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ON THE VIBRATIONS OF RODS, PLATES, ETC. 123
while the prongs move horizontally the portion between p and q vibrates vertically. To this portion there is usually welded or screwed, an elongated piece of steel, which shares this vertical motion, and does duty as a handle. When this handle is placed upon a sound-board, its vertical vibrations are communicated to it; a larger body of air is set in motion, and thus the sound of the fork augmented. A tuning-fork does not divide like a straight bar into four vibrating segments with three nodes; its second complete form of vibration, which corresponds to the first overtone, is with four nodes, two at the bottom and one on each prong. In some forks, examined by Helmholtz, the relative rates of the fundamental and first overtone, varied from 1 : 5'8 to 1 : 6"6. The overtones of tuning-forks are consequently very distant from the fundamental and from one another; the first overtone, as we see from the above, being more than two octaves above the fundamental. The rates of vibration of the whole series of overtones, starting with the first overtone, are approximately as 9, 25, 49, 81, &c, that is, as the squares of the odd numbers, 3, 5, 7, 9, &c.
These high overtones are very evanescent, and soon leave the fundamental tone pure and simple. This is especially the case, as already observed, when the fork is mounted on a resonance chamber, tuned to its fundamental. The fork should either be struck with a soft hammer, or carefully bowed. Striking with a hard metallic substance, favours the production of the higher partials, for the reason given in the case of pianoforte strings. Large forks, when too rapidly bowed, produce very powerful over­tones. The best method of keeping tuning-forks in continuous vibration, is by means of electro-magnets, as already described in Chap. VIII.
The pitch of a tuning-fork is only very slightly affected by heat. The effect of increase of temperature on a fork, is to slightly flatten it; for the fork itself expands, and its modulus of elasticity is lowered on heating; both of these causes combining to lower the pitch. The variation with temperature is only about one vibration in 21,000, for each degree Fahrenheit. Forks are also little affected by ill usage. A slight amount of rust is imperceptible in its influence on pitch; and with a very large amount, such as could only occur through great carelessness, the error is never likely to exceed 1 in 250. Eust about the bend has a much greater influence over the pitch, than at the ends. Tuning-forks are perhaps most injured, by wrenching or twisting of the prongs, such as might