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diff --git a/27125.txt b/27125.txt new file mode 100644 index 0000000..d176e2c --- /dev/null +++ b/27125.txt @@ -0,0 +1,2151 @@ +The Project Gutenberg EBook of The Splash of a Drop, by A. M. Worthington + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: The Splash of a Drop + +Author: A. M. Worthington + +Release Date: November 2, 2008 [EBook #27125] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK THE SPLASH OF A DROP *** + + + + +Produced by Chris Curnow, Greg Bergquist and the Online +Distributed Proofreading Team at https://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + + + + + _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 16 +INCHES 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 the +twinkling of an eye, and it may seem to some that a man who proposes to +discourse on the matter for an hour must have lost all sense of +proportion. If that opinion exists, I hope this evening to be able to +remove it, and to convince you that we have to deal with an exquisitely +regulated phenomenon, and one which very happily illustrates some of the +fundamental properties of fluids. It may be mentioned also that the +recent researches of Lenard in Germany and J.J. Thomson at Cambridge, on +the curious development of electrical charges that accompanies certain +kinds of splashes, have invested with a new interest any examination of +the mechanics of the phenomenon. It is to the mechanical and not to the +electrical side of the question that I shall call your attention this +evening. + +The first well-directed and deliberate observations on the subject that +I am acquainted with were made by a school-boy at Rugby some twenty +years ago, and were reported by him to the Rugby Natural History +Society. He had observed that the marks of accidental splashes of +ink-drops that had fallen on some smoked glasses with which he was +experimenting, presented an appearance not easy to account for. Drops of +the same size falling from the same height had made always the same +kind of mark, which, when carefully examined with a lens, showed that +the smoke had been swept away in a system of minute concentric rings and +fine striae. Specimens of such patterns, obtained by letting drops of +mercury, alcohol, and water fall on to smoked glass, are thrown on the +screen, and the main characteristics are easily recognized. Such a +pattern corresponds to the footprints of the dance that has been +performed on the surface, and though the drop may be lying unbroken on +the plate, it has evidently been taking violent exercise, and were our +vision acute enough we might observe that it was still palpitating after +its exertions. + +A careful examination of a large number of such footprints showed that +any opinion that could be formed therefrom of the nature of the motion +of the drop must be largely conjectural, and it occurred to me about +eighteen years ago to endeavour by means of the illumination of a +suitably-timed electric spark to watch a drop through its various +changes on impact. + +The reason that with ordinary continuous light nothing can be +satisfactorily seen of the splash, is not that the phenomenon is of such +short duration, but because the changes are so rapid that before the +image of one stage has faded from the eye the image of a later and quite +different stage is superposed upon it. Thus the resulting impression is +a confused assemblage of all the stages, as in the photograph of a +person who has not sat still while the camera was looking at him. The +problem to be solved experimentally was therefore this: to let a drop of +definite size fall from a definite height in comparative darkness on to +a surface, and to illuminate it by a flash of exceedingly short duration +at any desired stage, so as to exclude all the stages previous and +subsequent to the one thus picked out. The flash must be bright enough +for the image of what is seen to remain long enough on the eye for the +observer to be able to attend to it, and even to shift his attention +from one part to another, and thus to make a drawing of what is seen. If +necessary the experiment must be capable of repetition, with an exactly +similar drop falling from exactly the same height, and illuminated at +exactly the same stage. Then, when this stage has been sufficiently +studied, we must be able to arrange with another similar drop to +illuminate it at a rather later stage, say 1/1000 second later, and in +this way to follow step by step the whole course of the phenomenon. + +The apparatus by which this has been accomplished is on the table before +you. Time will not suffice to explain how it grew out of earlier +arrangements very different in appearance, but its action is very simple +and easy to follow by reference to the diagram (Fig. 1). + +AA' is a light wooden rod rather longer and thicker than an ordinary +lead pencil, and pivoted on a horizontal axle O. The rod bears at the +end A a small deep watch-glass, or segment of a watch-glass, whose +surface has been smoked, so that a drop even of water will lie on it +without adhesion. The end A' carries a small strip of tinned iron, which +can be pressed against and held down by an electro-magnet CC'. When the +current of the electro-magnet is cut off the iron is released, and the +end A' of the rod is tossed up by the action of a piece of india-rubber +stretched catapult-wise across two pegs at E, and by this means the drop +resting 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 carrying +at B a small horizontal metal ring, on which an ivory timing sphere of +the size of a child's marble can be supported. On cutting off the +current of the electro-magnet the ends A' and B' of the two levers are +simultaneously tossed up by the catapults, and thus drop and sphere +begin to fall at the same moment. Before, however, the drop reaches the +surface on which it is to impinge, the timing sphere strikes a plate D +attached to one end of a third lever pivoted at Q, and thus breaks the +contact between a platinum wire bound to the underside of this lever and +another wire crossing the first at right angles. This action breaks an +electric current which has traversed a second electro-magnet F (Fig. 2), +and releases the iron armature N of the lever NP, pivoted at P, thus +enabling a strong spiral spring G to lift a stout brass wire L out of +mercury, and to break at the surface of the mercury a strong current +that has circulated round the primary circuit of a Ruhmkorff's induction +coil; this produces at the surface of the mercury a bright +self-induction spark in the neighbourhood of the splash, and it is by +this flash that the splash is viewed. The illumination is greatly helped +by surrounding the place where the splash and flash are produced by a +white cardboard enclosure, seen in Fig. 2, from whose walls the light is +diffused. + +[Illustration: FIG. 2.] + +It will be observed that the time at which the spark is made will depend +upon the distance that the sphere has to fall before striking the plate +D, for the subsequent action of demagnetizing F and pulling the wire L +out of the mercury in the cup H is the same on each occasion. The modus +operandi is consequently as follows:--The observer, sitting in +comparative but by no means complete darkness, faces the apparatus as it +appears in Fig. 2, presses down the ends A'B' of the levers first +described, so that they are held by the electro-magnet C (Fig. 1); then +he presses the lever NP down on the electro-magnet F, sets the timing +sphere and drop in place, and then by means of a bridge between two +mercury cups, short-circuits and thus cuts off the current of the +electro-magnet C. This lets off drop and sphere, and produces the flash. +The stage of the phenomenon that is thus revealed having been +sufficiently studied by repetition of the experiment as often as may be +necessary, he lowers the plate D a fraction of an inch and thus obtains +a later stage. Not only is any desired stage of the phenomenon thus +easily brought under examination, but the apparatus also affords the +means of measuring the time interval between any two stages. All that +is necessary is to know the distance that the timing sphere falls in the +two 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 interval +between the corresponding stages will be about .0026 second. + +Having thus described the apparatus, which I hope shortly to show you in +action, I pass to the information that has been obtained by it. + +This is contained in a long series of drawings, of which a selection +will be presented on the screen. The First Series that I have to show +represents the splash of a drop of mercury 0.15 inch in diameter that +has fallen 3 inches on to a smooth glass plate. It will be noticed that +very soon after the first moment of impact, minute rays are shot out in +all directions on the surface. These are afterwards overflowed or +united, 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 cases +minute droplets of liquid would split off, to be left lying in a circle +on the plate, and visible in all subsequent stages. By counting these +droplets when they were thus left, the number of rays was ascertained to +have 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 a +very thin central film, so thin, in fact, as often to tear more or less +irregularly. 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 passes +into the 12-lobed annulus of Fig. 16. Then the whole contracts, but +contracts most rapidly between the lobes, the liquid then being driven +into and feeding the arms, which follow more slowly. In Fig. 21 the end +of this stage is reached, and now the arms continuing to come in, the +liquid rises in the centre; this is, in fact, the beginning of the +rebound of the drop from the plate. In the case before us the drops at +the ends of the arms now break off (Fig. 25), while the central mass +rises in a column which just fails itself to break up into drops, and +falls back into the middle of the circle of satellites which, it will be +understood, may in some cases again be surrounded by a second circle of +the still smaller and more numerous droplets that split off the ends of +the rays in Fig. 9. The whole of the 30 stages described are +accomplished in about 1/20 second, so that the average interval between +them 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 the +subordinate drops seen in the last six figures, are found lying in a +very complete circle after all is over, for there is generally some +slight disturbing lateral velocity which causes many to mingle again +with the central drop, or with each other. But even if only half or a +quarter 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 that +sometimes the surface of the central lake of liquid (Figs. 14, 15, 16, +17) was seen to be covered with beautiful concentric ripples, not shown +in the figures. + +The question now naturally presents itself, Why should the drop behave +in this manner? In seeking the answer it will be useful to ask ourselves +another question. What should we have expected the drop to do? Well, to +this I suppose most people would be inclined, arguing from analogy with +a solid, to reply that it would be reasonable to expect the drop to +flatten itself, and even very considerably flatten itself, and then, +collecting itself together again, to rebound, perhaps as a column such +as we have seen, but not to form this regular system of rays and arms +and subordinate drops. + +Now this argument from analogy with a solid is rather misleading, for +the forces that operate in the case of a solid sphere that flattens +itself and rebounds, are due to the bodily elasticity which enables it +not only to resist, but also to recover from any distortion of shape or +shearing of its internal parts past each other. But a liquid has no +power of recovering from such internal shear, and the only force that +checks the spread, and ultimately causes the recovery of shape, is the +_surface tension_, which arises from the fact that the surface layers +are always in a state of extension and always endeavouring to contract. +Thus we are at liberty when dealing with the motions of the drop to +think of the interior liquid as not coherent, provided we furnish it +with a suitable elastic skin. Where the surface skin is sharply curved +outwards, as it is at the sharp edge of the flattened disc, there the +interior liquid will be strongly pressed back. In fact the process of +flattening and recoil is one in which energy of motion is first expended +in creating fresh liquid surface, and subsequently recovered as the +surface contracts. The transformation is, however, at all moments +accompanied by a great loss of energy as heat. Moreover, it must be +remembered that the energy expended in creating the surface of the +satellite drops is not restored if these remain permanently separate. +Thus the surface tension explains the recoil, and it is also closely +connected with the formation of the subordinate rays and arms. To +explain this it is only necessary to remind you that a liquid cylinder +is an unstable configuration. As you know, any fine jet becomes beaded +and breaks into drops, but it is not necessary that there should be any +flow of liquid along the jet; if, for example, we could realize a rod of +liquid of the shape and size of this cylindrical ruler that I hold in my +hand, and liberate it in the air, it would not retain its cylindrical +shape, but would segment or divide itself up into a row of drops +regularly disposed according to a definite and very simple numerical +law, viz. that the distances between the centres of contiguous drops +would be equal to the circumference of the cylinder. This can be shown +by calculation to be a consequence of the surface tension, and the +calculation has been closely verified by experiment. If the liquid +cylinder were liberated on a plate, it would still topple into a regular +row of drops, but they would be further apart; this was shown by +Plateau. Now imagine the cylinder bent into an annulus. It will still +follow the same law,[1] _i.e._ it will topple into drops just as if it +were straight. This I can show you by a direct experiment. I have here a +small thick disc of iron, with an accurately planed face and a handle at +the back. In the face is cut a circular groove, whose cross section is a +semi-circle. I now lay this disc face downwards on the horizontal face +of the lantern condenser, and through one of two small holes bored +through to the back of the disc I fill the groove with quicksilver. Now, +suddenly lifting the disc from the plate, I release an annulus of +liquid, which splits into the circle of very equal drops which you see +projected on the screen. You will notice that the main drops have +between them still smaller ones, which have come from the splitting up +of the thin cylindrical necks of liquid which connected the larger drops +at the last moment. + +Now this tendency to segment or topple into drops, whether of a straight +cylinder or of an annulus, is the key to the formation of the arms and +satellites, and indeed to much that happens in all the splashes that we +shall examine. Thus in Fig. 12 we have an annular rim, which in Figs. 13 +and 14 is seen to topple into lobes by which the rays are united in +pairs, and even the special rays that are seen in Fig. 9 owe their +origin to the segmentation of the rim of the thin disc into which the +liquid has spread. The proceeding is probably exactly analogous to what +takes place in a sea wave that curls over in calm weather on a slightly +sloping shore. Any one may notice how, as it curls over, the wave +presents a long smooth edge, from which at a given instant a multitude +of jets suddenly shoot out, and at once the back of the wave, hitherto +smooth, is seen to be furrowed or "combed." There can be no doubt that +the cylindrical edge topples into alternate convexities and concavities; +at the former the flow is helped, at the latter hindered, and thus the +jets begin, and special lines of flow are determined. In precisely the +same way the previously smooth circular edge of Fig. 8 topples, and +determines the rays and lines of flow of Fig. 9. + +Before going on to other splashes I will now endeavour to reproduce a +mercury splash of the kind I have described, in a manner that shall be +visible to all. For this purpose I have reduplicated the apparatus which +you have seen, and have it here so arranged that I can let the drop fall +on to the horizontal condenser plate of the lantern, through which the +light passes upwards, to be afterwards thrown upon this screen. The +illuminating flash will be made inside the lantern, where the arc light +would ordinarily be placed. I have now set a drop of mercury in +readiness and put the timing sphere in place, and now if you will look +intently at the middle of the screen I will darken the room and let off +the splash. (The experiment was repeated four or five times, and the +figures seen were like those of Series X.) Of course all that can be +shown in this way is the outline, or rather a horizontal section of the +splash; but you are able to recognize some of the configurations already +described, and will be the more willing to believe that a momentary view +is after all sufficient to give much information if one is on the alert +and has acquired skill by practice. + +The general features of the splash that we have examined are not merely +characteristic of the liquid mercury, but belong to all splashes of a +liquid falling on to a surface which it does not wet, provided the +height of fall or size of the drop are not so great as to cause complete +disruption,[2] in which case there is no recovery and rebound. Thus a +drop of milk falling on to smoked glass will, if the height of fall and +size of drop are properly adjusted, give forms very similar to those +presented by a drop of mercury. The whole course of the phenomenon +depends, in fact, mainly on four quantities only: (1) the size of the +drop; (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 water +falling into water. + +In order the better to distinguish the liquid of the original drop from +that into which it falls, the latter was coloured with ink or with an +aniline dye, and the drop itself was of water rendered turbid with +finely-divided matter in suspension. Finally drops of milk were found to +be very suitable for the purpose, the substitution of milk for water not +producing 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 central +white patch represents the original drop, and the white parts round it +represent those raised portions of the liquid which catch the light. The +numbers under each figure give the time interval in seconds from the +occurrence of the first figure, or of the figure marked [Tau] = 0.] + + +SERIES II. + +_The Splash of a Drop, followed in detail by Instantaneous +Illumination._ + +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, and +descends at the bottom of a hollow with a raised beaded edge (Fig. 2). +This edge would be smooth and circular but for the instability which +causes it to topple into drops. As the drop descends the hollow becomes +wider and deeper, and finally closes over the drop (Fig. 3), which, +however, soon again emerges as the hollow flattens out, appearing first +near, but still below the surface (Fig. 4), in a flattened, lobed form, +afterwards rising as a column somewhat mixed with adherent water, in +which traces of the lobes are at first very visible. + +The rising column, which is nearly cylindrical, breaks up into drops +before or during its subsequent descent into the liquid. As it +disappears below the surface the outward and downward flow causes a +hollow to be again formed, up the sides of which an annulus of milk is +carried, while the remainder descends to be torn again a second time +into a vortex ring, which, however, is liable to disturbance from the +falling in of the drops which once formed the upper part of the +rebounding column. + +It is not difficult to recognize some features of this splash without +any apparatus beyond a cup of tea and a spoonful of milk. Any drinker of +afternoon tea, after the tea is poured out and before the milk is put +in, may let the milk fall into it drop by drop from one or two inches +above it. The rebounding column will be seen to consist almost entirely +of milk, and to break up into drops in the manner described, while the +vortex ring, whose core is of milk, may be seen to shoot down into the +liquid. But this is better observed by dropping ink into a tumbler of +clear water. + +Let us now increase the height of fall to 17 inches. Series III. +exhibits the result. All the characteristics of the last splash are +more strongly marked. In Fig. 1 we have caught sight of the little +raised rim of the hollow before it was headed, but in Fig. 2 special +channels of easiest flow have been already determined. The number of +ribs and rays in this basket-shaped hollow seemed to vary a good deal +with different drops, as also did the number of arms and lobes seen in +later figures, in a somewhat puzzling manner, and I made no attempt to +select drawings which are in agreement in this respect. It will be +understood that these rays contain little or none of the liquid of the +drop, which remains collected together in the middle. Drops from these +rays or from the larger arms and lobes of subsequent figures are often +thrown off high into the air. In Figs. 3 and 4 the drop is clean gone +below the surface of the hollow, which is now deeper and larger than +before. The beautiful beaded annular edge then subsides, and in Fig. 5 +we see the drop again, and in Fig. 6 it begins to emerge. But although +the drop has fallen from a greater height than in the previous splash, +the energy of the impact, instead of being expended in raising the same +amount of liquid to a greater height, is now spent in lifting a much +thicker 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 water +to flow up past the milk, which, still comparatively unmixed with water, +rides triumphant on the top of the emergent column. The greater relative +thickness of this column prevents it splitting into drops, and Figs. 10 +and 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. 12 +and 13), having been detached from the central mass, which descends to +be torn again, this time centrally into a well-marked vortex ring. + + +SERIES III. + +_The Splash of a Drop, followed in detail by Instantaneous +Illumination._ + +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 something +over a yard, no great change occurs in the nature of the splash, but the +emergent column is rather higher and thinner and shows a tendency to +split into drops. + +When, however, we double the volume of the drop and raise the height of +fall to 52 inches, the splash of Series IV. is obtained, which is +beginning to assume quite a different character. The raised rim of the +previous series is now developed into a hollow shell of considerable +height, which tends to close over the drop. This shell or dome is a +characteristic feature of all splashes made by large drops falling from +a considerable height, and is extremely beautiful. In the splash at +present under consideration it does not always succeed in closing +permanently, but opens out as it subsides, and is followed by the +emergence of the drop (Fig. 8). In Fig. 9 the return wave overwhelms the +drop for an instant, but it is again seen at the summit of the column in +Fig. 10. + + +SERIES IV. + +_The Splash of a Drop, followed in detail by Instantaneous +Illumination._ + +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 closes +permanently over the imprisoned air, the liquid then flowing down the +sides, which become thinner and thinner, till at length we are left with +a large bubble floating on the water (see Series V.). It will be +observed that the flow of liquid down the sides is chiefly along +definite channels, which are probably determined by the arms thrown up +at an earlier stage. The bubble is generally creased by the weight of +the liquid along these channels. It must be remembered that the base of +the bubble is in a state of oscillation, and that the whole is liable to +burst at any moment, when such figures as 6 and 7 of the previous series +will be seen. + +[Illustration: SERIES V. + +_The Splash of a Drop, followed in detail by Instantaneous +Illumination._ + +The Size of Drop and Height of Fall are the same as before, but the +hollow shell (see figs. 4 and 5 of the previous Series) does not succeed +in opening, but is left as a bubble on the surface. This explains the +formation 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-drops +leave on the smooth water of a lake, or pond, or puddle. Only the bigger +drops can do it, and reference to the number at the side of Fig. 5 of +Series IV. shows that the dome is raised in about two-hundredths of a +second. Should the domes fail to close, or should they open again, we +have the emergent columns which any attentive observer will readily +recognize, and which have never been better described than by Mr. R.L. +Stevenson, who, in his delightful _Inland Voyage_, speaks of the surface +of the Belgian canals along which he was canoeing, as thrown up by the +rain 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 more +mobile liquid, petroleum. + +It will now be interesting to turn to the splash that is produced when a +solid sphere, such as a child's marble, falls into water. + +I found to my great surprise that the character of the splash, at any +rate up to a height of 4 or 5 feet, depends entirely on the state of the +surface of the sphere. A polished sphere of marble about 0.6 of an inch +in diameter, rubbed very dry with a cloth just beforehand and dropped +from a height of 2 feet into water, gave the figures of Series VI., in +which it is seen that the water spreads over the sphere so rapidly, that +it is sheathed with the liquid even before it has passed below the +general level of the surface. The splash is insignificantly small and of +very short duration.[3] If the drying and polishing be not so perfect, +the configurations of Series VII. are produced; while if the sphere be +roughened with sandpaper, or _left wet_, Series VIII. is obtained, in +which it will be perceived that, as was the case with the liquid drop, +the water is driven away laterally, forming the ribbed basket-shaped +hollow, which, however, is now prolonged to a great depth, the drop +being followed by a cone of air, while the water seems to find great +difficulty in wetting the surface completely. Part of this column of air +was carried down at least 16 inches, and then only detached when the +sphere struck the bottom of the vessel. + + +SERIES VI., VII. + +_Splash of a Solid Sphere (a marble 1/2 inch in diameter falling 2 feet +into 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 always +happen, for the walls often closed over the hollow exactly as in Figs. 4 +and 5 of Series IV. Meanwhile the long and nearly cylindrical portion +below breaks up into bubbles which rise quickly to the surface. + +By increasing the fall to 5 feet we obtain the figures of Series IX. The +tube of Fig. 1 corresponds to the dome of Series IV. and V., and is not +only 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. Similar +results were obtained with other liquids, such as petroleum and alcohol. + +It is easy to show in a very striking manner the paramount influence of +the condition of the solid surface. I have here a number of similar +marbles; this set has been well polished by rubbing with wash leather. I +drop 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 trace +of splash. Now I pick them out and drop them in again (or to save +trouble, I drop in the place of these other wet ones), everything is +changed. You see how the air is carried to the very bottom of the +vessel, and you hear the "phloisbos" of the bubbles as they +rise to the surface and burst. These dry but rough marbles behave in +much the same way. + +Such are the main features of the Natural History of Splashes, as I made +it out between thirteen and eighteen years ago. Before passing on to the +photographs that I have since obtained, I desire to add a few words of +comment. I have not till now alluded to any imperfections in the timing +apparatus. But no apparatus of the kind can be absolutely perfect, and, +as a matter of fact, when everything is adjusted so as to display a +particular stage, it will happen that in a succession of observations +there is a certain variation in what is seen. Thus the configuration +viewed may be said to oscillate slightly about the mean for which the +apparatus is adjusted. Now this is due both to small imperfections in +the timing apparatus and to the fact that the splashes themselves do +actually vary within certain limits. The reasons are not very far to +seek. In the first place the rate of demagnetization of the +electro-magnets varies slightly, being partly dependent on the varying +resistance of the contacts of crossed wires, partly on the temperature +of the magnet, which is affected by the length of time for which the +current has been running. But a much more important reason is the +variation of the slight adhesion of the drop to the smoked watch-glass +that has supported it, and consequently of the oscillations to which, as +we shall see, the drop is subjected as it descends. Thus the drop will +sometimes strike the surface in a flattened form, at others in an +elongated form, and there will be a difference, not only in the time of +impact, but in the nature of the ensuing splash; consequently some +judgment is required in selecting a consecutive series of drawings. The +only way is to make a considerable number of drawings of each stage, and +then to pick out a consecutive series. Now, whenever judgment has to be +used, there is room for error of judgment, and moreover, it is +impossible to put together the drawings so as to tell a consecutive +story, without being guided by some theory, such as I have already +sketched, as to the nature of the motion and the conditions that govern +it. You will therefore be good enough to remember that this chronicle of +the events of a tenth of a second is not a mechanical record but is +presented by a fallible human historian, whose account, like that of +any other contemporary observer, will be none the worse for independent +confirmation. That confirmation is fortunately obtainable. In an attempt +made eighteen years ago to photograph the splash of a drop of mercury, I +was unable to procure plates sufficiently sensitive to respond to the +very short exposures that were required, and consequently abandoned the +endeavour. But in recent years plates of exquisite sensitiveness have +been produced, and such photographs as those taken by Mr. Boys of a +flying rifle bullet have shown that difficulties on the score of +sensitiveness 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 same +makers, and as a developer, Eikonogen solution of triple strength, in +which the plates were kept for about 40 minutes, the development being +conducted in complete darkness. + +A few preliminary trials with the self-induction spark produced at the +surface of mercury by the apparatus that you have seen at work, showed +that the illumination, though ample for direct vision, was not +sufficient for photography. When the current strength was increased, so +as to make the illumination bright enough for the camera, then the spark +became of too great duration, for it lasted for between 4 and 5 +thousandths of a second, within which time there was very perceptible +motion of the drop and consequent blurring. It was therefore necessary +to modify the apparatus so as to employ a Leyden-jar spark whose +duration was probably less than 10-millionths of a second. A very +slight change in the apparatus rendered it suitable for the new +conditions, but time does not permit me to describe the arrangements in +detail. It is, however, less necessary to do so as the method is in all +essentials the same as that described in this room two years ago by Lord +Rayleigh 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 shadow +photographs; they were obtained by allowing a drop of mercury to fall on +to the naked photographic plate itself, the illuminating spark being +produced vertically above it, and they give only a horizontal section of +the drop in various stages, revealing the form of the outline of the +part in contact with the plate, but of course telling nothing about the +shape of the parts above. The first series corresponds to a mercury +splash very similar to that first described, and the second to the +splash of a larger drop such as was not described. In each series, the +tearing of the thin central film to which allusion was made is well +illustrated. I think the first comment that any one would make is that +the photographs, while they bear out the drawings in many details, show +greater irregularity than the drawings would have led one to expect. On +this point I shall presently have something to say. + + +SERIES X. + +(1) _Instantaneous Shadow Photographs (life size) of the Splash of a +Drop 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 a +Drop 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 of +Series 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 the +resemblance. + + +SERIES XII. + +_Engravings from Instantaneous Photographs (16/17 of the real size) of +the 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 the +camera. Only the first of this series shows any detail in the interior. +The polished surface of the mercury is, in fact, very troublesome to +illuminate, and this splash proved the most difficult of all to +photograph. + +Series XIII. shows the splash of a drop of milk falling on to a smoked +glass plate, on which it runs about without adhesion just as mercury +would. Here there is more of detail. In Fig. 4 the central film is so +thin in the middle that the black plate beneath it is seen through the +liquid. In Fig. 8 this film has been torn. + +Series XIV. exhibits the splash of a water drop falling into milk. The +first four photographs show the oscillations of the drop about a mean +spherical figure as it approaches the surface. + +In the subsequent figures it will be noticed that the arms which are +thrown up at first, afterwards segment into drops which fly off and +subside (see Fig. 8), to be followed by a second series which again +subside (Fig. 11), to be again succeeded by a third set. In fact, so +long as there is any downward momentum the drop and the air behind it +are penetrating the liquid, and so long must there be an upward flow of +displaced liquid. Much of this flow is seen to be directed into the arms +along the channels determined by the segmentation of the annular rim. +This reproduction of the lobes and arms time after time on a varying +scale goes far to explain the puzzling variations in their number which +I mentioned in connection with the drawings. I had not, indeed, +suspected this, which is one of the few new points that the photographs +have so far revealed.[5] + + +SERIES XIII. + +_Engravings of Instantaneous Photographs (16/17 of the real size) of the +Splash 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 missing +figures 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 of +Water 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 you +will attribute firstly to the inventors of the sensitive plates, and +secondly to the skill and experience of Mr. Cole, I desire to add that +they are, as far as we know, the first really detailed objective views +that have been obtained with anything approaching so short an exposure. + +Even Mr. Boys' wonderful photographs of flying bullets were after all +but shadow-photographs, and did not so strikingly illustrate the +extreme sensitiveness of the plates, and I want you to distinguish +between 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 and +rays as shown by the photographs. The point is a curious and interesting +one. In the first place I have to confess that in looking over my +original drawings I find records of many irregular or unsymmetrical +figures, yet in compiling the history it has been inevitable that these +should be rejected, if only because identical irregularities never +recur. 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 very +difficult to detect irregularity. This is easily proved by projecting +on the screen with instantaneous illumination such a photograph as that +of Series X., Fig. 6. My experience is that most persons pronounce what +they have seen to be a regular and symmetrical star-shaped figure, and +they are surprised when they come to examine it by detail in continuous +light to find how far this is from the truth. Especially is this the +case if no irregularity is suspected beforehand. I believe that the +observer, usually finding himself unable to attend to more than a +portion of the rays in the system, is liable instinctively to pick out +for attention a part of the circumference where they are regularly +spaced, and to fill up the rest in imagination, and that where a ray may +be really absent he prefers to consider that it has been imperfectly +viewed. + +This opinion is confirmed by the fact that in several cases, I have +been able to observe with the naked eye a splash that was also +simultaneously photographed, and have made the memorandum "quite +regular," though the photograph subsequently showed irregularity. It +must, however, be observed that the absolute darkness and other +conditions necessary for photography are not very favourable for direct +vision. + +And now my tale is told, or rather as much of it as the limits of the +time allowed me will permit. I think you will agree that the phenomena +are very beautiful, and that the subject, commonplace and familiar +though 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 Liquid +Annulus," _Proceedings Royal Society_, No. 200, p. 49 (1879). + +[2] Readers who wish a more detailed account of a greater variety of +splashes are referred to papers by the author. _Proceedings Royal +Society_, vol. xxv. pp. 261 and 498 (1877); and vol. xxxiv. p. 217 +(1882). + +[3] Photographs obtained since this was written show that much may +happen after the stages here traced. + +[4] A detailed account of the optical, mechanical, and electrical +arrangements 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 due +to particles of lamp-black carried down by the drop from the surface of +the smoked watch-glass on which it rested. + +[6] Three of these photographs, viz. Nos. 11, 12, and 17, are reproduced +full size, as a frontispiece, by a _photographic_ process, to enable the +reader to form a more correct idea than can be gathered from the +engravings, of the amount of detail actually obtained, though even in +these reproductions much is inevitably lost. + + + + +THE ROMANCE OF SCIENCE. + +_Small post 8vo. Illustrated. Cloth boards._ + + _s. d._ + + Coal; and What We get from It. + By Professor RAPHAEL MELDOLA, F.R.S., F.I.C. 2 6 + + Colour Measurement and Mixture. + By Captain W. DE W. ABNEY, C.B., R.E., F.R.S. 2 6 + + Diseases of Plants. + By H. MARSHALL WARD, M.A., F.R.S., F.L.S. 2 6 + + Our Secret Friends and Foes. + By PERCY FARADAY FRANKLAND, Ph.D., B.Sc. (Lond.), + F.R.S. Second Edition, revised and enlarged 3 0 + + Soap Bubbles and the Forces which Mould Them. + By C.V. BOYS, A.R.S.M., F.R.S. 2 6 + + Spinning Tops. + By Professor J. 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