416 M. Duhamel on the Mtdtiple Soutids of Bodies. 



perimenls are to be found in previous memoirs of physicists 

 and geometers. All I ask is, that they should acknowledge 

 that there can no longer be two opinions on this matter: 1 

 shall but have learnt one thing, — that all are agreed ; that is 

 enough for me. 



The coexistence of several sounds emanating from one and 

 the same vibrating body is undoubtedly one of the most re- 

 markable phaenomena of acoustics. Experience shows that 

 sounds which may be produced singly by the same body may 

 often be produced in it simultaneously. This phaenomenon 

 has given rise to very various explanations, none of which has 

 obtained the complete assent of geometers and physicists. I 

 propounded, in 1840, some new views on this subject; and the 

 experiments which I made to confirm them appeared to throw 

 some light on the question. I was however not entirely satis- 

 fied, and announced that my researches on this point were not 

 terminated. The problem now appears to me completely 

 solved. I have for several years been in possession of its so- 

 lution. It seemed to me so natural, that I thought it would 

 present itself to others besides myself; and hence, no doubt, 

 the little eagerness I felt to call the attention of men of science 

 to it. Perhaps I might have remained silent still longer, had 

 not recent publications proved to me that there was still some- 

 thing to learn on this point. 



And we shall remark first, that there can be no occasion to 

 explain how we perceive several sounds at a time, any more 

 than to explain how we experience at once several sensations 

 of any other kind. Our aim should be to include the phaeno- 

 menon in question in a more general class of recognized phae- 

 nomena; but this is precisely what has not been sought by 

 those who have studied the subject ; it is what I have attempted 

 for several years, and in this 1 think I have now succeeded. 



I shall begin by recalling in a few words what had been 

 said before me on this subject. 



Father Mersenne, in his Harmonie Universellef after refuting 

 certain explanations that had been given of this phaenomenon, 

 sought to prove that it is produced by different reflexions of 

 the air on the surface of the body which emits several sounds 

 at a time. His theory not having been adopted, we shall 

 abstain from stating it in detail, and shall pass to that which 

 has obtained the assent of the greatest number of physicists. 



This theory, first suggested by Sauveur, has been so much 

 developed and extended by Daniel Bernouilli, that he is in 

 some measure considered as its author. This illustrious phi- 

 losopher, in his solution of the problem of vibrating strings, 

 considers the initial figure of the string as formed by the su- 



