[Ill.u.s.tration: FIG. 13]
[Ill.u.s.tration: 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 sh.o.r.e, 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. 15-a) 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. 15-b). 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.
[Ill.u.s.tration: FIG. 15-b
FIG. 15-a
Diagrams of a breaking wave.]
The tendency of the central column of Series I to separate into two parts is only another ill.u.s.tration 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 a.n.a.lysis.
Something, however, in the way of a general explanation will be given in a later chapter.
FOOTNOTES:
[D] _Statique Experimentale et Theorique des Liquides._
[E] See Worthington on the "Segmentation of a Liquid Annulus," _Proc.
Roy. Soc._, No. 200, 1879.
CHAPTER IV
THE SPLASH CONTINUED
I have stated that the addition of the milk to the water made but little difference in the character of the resulting splash. It does, however, make certain differences in detail, as will be gathered from an examination of the next Series I-a, which shows the effect of letting the water-drop fall from the same height into water instead of into milk. Such a splash is difficult to photograph unless the illumination is from behind. As shown in this way, the early figures of the crater might be unintelligible to the reader had he not already studied the same crater lighted up from the side. Sometimes, though the front of the crater is hardly visible directly, yet every lobe on it can be clearly traced in the inverted image seen by reflection.
The most noticeable difference between the two splashes is perhaps the very much greater number of ripples seen with the splash in pure water.
This is partly because, with the illumination behind, such ripples are more easily visible, but arises chiefly from the fact that ripples are not so readily propagated over the surface of milk on account both of its smaller surface-tension and its greater viscosity. The first appearance of outward-spreading ripples is in No. 6, just round the subsiding crater.
[Ill.u.s.tration: SERIES I-a
Water into water (40 cm. fall). Scale 9/10.
1 T = 0 2 0004 sec.
3 0013 sec.
4 0018 sec.]
[Ill.u.s.tration: SERIES I-a--(_continued_)
5 0026 sec.
6 0042 sec.
7 0058 sec.
8 0073 sec.]
Since the origination of these ripples is an interesting phenomenon from a physical point of view, as throwing light on the dispersion of waves travelling with different velocities, special precautions were taken to secure the most favourable conditions, and in order to clean the surface after the arrival of each drop, which inevitably brings down a little adherent lamp-black, a continuous slow stream of fresh water was maintained which swept the contaminated surface-liquid away over the edge of the vessel.
The effect of this precaution is seen by a comparison of the photographs No. 11 and No. 11-a. In the first the surface was kept quite clean in the way described; in the second it had only been cleaned by skimming it with a fine wire-gauze dish.
The beginning of the descent of the first central column seems to be marked by the appearance of a slight depression round its base, which has just not begun in No. 11-a, and has just begun in No. 11, and goes on increasing in Figs. 12 and 13.
[Ill.u.s.tration: SERIES I-a--(_continued_)
Running water. Scale reduced to 6/10.
9 0087 sec.
10 0014 sec.
11 0139 sec.
11-a 0139 sec.]
[Ill.u.s.tration: SERIES I-a--(_continued_)
Running water. Scale 6/10.
12 0163 sec.
13 0185 sec.
14 0207 sec.
15 0227 sec.]
The same feature marks the beginning of the descent of the secondary central column, which is still rising in Fig. 17, is just poised in Fig.
18, and thence onwards shows a gradually increasing central depression.
These last four figures carry us to a rather later stage than was reached in Series I.
It should be noticed that in this Series the water-drop used was of smaller diameter than that of Series I, weighing 13 grams as against 2 grams. By employing the smaller drop, we diminish irregularities due to oscillations of form set up on release, for the smaller drop is more spherical when lying on the dropping cup than the larger; a few photographs taken for comparison with the full-sized drop showed, however, extremely little difference in the splashes at this height of fall.
[Ill.u.s.tration: SERIES I-a--(_continued_)
Still water. Scale 9/10.
16 0247 sec.
17 0266 sec.
18 0294 sec.]
[Ill.u.s.tration: SERIES I-a--(_continued_)
Still water. Scale 9/10.
19 0285 sec.