The reader's attention has now been directed to various features which, with certain modifications, will be found in many of the splashes that we shall examine; but so far the language used has been simply descriptive and in no way explanatory. Instead of going on to describe other splashes in the same way, and thus to accumulate a great mass of uncoÖrdinated descriptive detail, it will be better to pause for a moment in order to become acquainted with certain principles connected with the behaviour of liquids, the application of which will go a long way towards explaining what we see going on in any splash.

The first principle to be understood is that the surface layers of any liquid behave like a uniformly stretched skin or membrane, which is always endeavouring to contract and to diminish its area. If the surface is flat, like the surface of still liquid in a bowl, this surface-tension has only the effect of exerting a small inward pull on the walls of the bowl. But if the surface is curved, with a convexity outwards, then the surface layers, on account of their tension, press the interior liquid back, and thus tend to check the growth of any protuberance; while, on the other hand, if the surface is concave outwards, then the surface-tension tends to pull the interior liquid forward, and so to diminish the concavity.

Direct evidence of this surface-tension is easy to cite. We have it in any pendent drop, such as any of those shown in the accompanying figures.

If we ask ourselves how it is that the liquid in the interior of one of these drops does not flow out, pressed as it is by the liquid above it, the answer is that everywhere the stretched skin presses it back. A soap-bubble too presses on the air in its interior, both the outside layers and the inside layers of the thin film being curved over the interior space. This is the reason that a soap-bubble blown on the bowl of a pipe will slowly collapse again if we remove the stem of the pipe from our mouth. The bubble drives the interior air back through the pipe. And it is easy to show that if two soap-bubbles be blown on the ends of two tubes which can be connected together by opening a tap between them, then the smaller will collapse and blow out the larger. The reason of this is that in the bubble of smaller radius the surface layers are more sharply curved, and therefore exert a greater pressure on the air within. Thus if a strap be pulled at each end with a total tension T and bent over a solid cylinder of small radius, as in Fig. 6, it is easy to see that the pressure on the surface of the part of the cylinder touched by the strap is less than if the strap be bent over an equal area on a cylinder of larger radius (Fig. 7). The tension of the surface layers of a liquid causes them to act on the liquid within, exactly as does the stretched strap on the solid in these figures. If at any place the liquid presents, as it generally does, not a cylindrical surface, but one with curvature in two directions, then the pressure corresponds to what would be produced by two straps crossing at right angles, laid one over the other, each with the curvature of the surface in its direction (Fig. 8).

We can now understand why the drop that has been lying on the watch-glass should oscillate in its descent. The sharp curvature of the edge AA of the drop (see Fig. 9) tells us that the liquid there is pushed back by the pressure of the stretched surface layers, and when the supporting glass is removed the sides of the drop move inwards, driving the liquid into the lower part, the tendency being to make the drop spherical, and so to equalize the pressure of the surface at all points. But in the process the liquid overshoots the mark, and the drop becomes elongated vertically and flattened at the sides. This causes the curvature at top and bottom to be sharper than at the sides, and on this account the back-pressure of the ends soon checks the elongation and finally reverses the flow of liquid, and the drop flattens again. As an example of the way in which a concavity of the surface is pulled out by the surface-tension may be cited the dimples made by the weight of an aquatic insect, where its feet rest on the surface without penetrating it.

This same surface-tension checks the rise of the crater, and would cause it to subside again even without the action of gravity. Thus the pressures of the sharply curved crater-edge on the liquid between the crater walls are indicated by the dotted arrows in Fig. 10, and arise from the surface-tension indicated by the full arrows. During the early part of the splash the surface-tension is more important than gravity in checking the rise of the walls. For, as the numbers show, the crater of Series I is already at about its maximum height in No. 4, i.e. about seven-thousandths of a second after first contact. In this time the fall due to gravity would be only about 1/100 of an inch. Thus if gravity had not acted the crater would only have risen about 1/100 of an inch higher. The same reasoning applies to the rise of the central column, but here the curvature at the summit is much less sharp. The numbers show that the column reaches its maximum height in about 5/100 of a second after its start in No. 10, and in this time the fall due to gravity is about half an inch, so that gravity has reduced the height by this amount.

The second principle which I will now mention enables us to explain the occurrence of the jets and rays at the edge of the crater and their splitting into drops.

It was shown in 1873 by the blind Belgian philosopher, Plateau,[D] that a cylinder of liquid is not a figure of stable equilibrium if its length exceeds about 3-1/7 times its diameter. Thus a long cylindrical rod of liquid, such as Fig. 11, if it could be obtained and left for a moment to itself, would at once topple into a row of sensibly equal, equidistant drops, the number of which is expressed by a very simple law, viz. that for every 3-1/7 times the diameter there is a drop, or that the distance between the centres of the drops is equal to the circumference of the cylinder.

The cause of this instability is the action of the same skin-tension that we have already spoken of. Calculation shows, and Plateau was able to confirm the calculation by experiment, that if through chance agitations lobes are formed at a nearer distance apart than 3-1/7 times the radius, with hollows between as in the accompanying Fig. 12, then the curvatures will be such as to make the skin-tension push the protuberances back and pull the hollows out. But if the protuberances occur at any greater distances apart than the length of the perimeter, then the sharper curvature of the narrower parts will drive the liquid there into the parts already wider, thus any such an initial accidental inequality of diameter will go on increasing, or the whole will topple into drops.

At the last moment the drops are joined by narrow necks of liquid (Fig. 13), which themselves split up into secondary droplets (Fig. 14).

What we have said of a straight liquid cylinder applies also to an annulus of liquid made by bending such a cylinder into a ring. This also will spontaneously segment or topple into drops according to the same law.[E] Now the edge of the crater is practically such a ring, and it topples into a more or less regular set of protuberances, the liquid being driven from the parts between into the protuberances.

Now while the crater is rising the liquid is flowing up from below towards the rim, and the spontaneous segmentation of the rim means that channels of easier flow are created, whereby the liquid is driven into the protuberances, which thus become a series of jets. These are the jets or arms which we see at the edge of the crater. Examination with a lens of some of the craters will show that the lines of easier flow leading to a jet are often marked by streaks of lamp-black in Series I, or by streaks of milk in Series II. This explanation of the formation of the jets applies also to a similar phenomenon on a much larger scale, with which the reader will be already familiar. If he has ever watched on a still day, on a straight, slightly shelving sandy shore, the waves that have just impetus enough to curl over and break, he will have noticed that up to a certain moment the wave presents a long, smooth, horizontal cylindrical edge (see Fig. 15a) from which, at a given instant, are shot out an immense array of little jets which speedily break into foam, and at the same moment the back of the wave, hitherto smooth, is seen to be furrowed or combed (see Fig. 15b). The jets are due to the segmentation of the cylindrical rim according to Plateau's law, and the ridges between the furrows mark the lines of easier flow determined by the position of the jets.

The tendency of the central column of Series I to separate into two parts is only another illustration of the same instability of a liquid cylinder. The column, however, is much thicker than the jets, and its surface is therefore less sharply curved, and consequently the inward pressure of the stretched curved surface is relatively slight and the segmentation proceeds only slowly. Since this segmentation must originate in some accidental tremor, we see how it is that the summit of the column may succeed in separating off on some occasions and not on others. As a matter of fact, the height of fall for this particular splash was purposely selected, so that the column thrown up should just not succeed in dividing in order that the formation of the subsequent ripples might not be disturbed by the falling in of the drops split off. But, as the reader will have perceived, the margin allowed was not quite sufficient.

The two principles that I have now explained, viz. the principle of the skin-tension, and the principle of the instability and spontaneous segmentation of a liquid cylinder, jet, or annulus, will go far to explain much that we shall see in any splash, but it is well that the reader should realize how much has been left unexplained. Why, for example, should the crater rise so suddenly and vertically immediately round the drop as it enters? Why should the drop spread itself out as a lining over the inside of the crater, turning itself inside out, as it were, and making an inverted umbrella of itself? Why when the crater subsides should it flow inwards rather than outwards, so as to throw up such a remarkable central column?

These questions, which demand that we should trace the motion of every particle of the water back to the original impulse given by the impact of the drop, are much more difficult to answer, and can only be satisfactorily dealt with by a complicated mathematical analysis. Something, however, in the way of a general explanation will be given in a later chapter.