1 T = 0 2 0001 sec.

3 0002 sec.

4 0003 sec.]

THE INFLUENCE OF TEMPERATURE.

It was found that if a polished sphere was heated in boiling water, quickly rubbed dry, and let fall while still hot, a very marked difference was produced. With the sphere hot, the height of fall can be much increased before the splash becomes "rough." Thus with paraffin oil, the height with a nickel-plated sphere rose from 222 cm. to 293 cm., and with water from 157 cm. to 234 cm.

THE REMARKABLE INFLUENCE OF A FLAME HELD NEAR THE LIQUID, AND TRAVERSED BY THE SPHERE IN ITS FALL.

In our search for the explanation of the difference between the rough and the smooth splash, it occurred to us to let the smooth sphere drop through a flame held near the liquid, and the result was very remarkable. With paraffin oil (and the sphere hot) the airless height now rose from 293 cm. to 453 cm., and with water and a cold sphere, it rose from 157 cm. to over 258 cm., which was the greatest height that the laboratory would permit. Either the luminous flame of a bat's-wing burner or the flame of a Bunsen burner held nearly horizontal produces the effect, provided the flame is held near enough to the surface of the liquid, and it is a very striking experiment to let the polished sphere fall several times from a height which gives a large volume of bubbles rising with much noise to the surface, and then to let it fall through the flame, and to observe the complete change in the phenomenon. On a sphere already roughened the flame has no observable effect.

THE SUPPOSITION OF ELECTRIFICATION TESTED AND REJECTED.

The behaviour with a flame led at first to the supposition that we had to deal with an electrical phenomenon, for a flame would certainly discharge completely any electrified sphere pa.s.sing through it, and it appeared reasonable to suppose that the sphere might become electrified by friction with the air through which it fell.

It required a long series of experiments, into the details of which I need not now ask my readers to enter, to prove that this tempting explanation was untenable, and that there was no reason to believe that electrification had anything to do with the matter.

EXPERIMENTS IN VACUO.

It remained to examine what part was played by the air in the whole transaction. This could only be settled by removing the air and letting the spheres, whether rough or smooth, fall through a vacuum into the liquid, or rather through a s.p.a.ce occupied only by the vapour of the liquid in use.

Instantaneous photographs obtained under these conditions showed that the presence of the air has no material influence on the early course of the splash, and that a sphere which gives a "smooth" splash in air will give a "smooth" splash in vacuo, while if the splash is "rough" in air, it will also be "rough" in vacuo.

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 pa.s.sed near them and afforded a measure of the displacement of the fluid at different points. For details see _Phil. 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.

CHAPTER IX

THE EXPLANATION OF THE CAUSE OF DIFFERENCE BETWEEN THE TWO SPLASHES

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 of compression 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, and 99.)

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 const.i.tute 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 instant there 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.

[Ill.u.s.tration: 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 the surface 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 317 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 171 cm. gave a perfectly rough splash when the surface was visibly dimmed with fine dust, and with a second similar sphere a fall of 167 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 att.i.tude 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 on page 113. The liquid used was water, and the sphere was of polished serpentine, 257 centim. in diameter, falling 14 centim.

In Fig. 1 of Series XVI the sphere was dusted on the _right-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 (see p. 91).

The point of departure at which the liquid left the sphere is well marked, and a tangent from this point pa.s.ses through the outermost conspicuous droplets that must have been projected from it.

In Fig. 2 the sphere was dusted _at 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 the gradual pa.s.sage 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.

[Ill.u.s.tration: SERIES XVI

Spheres dusted at one side.

1 2 3]

We observe that in Figs. 1 and 2 (as also in Fig. 6 of page 91) the continuous film or sh.e.l.l 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.

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 and the tangential momentum of the liquid, we may cite the following points:--

A _liquid_ sphere 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 75 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 splash becomes "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.