A^^Kproduced hy Vibrating Bodies. 29 



positions, whilst beyond they are often projected from the 

 string. Waliis considered the fact so curious and so novel, 

 that he gave it a place in his Treatise on Algebra. It resulted 

 clearly from the experiments of Noble and Pigot, that the 

 same string can separately produce the different harmonics 

 of the fundamental tone, and that, for this, it divides itself into 

 aliquot parts which vibrate alternately in a contrary direction, 

 remaining separated by immoveable points or nodes. 



The cause of the phaenomenon being thus clearly charac- 

 terized in the particular case of vibrating strings, it remained 

 to generalize it. Daniel Bernouilli by ingenious experiments 

 treated the case, perhaps the most difficult, of wind-instru- 

 ments, and finally experiment reached by degrees all pos- 

 sible cases, so that it is proved that a sonorous body can pro- 

 duce a considerable series of very different sounds, and that 

 for each of them it divides into a corresponding system of 

 vibrating parts and nodal su r faces* rn^: in ar 



It would perhaps be proper now lo examine the connexion 

 which exists between multiple sounds and the cause of the 

 different sounds which bodies can give successively. How- 

 ever, to suit my purpose, I shall first say a few words on the 

 processes which physicists have devised for drawing a varied 

 succession of isolated sounds from the same sonorous body. 

 I shall limit myself to the case of vibrating strings, the only 

 one which has presented notable difficulties. 



When Noble and Pigot made their capital experiment, 

 only a single regular means was known of making a string pro- 

 duce its harmonics successively. It was not touched, it was not 

 directly vibrated with the bow, but the harmonic which it was 

 desired to raise was sounded at a distance, and instantly the 

 string began to vibrate, to form its nodes and produce the 

 harmonic. This communication of movement by the air and 

 the supports of the string, or, as was then said, this com- 

 munication of sounds by sympathy, had been discovered by 

 Fracaster. Mersennus had made the experimental analysis 

 of it with care, and had found that the sounds most apt to 

 excite by sympathy the vibrations of a string form the differ- 

 ent harmonics of the fundamental tone; he had also remarked 

 that the fifth, the fourth, the major third and other conso- 

 nances, produce also feeble vibrations, when the string is per- 

 fect, long, and stretched on a suitable instrument. I'he fol- 

 lowing case is perhaps not wholly unworthy to be mentioned. 

 Two strings are stretched on a sonometer, and they are set 

 so near to unison as to give beats when they vibrate si- 

 multaneously. Then if one of them be made to vibrate di- 

 rectly, the string which has not been touched experiences very 



