424 M. Duhamel on the Multiple Sounds of Bodies. 



This proves two important things ; namely, first, that the sound 

 which is heard is transmitted by the wire alone ; and in the 

 second place, that it only proceeds from the point where it is 

 joined to the surface, and that the other parts of this surface 

 do not act perceptibly upon it by the medium of the air; for 

 if that were the case, we should still hear a sound when this 

 wire was stretched throughout its whole length, except near 

 the point where it is attached. 



Once in possession of so simple and sure a process for ascer- 

 taining the sound emitted by any point of the surface of a vi- 

 brating body, I applied it to the investigation for which 1 had 

 devised it, and the following are the results at which I have 

 arrived. 



I caused a square plate to vibrate so as to produce two 

 sounds ; I fixed the end of a thread of caoutchouc succes- 

 sively at different points of the surface, and I always heard the 

 two sounds, satisfying myself that they were transmitted only 

 by the wire ; this took place even at the points where the geo- 

 metrical influence of one of the movements was imperceptible. 

 Whence it follows that each point of the plate emits the double 

 sound, as the theory which I have explained had rigorously 

 established ; and they are distinguished by this method, even 

 when one of them has become so feeble that it would no longer 

 be heard through the medium of the air. 



When the plate emitted three sounds, the wire still gave 

 the sensation. Instead of a plate, bells, strings, or bodies of 

 any form may be chosen, and the same fact will generally be 

 observed. Nevertheless we may imagine such forms as that 

 this law would be liable to exceptions, and not to hold good 

 over the whole extent of the surface. It might be that the move- 

 ment relative to one of the sounds would be weak in certain 

 parts of the surface, that even though it existed there singly, 

 it would make no sound heard ; in this case, still more, it 

 would not be heard if this movement were combined with 

 another ; and it will always be easily ascertained that the par- 

 ticular cases which, at first sight, would seem to constitute 

 exceptions, are explained naturally by meansof our principles. 



I shall sum up the whole of this memoir by saying that I 

 have established theoretically and experimentally the following 

 proposition : — 



If the vibratory motion of a -point be decomposed into several 

 others, the ear is perceptibly affected in the same manner by the 

 movement of this point, as it would be by so many distinct points, 

 each under the influence of one of these component motions. 



The phaenomenon of the multiplicity of sounds emitted by 

 a single point is thus referred to that of the simultaneous 



