self-induction spark produced at thesurface of mercury by the apparatus that you have seen at work, showedthat the illumination, though ample for direct vision, was notsufficient for photography. When the current strength was increased, soas to make the illumination bright enough for the camera, then the sparkbecame of too great duration, for it lasted for between 4 and 5thousandths of a second, within which time there was very perceptiblemotion of the drop and consequent blurring. It was therefore necessaryto modify the apparatus so as to employ a Leyden-jar spark whoseduration was probably less than 10-millionths of a second. A veryslight change in the apparatus rendered it suitable for the newconditions, but time does not permit me to describe the arrangements indetail. It is, however, less necessary to do so as the method is in allessentials the same as that described in this room two years ago by LordRayleigh in connection with the photography of a breaking soap-film. [4]I therefore pass at once to the photographs themselves. The first two series (X. And XI. ) may be described as shadowphotographs; they were obtained by allowing a drop of mercury to fall onto the naked photographic plate itself, the illuminating spark beingproduced vertically above it, and they give only a horizontal section ofthe drop in various stages, revealing the form of the outline of thepart in contact with the plate, but of course telling nothing about theshape of the parts above. The first series corresponds to a mercurysplash very similar to that first described, and the second to thesplash of a larger drop such as was not described. In each series, thetearing of the thin central film to which allusion was made is wellillustrated. I think the first comment that any one would make is thatthe photographs, while they bear out the drawings in many details, showgreater irregularity than the drawings would have led one to expect. Onthis point I shall presently have something to say. SERIES X. (1) _Instantaneous Shadow Photographs (life size) of the Splash of aDrop of Mercury falling 8 cm. On to the Photographic Plate. _ [Illustration: 1 Actual size of the Drop, 4·83 mm. ] [Illustration: 2 [Tau] = 0] [Illustration: 3] [Illustration: 4] [Illustration: 5] [Illustration: 6] [Illustration: 7 [Tau] = ·048 sec. ] SERIES XI. (2) _Instantaneous Shadow Photographs (life size) of the Splash of aDrop of Mercury falling 15 cm. On to Glass. _ [Illustration: 1 Actual size, 4·83 mm. In diameter. ] [Illustration: 2 [Tau] = 0 sec. ] [Illustration: 3] [Illustration: 4 4A [Tau] = ·0032 sec. ] [Illustration: 5 [Tau] = ·0063 sec. ] [Illustration: 5A [Tau] = ·0094 sec. ] [Illustration: 6 [Tau] = ·0134 sec. ] Comparing the first set of drawings (pp. 20-24) with the photographs ofSeries X. , it will be seen that Photograph 2 corresponds to drawing 4 or 5 " 3 " " 9 " 4 " " 18 " 6 " " 20 " 7 " " 24 but the irregularity of the last photograph almost masks theresemblance. SERIES XII. _Engravings from Instantaneous Photographs (16/17 of the real size) ofthe Splash of a Drop of Mercury, 4·83 mm. In diameter, falling 8·9 cm. On to a hard polished surface. _ [Illustration: 1] [Illustration: 2 [Tau] = 0 sec. ] [Illustration: 3] [Illustration: 4] [Illustration: 5] [Illustration: 6 [Tau] = ·0195 sec. ] Series XII. Gives an objective view of a mercury splash as taken by thecamera. Only the first of this series shows any detail in the interior. The polished surface of the mercury is, in fact, very troublesome toilluminate, and this splash proved the most difficult of all tophotograph. Series XIII. Shows the splash of a drop of milk falling on to a smokedglass plate, on which it runs about without adhesion just as mercurywould. Here there is more of detail. In Fig. 4 the central film is sothin in the middle that the black plate beneath it is seen through theliquid. In Fig. 8 this film has been torn. Series XIV. Exhibits the splash of a water drop falling into milk. Thefirst four photographs show the oscillations of the drop about a meanspherical figure as it approaches the surface. In the subsequent figures it will be noticed that the arms which arethrown up at first, afterwards segment into drops which fly off andsubside (see Fig. 8), to be followed by a second series which againsubside (Fig. 11), to be again succeeded by a third set. In fact, solong as there is any downward momentum the drop and the air behind itare penetrating the liquid, and so long must there be an upward flow ofdisplaced liquid. Much of this flow is seen to be directed into the armsalong the channels determined by the segmentation of the annular rim. This reproduction of the lobes and arms time after time on a varyingscale goes far to explain the puzzling variations in their number whichI mentioned in connection with the drawings. I had not, indeed, suspected this, which is one of the few new points that the photographshave so far revealed. [5] SERIES XIII. _Engravings of Instantaneous Photographs (16/17 of the real size) of theSplash of a Drop of Milk falling 20 cm. On to smoked glass. _ [Illustration: 1] [Illustration: 2 [Tau] = 0 sec. ] [Illustration: 3 [Tau] = ·0025 sec. ] (It was not found possible to reproduce satisfactorily the missingfigures of this series. ) [Illustration: 7 [Tau] = ·0128 sec. ] [Illustration: 8 [Tau] = ·0149 sec. ] [Illustration: 9 [Tau] = ·0149 sec. ] SERIES XIV. _Engravings of Instantaneous Photographs of the Splash of a Drop ofWater falling 40 cm. Into Milk. _ Scale about 6/10 of actual size. [Illustration: 1] [Illustration: 2] [Illustration: 3] [Illustration: 4 [Tau] = 0 sec. ] [Illustration: 5] [Illustration: 6 [Tau] = ·0056 sec. ] [Illustration: 7 [Tau] = ·0163 sec. ] [Illustration: 8] [Illustration: 9 [Tau] = ·0182 sec. ] [Illustration: 10 [Tau] = ·0197 sec. ] [Illustration: 11 [Tau] = ·0262 sec. ] [Illustration: 12 [Tau] = ·0391 sec. ] [Illustration: 13 [Tau] = ·0514 sec. ] [Illustration: 14 [Tau] = ·0601 sec. ] [Illustration: 15] [Illustration: 16 [Tau] = ·080 sec. ] [Illustration: 17] [Illustration: 18 [Tau] = ·101 sec. ] With respect to these photographs, [6] the credit of which I hope youwill attribute firstly to the inventors of the sensitive plates, andsecondly to the skill and experience of Mr. Cole, I desire to add thatthey are, as far as we know, the first really detailed objective viewsthat have been obtained with anything approaching so short an exposure. Even Mr. Boys' wonderful photographs of flying bullets were after allbut shadow-photographs, and did not so strikingly illustrate theextreme sensitiveness of the plates, and I want you to distinguishbetween such and what (to borrow Mr. F. J. Smith's phrase) I call an"objective view. " It remains only to speak of the greater irregularity in the arms andrays as shown by the photographs. The point is a curious and interestingone. In the first place I have to confess that in looking over myoriginal drawings I find records of many irregular or unsymmetricalfigures, yet in compiling the history it has been inevitable that theseshould be rejected, if only because identical irregularities neverrecur. Thus the mind of the observer is filled with an ideal splash--an"Auto-Splash"--whose perfection may never be actually realized. But in the second place, when the splash is nearly regular it is verydifficult to detect irregularity. This is easily proved by projectingon the screen with instantaneous illumination such a photograph as thatof Series X. , Fig. 6. My experience is that most persons pronounce whatthey have seen to be a regular and symmetrical star-shaped figure, andthey are surprised when they come to examine it by detail in continuouslight to find how far this is from the truth. Especially is this thecase if no irregularity is suspected beforehand. I believe that theobserver, usually finding himself unable to attend to more than aportion of the rays in the system, is liable instinctively to pick outfor attention a part of the circumference where they are regularlyspaced, and to fill up the rest in imagination, and that where a ray maybe really absent he prefers to consider that it has been imperfectlyviewed. This opinion is confirmed by the fact that in several cases, I havebeen able to observe with the naked eye a splash that was alsosimultaneously photographed, and have made the memorandum "quiteregular, " though the photograph subsequently showed irregularity. Itmust, however, be observed that the absolute darkness and otherconditions necessary for photography are not very favourable for directvision. And now my tale is told, or rather as much of it as the limits of thetime allowed me will permit. I think you will agree that the phenomenaare very beautiful, and that the subject, commonplace and familiarthough it is, has yet proved worthy of an hour's attention. THE END. _Richard Clay & Sons, Limited, London & Bungay. _ FOOTNOTES: [1] See Worthington on the "Spontaneous Segmentation of a LiquidAnnulus, " _Proceedings Royal Society_, No. 200, p. 49 (1879). [2] Readers who wish a more detailed account of a greater variety ofsplashes are referred to papers by the author. _Proceedings RoyalSociety_, vol. Xxv. Pp. 261 and 498 (1877); and vol. Xxxiv. P. 217(1882). [3] Photographs obtained since this was written show that much mayhappen after the stages here traced. [4] A detailed account of the optical, mechanical, and electricalarrangements employed, written by Mr. Cole, will be found in _Nature_, vol. I. , p. 222 (July 5, 1894). [5] The black streaks, seen especially in Figs. 11, 15, and 16, are dueto particles of lamp-black carried down by the drop from the surface ofthe smoked watch-glass on which it rested. [6] Three of these photographs, viz. Nos. 11, 12, and 17, are reproducedfull size, as a frontispiece, by a _photographic_ process, to enable thereader to form a more correct idea than can be gathered from theengravings, of the amount of detail actually obtained, though even inthese reproductions much is inevitably lost. 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