The ripples of the tide leave their impressions upon the sand over which they pass. The ripples produced by sonorous vibrations have been proved by Faraday competent to do the same. Attaching a plate of glass to a long flexible board, and pouring a thin layer of water over the surface of the glass, on causing the board to vibrate its tremors chase the water into a beautiful mosaic of ripples. A thin stratum of sand strewed upon the plate is acted upon by the water, and carved into patterns, of which Fig. 81 is a reduced specimen. SUMMARY OF CHAPTER IV A rod fixed at both ends and caused to vibrate transversely divides itself in the same manner as a string vibrating transversely. But the succession of its overtones is not the same as those of a string, for while the series of tones emitted by the string is expressed by the natural numbers 1, 2, 3, 4, 5, etc., the series of tones emitted by the rod is expressed by the squares of the odd numbers 3, 5, 7, 9, etc. A rod fixed at one end can also vibrate as a whole, or can divide itself into vibrating segments separated from each other by nodes. In this case the rate of vibration of the fundamental tone is to that of the first overtone as 4:25, or as the square of 2 to the square of 5. From the first division onward the rates of vibration are proportional to the squares of the odd numbers 3, 5, 7, 9, etc. With rods of different lengths the rate of vibration is inversely proportional to the square of the length of the rod. Attaching a glass bead silvered within to the free end of the rod, and illuminating the bead, the spot of light reflected from it describes curves of various forms when the rod vibrates. The kaleidophone of Wheatstone is thus constructed. The iron fiddle and the musical box are instruments whose tones are produced by rods, or tongues, fixed at one end and free at the other. A rod free at both ends can also be rendered a source of sonorous vibrations. In its simplest mode of division it has two nodes, the subsequent overtones correspond to divisions by 3, 4, 5, etc., nodes. Beginning with its first mode of division, the tones of such a rod are represented by the squares of the odd numbers 3, 5, 7, 9, etc. The claque-bois, straw-fiddle, and glass harmonica are instruments whose tones are those of rods or bars free at both ends, and supported at their nodes. When a straight bar, free at both ends, is gradually bent at its centre, the two nodes corresponding to its fundamental tone gradually approach each other. It finally assumes the shape of a timing-fork which, when it sounds its fundamental note, is divided by two nodes near the base of its two prongs into three vibrating parts. There is no division of a tuning-fork by three nodes. In its second mode of division, which corresponds to the first overtone of the fork, there is a node on each prong and two others at the bottom of the fork.