The Messrs. Weber have described in their 'Wellenlehre' an effect of wave-motion which it is very easy to obtain. When a boat moves through perfectly smooth water, and the rower raises his oar out of the water, drops trickle from its blade, and each drop where it falls produces a system of concentric rings. The circular waves as they widen become depressed, and, if the drops succeed each other with sufficient speed, the rings cross each other at innumerable points. The effect of this is to blot out more or less completely all the circles, and to leave behind two straight divergent ripple-lines, which are tangents to all the external rings; being in fact formed by the intersections of the latter, as a caustic in optics is formed by the intersection of luminous rays. [Fig. 48], which is virtually copied from M. Weber, will render this description at once intelligible. The boat is supposed to move in the direction of the arrow, and as it does so the rings which it leaves behind widen, and produce the divergence of the two straight resultant lines of ripple.
RIPPLES DEDUCED FROM RINGS.
The more quickly the drops succeed each other, the more frequent will be the intersections of the rings; but as the speed of succession augments we approach the case of a continuous vein of liquid; and if we suppose the continuity to be perfectly established, the ripples will still be produced with a smooth space between them as before. This experiment may indeed be made with a well-wetted oar, which on its first emergence from the water sends into it a continuous liquid vein. The same effect is produced when we substitute for the stream of liquid a solid rod—a common walking-stick for example. A water-fowl swimming in calm water produces two divergent lines of ripples of a similar kind.
We have here supposed the water of the lake to be at rest, and the liquid vein or the solid rod to move through it; but precisely the same effect is produced if we suppose the rod at rest and the liquid in motion. Let a post, for example, be fixed in the middle of a flowing river; diverging from that post right and left we shall have lines of ripples exactly as if the liquid were at rest and the post moved through it with the velocity of the river. If the same post be placed close to the bank, so that one of its edges only shall act upon the water, diverging from that edge we shall have a single line of ripples which will cross the river obliquely towards its centre. It is manifest that any other obstacle will produce the same effect as our hypothetical post. In the words of Professor Forbes, "the slightest prominence of any kind in the wall of such a conduit, a bit of wood or a tuft of grass, is sufficient to produce a well-marked ripple-streak from the side towards the centre."
MEASURE OF DIVERGENCE OF RIPPLES.
The foregoing considerations show that the divergence of the two lines of ripples from the central post, and of the single line in the case of the lateral post, have their mechanical element, if I may use the term, in the experiment of the Messrs. Weber. In the case of a swimming duck the connexion between the diverging lines of ripples and the propagation of rings round a disturbed point is often very prettily shown. When the creature swims with vigour the little foot with which it strikes the water often comes sufficiently near to the surface to produce an elevation,—sometimes indeed emerging from the water altogether. Round the point thus disturbed rings are immediately propagated, and the widening of those rings is the exact measure of the divergence of the ripple lines. The rings never cross the lines;—the lines never retreat from the rings.
RIPPLES AND VEINS DUE TO DIFFERENT CAUSES.
If we compare the mechanical actions here traced out with those which take place upon a glacier, I think it will be seen that the analogy between the ripples and the veined structure is entirely superficial. How the structure ascribed to the Glacier de Lys is to be explained I do not know, for I have never seen it; but it seems impossible that it could be produced, as ripples are, by a fixed obstacle which "cleaves a descending stream." No one surely will affirm that glacier-ice so closely resembles a fluid as to be capable of transmitting undulations, as water propagates rings round a disturbed point. The difficulty of such a supposition would be augmented by taking into account the motion of the individual liquid particles which go to form a ripple; for the Messrs. Weber have shown that these move in closed curves, describing orbits more or less circular. Can it be supposed that the particles of ice execute a motion of this kind? If so, their orbital motions may be easily calculated, being deducible from the motion of the glacier compounded with the inclination of the veins. If so important a result could be established, all glacier theories would vanish in comparison with it.
POSITION OF RIPPLES NOT THAT OF STRUCTURE.