But now suppose the one system to be retarded only _half a wave-length_; it is perfectly clear that, in this case the first ridge of the retarded system would fall in with the first _furrow_ of the unretarded system, and instead of coincidence we should have interference. One system, in fact, would tend to make a hollow at the point referred to, the other would tend to make a hill, and thus the two systems would oppose and neutralize each other, so that neither the hollow nor the hill would be produced; the water would maintain its ordinary level. What is here said of a single half-wave-length of retardation, is also true if the retardation amount to any _odd_ number of half-wave-lengths. In all such cases we should have the ridge of the one system falling in with the furrow of the other; a mutual destruction of the waves of both systems being the consequence. The same remarks apply when the point, instead of being equally distant from both stones, is an even or an odd number of semi-undulations farther from the one than from the other. In the former case we should have coincidence, and in the latter case interference, at the point in question. [Sidenote: LIQUID WAVES.] To the eye of a person who understands these things, nothing can be more interesting than the rippling of water under certain circumstances. By the action of interference its surface is sometimes shivered into the most beautiful mosaic, shifting and trembling as if with a kind of visible music. When the tide advances over a sea-beach on a calm and sunny day, and its tiny ripples enter, at various points, the clear shallow pools which the preceding tide had left behind, the little wavelets run and climb and cross each other, and thus form a lovely _chasing_, which has its counterpart in the lines of light converged by the ripples upon the sand underneath. When waves are skilfully generated in a vessel of mercury, and a strong light reflected from the surface of the metal is received upon a screen, the most beautiful effects may be observed. The shape of the vessel determines, in part, the character of the figures produced; in a circular dish of mercury, for example, a disturbance at the centre propagates itself in circular waves, which after reflection again encircle the centre. If the point of disturbance be a little removed from the centre, the intersections of the direct and reflected waves produce the magnificent chasing shown in the annexed figure (16), which I have borrowed from the excellent work on Waves by the Messrs. Weber. The luminous figure reflected from such a surface is exceedingly beautiful. When the mercury is lightly struck by a glass point, in a direction concentric with the circumference of the vessel, the lines of light run round the vessel in mazy coils, interlacing and unravelling themselves in the most wonderful manner. If the vessel be square, a splendid mosaic is produced by the crossing of the direct and reflected waves.