422 M. Duhamel on the Multiple Sounds of Bodies. 



end of the same time, in the movements of the system corre- 

 sponding to the different movements composing the first points. 



But, according to the preceding remark, our organs will 

 be affected in the same manner by the movement of a point of 

 the medium, or by an identical movement attributed to another 

 point near the first. Hence results the following propo- 

 sition : — 



When any point of the medium 'vohich surrounds us is affected 

 by a movement resulting from the composition of several other Sy 

 all parts of our organs are sensibly affected in the same man- 

 ner as they would be if these different component movements^ 

 instead of being united in the same point, existed separately at 

 different points of the first. 



And reciprocally : — 



If several points of a medium affected by different vibratory 

 movements cause us to hear several sounds at once, it nsoill suffce^ 

 in order that a single point of the medium should cause us to 

 hear all these same sounds at a time, to give to this point the 

 movement resulting from the composition of the former ernes. 



It is seen, then, as we stated, that the phaenomenon of the 

 multiplicity of the sounds which the same body gives, enters 

 into another class of phaenomena, that of the coexistence of 

 the sounds produced by distinct bodies which simultaneously 

 agitate the medium. It suffices, in fact, that the initial state 

 of a sonorous body, with respect to the displacement of its 

 molecules and the impressed velocities, be considered as re- 

 sulting from the composition of several initial states corre- 

 sponding to different simple sounds which it can produce, for 

 all these sounds to be produced in us, by each of the points 

 of the surface of this body. 



It is possible, moreover, that one of these sounds may be 

 produced more strongly than another in certain parts of the 

 body, and even that there may be points in which it entirely 

 predominates. These different circumstances will depend on 

 the velocity in the different vibrations which are compounded 

 at each point. In fact, since we receive the same impressions 

 as if distinct points of the medium were respectively excited 

 by these elementary movements, the simultaneous sounds 

 which will proceed from the same point will have very differ- 

 ent intensities, if the magnitude of the velocities is itself very 

 different in the component vibrations. Experiment confirms 

 this proposition ; for, as I have already had occasion to say, 

 when a body emits several sounds at a time, there are portions 

 of its surface which seem to give only one sound, although we 

 may convince ourselves, by particular processes, that they 

 emit several others. 



