JJ& M. J. Antoine on the Multiple Sounds 



we have seen in the ordinary theorj' of sounds that the string 

 produces this tone by striking the air at all its points. 



M. Duhamel, whilst reproducing the preceding proposition 

 in the same memoir, changes its sense very materially, when he 

 says that each of the sounds exists in one or more finite parts 

 of the surface, and appears to be perceptible there only. The 

 isolation of each sound is therefore not absolute, but approxi- 

 mative; with this interpretation, the proposition of M. Du- 

 hamel allows of the string producing the fundamental tone by 

 striking the surrounding air at all its points: only, the energy 

 of the shocks will vary throughout the extent of the string, and 

 ma}' be very great in one finite part of the string, with reference 

 to other parts. In this sense, the proposition would have little 

 novelty. 



In the second part of his memoir, M. Duhamel becomes 

 more explicit ; he abandons entirely the absolute sense of the 

 first form of his proposition, that is to say, that which would 

 be a real novelty, and admits, what is far from being anything 

 new, that, during the multiple sounds of a body, there are 

 portions of the surface which seem to give only one sound, 

 although however we may be sure that they give out several 

 others. In the case of the vibrating string, that is as much as 

 to say, if I am not mistaken, that the middle of the string does 

 not contribute directly to the production of the octave, and 

 that the parts adjoining this middle contribute to it only in a 

 scarcely perceptible manner, which is evident. 



In the second part of his memoir, M. Duhamel adopts fully 

 the received ideas on the multiple sound of bodies, but he 

 presents them under a form which is peculiar to himself, and 

 which we proceed to examine. 



He admits, as every one does, that when a string produces 

 the ftindamental tone and its octave, its vibratory movement 

 is composed of the two movements which correspond to the 

 separate production of these two sounds; he does not seek to 

 prove experimentally that it is so, but he shows that if the 

 movement of the string is compounded as we have just said, 

 there must result from it the simultaneous sensation of the 

 fundamental sound and its octave. 



In the common theory of multiple sounds, this consequence 

 is in some sort immediate. When the entire string makes a 

 vibration, its two halves which vibrate at the same time make 

 two, and thence it follows that it strikes the air four times 

 during a complete vibration ; but the shocks are not identical, 

 they only resemble one another alternately two to two; the ear 

 is sensible to this periodical return of such shocks, and thence 

 the origin of tlie compound sensation which is perceived. 



