M. Duhamel 07i the Multiple Sounds of Bodies. 423 



Experiments tvhich confirm the preceding theory. 



The theoretical considerations on which I have founded 

 the explanation of the multiple sounds of bodies, seem to me 

 incapable of giving rise to any difficulty; and the assump- 

 tion cannot be denied, that the movement of a single point 

 may produce the sensation of several sounds, as soon as we 

 admit that this effect may result from the movement of several. 

 Nevertheless I have thought it not uninteresting to demon- 

 strate this fact experimentally. The first thing required was to 

 find an accurate method for determining the sound given by 

 each point of the surface of the vibrating body. I was at first 

 obliged to give up that which I had already employed, to depict 

 upon a disturbed plane the movement of the vibrating point, 

 since the object was to verify a sensation ; and it could not 

 even have been affirmed that a movement which might have 

 appeared to depict the same vibrations as when only one sound 

 was heard, would not have contained some difference imper- 

 ceptible to the eye, but which would have produced an effect 

 sensible to the ear : it was therefore to be referred solely to 

 this last sense. I tried different processes, the results of which 

 were always attended with uncertainty, and I at last stopped 

 at that which I shall proceed to describe and which is free 

 from all error. 



I shall first call to mind, that when a rod or an elastic wire, 

 indefinitely extended in one direction, has its extremity sub- 

 jected to any small movement, each of its points is affected 

 successively with this same movement, which is propagated 

 with a constant velocity. If the wire is of a definite length, 

 this first movement is complicated with a second, which de- 

 pends on the length of the wire, but is insensible with relation 

 to the other ; and experiment shows, in fact, that the only 

 sound which the wire or the rod transmits, is that which 

 corresponds to the vibrations communicated to its extremity. 



Hence it results that an effectual mode of studying the 

 proper movement of any point of the surface in a vibrating 

 body, will be to fix to it one of the extremities of an elastic 

 wire, to put the other extremity in communication with one 

 ear, closing the other carefully, and preventing the sound 

 reaching the first except by the medium of the wire. This 

 is very easily accomplished, and it is easy also to verify its 

 success. In fact, it is to be remarked, that the wire must be 

 stretched for the sound to be perceptible: the entire wire can 

 at pleasure be stretched, or that part can be left unstretched 

 which is near the vibrating surface ; and we find that in the 

 first case a very distinct sound is heard, but none in the second. 



