produced by Vibrating Bodies. 51 



the trembling of the string is felt and the sound is no longer 

 obtained. 



We may thus prove the existence of the nineteen vibrating 

 parts, by passing the bow successively on each of them ; by 

 this manoeuvre the sound will not be changed. If the bow 

 approaches too near one of the nodes, the harmonic produced 

 instantly disappears, and the fundamental generally supplies 

 its place. 



If it is desired to ascertain the position of the nodes, by 

 means of light bodies placed astride upon the string, circles 

 of paper must be used strung through the middle, or better 

 still, a wire ring, in order that if the bow does not succeed 

 at the first stroke in producing an harmonic, the light bodies 

 may not be thrown off from the string. 



The uneven divisions are not the only ones which maybe pro- 

 duced by vibrating the string directly with the bow. The even 

 divisions are obtained by drawing the bow skilfully at a pro- 

 per distance from the nodes which it is wished to form. The 

 success of the experiment will be rendered easy by touching 

 an instant only one of the nodes. 



The method which I have just pointed out may also serve 

 to bring out with force, or to silence certain sounds in the 

 concert of the harmonics which ordinarily accompany the fun- 

 damental tone. 



After this perhaps too long digression, I revert to the prin- 

 cipal question. When the cause of the successive sounds which 

 a body can give had been proved by experiment, the expla- 

 nation of multiple sounds very naturally followed, — the expla- 

 nation of which so greatly puzzled Father Mersennus. It is 

 easy, in fact, to conceive that when different modes of vibra- 

 tions, capable of existing isolated ly in a body, are produced 

 in it together, each of them gives out the sound which corre- 

 sponds to it. M. Biot has developed this theory with ele- 

 gance ; it has since been reproduced in the works of physi- 

 cists. I know not for what reasons M. Duhamel has not even 

 mentioned it. 



The exactitude of the commonly admitted theory on mul- 

 tiple sounds, is confirmed and in some sort submitted to the 

 eye, in the phaenomenon of multiple strings and rods, which 

 is perceived when they are made to yield different sounds 

 simultaneously. To appreciate what there is completely de- 

 monstrative in this phaenomenon, it is sufficient to bring at- 

 tention to the facts. 



When a rod AB, fig. 1, fixed in A, vibrates on each side 

 its position of equilibrium AB between the extreme posi- 

 tions AC, AD, in a breadth which exceeds its thickness^ 



