FOOTNOTES:

FOOTNOTES:[G]Some useful information about the internal flow of the liquid was obtained by the device of letting the sphere descend between two slowly ascending streams of very minute bubbles liberated by electrolysis at two electrodes placed in the liquid. These streams, initially straight and vertical, were displaced and distorted as the sphere passed near them and afforded a measure of the displacement of the fluid at different points. For details seePhil. Trans. Roy. Soc., Vol. 194, p. 178 (1900).[H]Glycerine was found to be a rather treacherous liquid, requiring special precautions for which the reader who desires details is referred to the original memoir.Phil. Trans. Roy. Soc., Series A, 1900. Vol. 194, p. 198.

[G]Some useful information about the internal flow of the liquid was obtained by the device of letting the sphere descend between two slowly ascending streams of very minute bubbles liberated by electrolysis at two electrodes placed in the liquid. These streams, initially straight and vertical, were displaced and distorted as the sphere passed near them and afforded a measure of the displacement of the fluid at different points. For details seePhil. Trans. Roy. Soc., Vol. 194, p. 178 (1900).

[H]Glycerine was found to be a rather treacherous liquid, requiring special precautions for which the reader who desires details is referred to the original memoir.Phil. Trans. Roy. Soc., Series A, 1900. Vol. 194, p. 198.

I have some hope that, by the enumeration of the many surprising and puzzling facts mentioned in the last chapter, I may have succeeded in producing in the mind of my reader some sympathy with the state of perplexity of Mr. Cole and myself when, after four years of experimenting, we found ourselves still unable to answer the question, "Why does the rough sphere make one kind of splash, the smooth sphere another kind?"

By reflecting, however, on all the facts at our disposal, we were at last led to what seems to be an entirely satisfactory explanation, and one moreover which we were able to test by further experiment.

This explanation may be stated as follows:—

When a sphere, either rough or smooth, first strikes the liquid, there is an impulsive pressure between the two, and the column of liquid lying vertically below the elementary area of first contact is compressed. For very rapid displacements the liquid on account of its viscosity behaves like a solid. In the case of a solid rod we know that the head would be somewhat flattened out by a similar blow, and a wave ofcompression would travel down it; to this flattening or broadening out of the head of the column corresponds the great outward radial velocity, tangential to the surface, initiated in the liquid, of which we have abundant evidence in many of the photographs. (See pp.75,87, and99.)

Into this outward-flowing sheath the sphere descends, and since each successive zone of surface which enters is more nearly parallel to the direction of motion of the sphere, the displacement of liquid is most rapid at the lowest point, from the neighbourhood of which fresh liquid is supplied to flow along the surface. Whether the rising sheath shall leave the surface of the sphere, or shall follow it, depends upon the efficiency of the adhesion to the sphere. If the sphere is smooth and clean, the molecular forces of cohesion will guide the nearest layers of the advancing edge of the sheath, and will thus cause the initial flow to be along the surface of the sphere.

To pull any portion of the advancing liquid out of its rectilinear path the sphere must have rigidity. If the advancing liquid meets loosely attached particles, e.g. of dust, these will constitute places of departure from the surface of the sphere; the dust will be swept away by the momentum of the liquid which, being no longer in contact with the sphere, perseveres in its rectilinear motion. If the dust particles are few and far between, the cohesion of the neighbouring liquid will bring back the deserting parts, but if the places of departure are many, then the momentum of the deserters will prevail. Thus at every instantthere is a struggle between the momentum of the advancing edge of the sheath and the cohesion of the sphere; the greater the height of fall the greater will be the momentum of the rising liquid, and the less likely is the cohesion to prevail, and the presence or absence of dust particles may determine the issue of the struggle.

Roughness of the surface will be equally efficient in causing the liquid to leave the sphere. For the momentum will readily carry the liquid past the mouth of any cavities (see Fig. 20), into which it can only enter with a very sharp curvature of its path. It is to be observed that the surface-tension of the air-liquid surface of the sheath will act at all times in favour of the cohesion of the sphere, and even if the film has left the sphere the surface-tension will tend to make it close in again, but we should not be right in attributing much importance to this capillary pressure which, with finite curvatures, is a force of a lower order of magnitude than the cohesion, and, as the photographs now to be shown will clearly show, is incompetent to produce the effects observed.

Fig. 20

Having arrived at this general explanation, we proceeded to test it.

EXPERIMENTS ON THE INFLUENCE OF DUST.

In the first place, to test the influence of dust, the experiment was made of deliberately dusting thesurface of the sphere. For this purpose a highly polished nickelled sphere was held in a pair of crucible tongs by an electrified person standing on an insulating stool, and by him presented to any dusty object that stood or could be brought within reach. Particles of dust soon settled on the electrified sphere, which was then carefully placed on the dropping ring with the dusty side lowest. The liquid used was paraffin oil, and the height of fall was 31·7 cm., at which this sphere when not dusted gave always a quite airless splash. When dusted an enormous bubble of air was carried down on each occasion. Although the sphere when laid on the dropping ring must have completely lost the electrical charge, yet it seemed worth while to go through the same electrifying process without dusting. The result showed that no change was produced. In order to see how far the influence of dust would go, the height of fall was now reduced, and it was found that with sphere (1) a fall of 17·1 cm. gave a perfectly rough splash when the surface was visibly dimmed with fine dust, and with a second similar sphere a fall of 16·7 cm. availed. If the surface was only slightly dusty, then at these low heights the splash remained "smooth."

It then occurred to us to try the effect of partial or local dusting, for we had already found by experimenting with a marked sphere that the method of dropping did not impart any appreciable rotation to the sphere, which reached the liquid in the attitude with which it started from the dropping ring.Accordingly, after dusting the sphere in the manner already described, the dust was carefully rubbed away from all but certain parts whose position was recorded. The experiments were very successful, and the results are shown onpage 113. The liquid used was water, and the sphere was of polished serpentine, 2·57 centim. in diameter, falling 14 centim.

In Fig. 1 of Series XVI the sphere was dusted on theright-hand side, and a "sound of splash" was recorded. On the left side we see that there is no disturbance of the "smooth splash"; on the right is a "pocket" of air such as was obtained by accident in Series IX, Fig. 6 (seep. 91). The point of departure at which the liquid left the sphere is well marked, and a tangent from this point passes through the outermost conspicuous droplets that must have been projected from it.

In Fig. 2 the sphere was dustedat the top and on the right-hand side, but not much more than half-way down, and the configuration corresponds entirely to the facts. Here again a tangent from the well-marked drops on the right-hand side leads very nearly to the place of departure from the surface of the sphere.

In Fig. 3 the sphere was dusted near the bottom only. The appearance on the left-hand side seems to show that the liquid has, after leaving the sphere, again been brought within reach. This recovery at an early stage is explained by reference to photographs of Series VI (p. 81) of the splash of a rough sphere, which show that even the rough sphere is soon wetted for some distance up the sides, by thegradual passage of the sphere into the divergently flowing cone of liquid which surrounds the lower part. When the liquid again touches a polished part the film will be again guided up it in the manner already explained.

SERIES XVI

Spheres dusted at one side.

We observe that in Figs. 1 and 2 (as also in Fig. 6 ofpage 91) the continuous film or shell of liquid no longer reaches the outermost droplets that once have been at its edge. It must evidently have been pulled in by its own surface-tension, which of course will cease to exercise any inward pull on a drop that has once separated.

The influence of dust, thus incontestably proved, seems also to afford a satisfactory explanation of—

(1) The effect of a flame.(2) The effect of heating.(3) The variable and uncertain effects of electrification.

(1) The effect of a flame.

(2) The effect of heating.

(3) The variable and uncertain effects of electrification.

For, (1), we may suppose that the flame burns off minute particles of dust; (2), we know from Aitken's experiments[I]that dust from the atmosphere will not settle on a surface hotter than the air; (3) an electrified sphere descending through the air would attract dust to its surface unless it happened, as well might happen, that the air round about it, with its contained dust, had become itself similarly charged through the working of the electrical machine.

In further confirmation of our view that the leading clue to the explanation of the motion is the struggle between the adhesion of the rigid sphere andthe tangential momentum of the liquid, we may cite the following points:—

Aliquidsphere makes a "rough" splash, and the photographs obtained show that the lower part of the in-falling drop is swept away by the tangential flow, while the upper part is still undistorted. Here we have cohesion but no rigidity.

Also we find that the "rough" splash is obtained by any process which gives a non-rigid surface to the sphere. Thus the splash made by a marble freshly roughened by sand-papering, or by grinding between two files and let fall from the very small height of 7·5 cm., can be practically controlled by attending to the condition of the surface. If the surface is quite dry and still covered with the fine powder resulting from the process of roughening, the splash is "rough," and a great bubble of air is taken down. But if this coat of powder, which has neither cohesion nor shearing strength, be removed by rubbing, the splash (under this low velocity) is "smooth." Again, a marble freshly sand-papered and covered with the resulting powder, if let fall from 12 or 15 cm., gives a rough splash. The same marble picked out of the liquid and very quickly dropped in again from the same height, will give again a rough splash. Here the liquid film is thick and "shearable." But if the same sphere be allowed to drain or be lightly wiped, the splash will be smooth. We may conjecture that in this case enough fluid is left to fill up the interstices, but that the coat is not thick enough to shear easily. If, however, the sphere be thoroughly dried, the splashbecomes "rough" again. This gives us the explanation of the facts already recorded in respect of the splash of a wet sphere. This splash was always irregular; the liquid drifted to one side where it would shear, while it disappeared from the other or became there too thin to shear, though sufficient to fill up crevices.

EXPLANATION OF THE RIBS OR FLUTINGS IN THE SPLASH OF A SMOOTH SPHERE.

The fact thus established experimentally, that the surface of a smooth sphere must be rigid if the film is to envelop it closely, suggests also a satisfactory explanation of the flutings. For we know from other researches on the motion of liquids,[J]that a layer of liquid actually in contact with a solid can have no motion relative to the solid, but must move with it. Thus in the film or sheath which rises over and envelops the sphere, the layer of liquid next to the solid must be moving downwards with it, while the outermost layers at least are moving upwards; thus there must be a strong viscous shear in the film impeding its rise. If by any fortuitous oscillation a radial rib arises, this will be a channel in which the liquid, being farther from the surface, will be less affected by the viscous drag; it will therefore be a channel of more rapid flow and diminished pressure, into which, therefore, the neighbouring liquid will be forced from either side. Thus a rib once formed is in stable equilibrium, and will correspond to a jet atthe edge of the rim. This explains the persistence of the ribs when once established, and we may attribute their regular distribution to the fact that they first originate in the spontaneous segmentation of the annular rim at the edge of the advancing sheath. This explanation quite accords with the appearance of such figures as Fig. 6 ofpage 91and Figs. 1 and 2 ofpage 113, in which, firstly, we see that the flutings are absent from that part of the sheath which has left the sphere, and, secondly, we see how much higher in every case the continuous film has risen in that part which has left the sphere than in the part which has clung to it, and has been hindered by the viscous drag. Especially is this the case in Fig. 2, Series XIV (p. 105), where the liquid was pure glycerine. The effect of the viscous drag is, in fact, most marked in the most viscous liquid, and it is also in the viscous liquid that the ribs are most strongly marked.

INFLUENCE OF THE NATURE OF THE LIQUID EXPLAINED.

Finally, in confirmation of our explanation, we have the fact that with a liquid of small density and surface-tension, such as paraffin oil, a much smaller velocity of impact with a highly polished sphere suffices to give a "rough" splash than with water, a liquid of greater density and surface-tension, the reason being without doubt that the tangential velocity given by the impact is greater with the lighter liquid, as, indeed, is proved to be the case by the greater height to which the surrounding sheath is thrown up. The surface-tension also being smaller, the less is the abatement of velocity on account of work done in extending the surface.

FOOTNOTES:[I]SeeNature, vol. xxix., January 31, 1884.[J]See Whetham on "The Alleged Slipping at the Boundary of a Liquid in Motion."Phil. Trans. Roy. Soc., Vol. 181 (1890).

[I]SeeNature, vol. xxix., January 31, 1884.

[J]See Whetham on "The Alleged Slipping at the Boundary of a Liquid in Motion."Phil. Trans. Roy. Soc., Vol. 181 (1890).

We have now reached the end of the story, as far at least as I am able to tell it. But there is certainly more to be found out. No one has yet examined what happens when a rough sphere enters a liquid with a very high velocity. That the motion set up must differ from that at a low velocity is apparent to any one who has thrown stones from a low bridge into deep water below. The stone that is thrown with a great velocity makes neither quite the same sound nor the same kind of splash as a slow-falling stone, and though in the light of our present knowledge we may conjecture the kind of difference to be expected, yet experience has taught me that the subject is so full of unexpected turns that it is better to wait for the photographic record than to speculate without it.

It would be an immense convenience, as was suggested in the first chapter, if we could use a kinematograph and watch such a splash in broad daylight, without the troublesome necessity of providing darkness and an electric spark. But the difficulties of contriving an exposure of the whole lens short enoughto prevent blurring, either from the motion of the object, or from that of the rapidly-shifting sensitive film, are very great, and any one who may be able to overcome them satisfactorily, will find a multitude of applications awaiting his invention.

But even were the photographic record complete, what does it amount to? All that we have done has been merely to follow the rapid changes of form that take place in the bounding surface of the liquid. The interior particles of the liquid itself have remained invisible to us. But it is precisely the motion of these particles that the student of hydrodynamics desires to be able to trace. His study is so difficult that even in the apparently simple case of the gently-undulating surface of deep water, the reasoning necessary to discover the real path of any particle can at present only be followed by the highly-trained mathematician. In other and more complicated cases such as are exemplified by the sudden disturbances that we have studied, any definite information that can be obtained, even as to the motion of the surface, may afford a clue to the solution of important questions; and I have been encouraged to hope that the observations here recorded may serve as a useful basis of experimental fact in a confessedly difficult subject.

To take a single illustration of a possible application in an unexpected quarter, I would invite the attention of the reader to the two photographs in thefrontispiece, which exhibit the splash of a projectile on striking the steel armour-plate of a battleship. These are ordinary photographs taken after the platehad been used as a target. They represent the side on which the projectile has entered. In one picture the projectile is still seen embedded in the plate.

No one looking at these photographs can fail to be struck with the close resemblance to some of the splashes that we have studied. There is the sameslightupheaval of the neighbouring surface, the same crater, with the same curled lip, leading to the inference that under the immense and suddenly applied pressure, the steel has behaved like a liquid.

Such flow of metals under great pressure is familiar enough to mechanical engineers, but what I desire to suggest is, that from a study of the motions set up in a liquid in an analogous case, it may be possible to deduce information about the distribution of internal stress, which may apply also to a solid, and may thus lead to improvements in the construction of a plate that is intended to resist penetration.

A slight delay in the passage of this book through the press has enabled me to obtain some of the missing information referred to in the opening paragraph of the last chapter.

If any reader who may have been persuaded to try for himself the simple experiment mentioned at the beginning of Chapter VII, will extend his observations by increasing the height of fall of the roughened marble to 4 or 5 feet (say to 140 centim.), he will find that while, as before, much air is still carried down, there is nevertheless, now, no rebounding jet projected high into the air, such as is invariably seen with the lower fall of 2 feet (60 centim.), and he will notice a curious "seething" appearance at the surface.[K]Thinking that this appearance which the naked eye detects must be due to an entanglement of the rising jet with the bubble, which entanglement was likely to produce confused motions that could not be profitably studied, I had not till now been sufficiently curious to examine what really happened. But certain recent observations of the persistence with which the seething motion again and again recurred when a stone was dropped or thrown into a river, led me to suspect that something required investigation. I was, however, quite unprepared to find the remarkable change of procedure that is revealed by the following series of photographs (Series XVII), in the taking of which I owe much to the kind and skilful assistance of Dr. Bryan. The earlier figures show the very rapid rise of the crater and its closing as a bubble much before the entrapped column of air divides. Before the division takes place, the liquid now flowing in from all sides closes over the upper end of the long air-tube, separates it from the air outside, andforms a downward jet which shoots down the middle of the air-tube in pursuit of the sphere. The first formation of this jet is not easy to observe, because the view is obscured by much splashing and turbulent vortical motion resulting apparently from the collision of the streams that converge from all sides on the axis of the air-tube at its upper end. Thus in Fig. 5 the jet is not yet well established, or at least not easily discerned; but in Fig. 6 the turbulence has cleared away from the upper part, and from this stage onwards the jet is well seen in all the figures, and it persists long after the segmentation of the air column has taken place. The reader must not suppose that this jet is a merefallingof the water under the action of gravity, for the rapidity with which it advances is far greater than could be accounted for in this way; indeed, as the "times" show, the effect of gravity during the establishment of the jet is insignificant.

SERIES XVII

Rough sphere falling 140 cm. into water. Scale 2/3.

The segmentation of the air column appears to be independent of the jet; but some photographs, such as Fig. 7, show the jet striking the side and breaking into the surrounding liquid with a great accompaniment of "air-dust."

SERIES XVII—(continued)

N.B.—Each of these figures is made up from two photographs; one of the upper and one of the lower portion taken from different splashes, but with the same "timing."

The reader will observe that after division of the air-tube has taken place, say from Fig. 9 onwards, the water entering the jet at the top and coming out again at the bottom must circulate as in a vortex ring, part of the core of which is filled with the air surrounding the jet.

It is also to be observed that after the establishment of the jet, there is a steady increase in the size of the heap above the surface; but it is not easy in any given photograph to say how much of this protuberance is air and how much is water. An examination of Figs. 7, 8, and 9 shows that the place of origin of the jet is gradually lifted above the level of the free surface.

That the jet we now see should be directed downwards rather than upwards may, I think, be explained in a general way as follows:—The great initial momentum of the sphere causes it to continue in rapid motion after the bubble has closed, thus the sphere acts as a sort of piston, which by increasing the length of the air-tube diminishes the pressure in it and so sucks in the bubble, which is driven down by the greater atmospheric pressure above. The converging horizontal inflow near the mouth of the air-tube cannot, of course, produce the downward-directed jet without an equal and opposite generation of momentum upwards; but this is now expended, not in producing a similar upward jet, but in balancing the excess of atmospheric pressure. The reaction, in fact, to the projection of the jet downwards, is the force which holds up and slowly raises the roof of the long air-shaft.

SERIES XVII—(continued)

When, as in the last figure of Series VI,p. 85, we saw the upward-directed jet, then also there must have been an equal and opposite generation of downward momentum distributed in some way through the liquid below the basin, of which, however, there could be no visible sign. Hence we see that the present downward jet is, in a sense, not a new phenomenon, but one which, having existed unnoticed before, is now rendered visible to us by reason of its being produced in air instead of in water.

By means of a hole bored through the ceiling of the dark room, the fall was then increased to 281 centim. (just over 9 feet). The very beautiful earlier stages of the splash at this height are shown in Series XVIII. Fig. 4 shows very well the internal splashing at the top of the air-column which accompanies the initiation of the jet. Some later photographs taken at this height (not yet quite presentable) show the jet passing right down the narrow neck of air-tube and probably striking the top of the sphere, the descent of which must thus be liable to a curious irregularity.

A further increase of the height of fall to 686 centim. (22-1/2 feet) was found to produce but little change in the phenomena.

SERIES XVIII

Early stages of the splash of a rough sphere (diam. 1·5 centim.) falling 281 centim. (about 9 feet) into water.

FOOTNOTES:[K]I can recommend any reader who is not afraid of being late for breakfast to keep a bag of marbles in his bath-room.

[K]I can recommend any reader who is not afraid of being late for breakfast to keep a bag of marbles in his bath-room.

PRINTED BYWILLIAM BRENDON AND SON, LTDPLYMOUTH

Transcriber's NoteThe following changes have been made to the original text.Page 10: "the same in 1, 3 and 4" changed to "the same in 1, 2 and 4"Page 66: "·04 of a gram" changed to "0·4 of a gram"Page 77: Added full stop to image caption 9 "0·042 sec."Page 103: Added label "2" to image caption

The following changes have been made to the original text.

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