Part 33 (1/2)
[B] 'Proceedings of the Royal Inst.i.tution,' vol. ii. p. 324.
THE RIPPLE-THEORY OF THE VEINED STRUCTURE.
(29.)
[Sidenote: THEORY STATED.]
[Sidenote: THEORY EXAMINED.]
The a.s.sumption of oblique sliding, and the production thereby of the marginal structure, have, however, been fortified by considerations of an ingenious and very interesting kind. ”How,” I have asked, ”can the oblique structure persist across the lines of greatest differential motion throughout the length of the glacier?” But here I am met by another question which at first sight might seem equally unanswerable--”How do ripple-marks on the surface of a flowing river, which are nothing else than lines of differential motion of a low order, cross the river from the sides obliquely, while the direction of greatest differential motion is parallel to the sides?” If I understand aright, this is the main argument of Professor Forbes in favour of his theory of the oblique marginal structure. It is first introduced in a note at page 378 of his 'Travels;' he alludes to it in a letter written the following year; in his paper in the 'Philosophical Transactions' he develops the theory. He there gives drawings of ripple-marks observed in smooth gutters after rain, and which he finds to be inclined to the course of the stream, exactly as the marginal structure is inclined to the side of the glacier. The explanation also embraces the case of an obstacle placed in the centre of a river. ”A case,” writes Professor Forbes, ”parallel to the last mentioned, where a fixed obstacle cleaves a descending stream, and leaves its trace in a fan-shaped tail, is well known in several glaciers, as in that at Ferpecle, and the Glacier de Lys on the south side of Monte Rosa; particularly the last, where the veined structure follows the law just mentioned.” In his Twelfth Letter he also refers to the ripples ”as exactly corresponding to the position of the icy bands.” In his letter to Dr. Whewell, published in the 'Occasional Papers,' page 58, he writes as follows:--”The same is remarkably shown in the case of a stream of water, for instance a mill-race. Although the movement of the water, as shown by floating bodies, is exceedingly nearly (for small velocities sensibly) parallel to the sides, yet the variation of the speed from the side to the centre of the stream occasions a _ripple_, or molecular discontinuity, which inclines forwards from the sides to the centre of the stream at an angle with the axis depending on the ratio of the central and lateral velocity. The veined structure of the ice corresponds to the ripple of the water, a molecular discontinuity whose measure is not comparable to the actual velocity of the ice; and therefore the general movement of the glacier, as indicated by the moraines, remains sensibly parallel to the sides.” This theory opens up to us a series of interesting and novel considerations which I think will repay the reader's attention. If the ripples in the water and the veins in the ice be due to the same mechanical cause, when we develop clearly the origin of the former we are led directly to the explanation of the latter. I shall now endeavour to reduce the ripples to their mechanical elements.
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.
[Sidenote: RIPPLES DEDUCED FROM RINGS.]
[Ill.u.s.tration: Fig. 48. Diagram explanatory of the formation of Ripples.]
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 s.p.a.ce 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 subst.i.tute 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 gra.s.s, is sufficient to produce a well-marked ripple-streak from the side towards the centre.”
[Sidenote: 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.
[Sidenote: 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 a.n.a.logy 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.
[Sidenote: POSITION OF RIPPLES NOT THAT OF STRUCTURE.]
There is another interesting point involved in the pa.s.sage above quoted.
Professor Forbes considers that the ripple is occasioned by the variation of speed from the side to the centre of the stream, and that its _inclination_ depends on the ratio of the central and lateral velocity. If I am correct in the above a.n.a.lysis, this cannot be the case. The inclination of the ripple depends solely on the ratio of the river's translatory motion to the velocity of its wave-motion. Were the lateral and central velocities alike, a momentary disturbance at the side would produce a _straight_ ripple-mark, whose inclination would be compounded of the two elements just mentioned. If the motion of the water vary from side to centre, the velocity of wave-propagation remaining constant, the inclination of the ripple will also vary, that is to say, we shall have a _curved_ ripple instead of a straight one.
This, of course, is the case which we find in Nature, but the curvature of such ripples is totally different from that of the veined structure.
Owing to the quicker translatory movement, the ripples, as they approach the centre, tend more to parallelism with the direction of the river; and after having pa.s.sed the centre, and reached the slower water near the opposite side, their inclination to the axis gradually augments.
Thus the ripples from the two sides form a pair of symmetric curves, which cross each other at the centre, and possess the form _a o b_, _c o d_, shown in Fig. 49. A similar pair of curves would be produced by the reflection of these. Knowing the variation of motion from side to centre, any competent mathematician could find the equation of the ripple-curves; but it would be out of place for me to attempt it here.
[Ill.u.s.tration: Fig. 49. Diagram explanatory of the formation of Ripples.]
THE VEINED STRUCTURE AND PRESSURE.