M. Duhamel on the Multiple Sounds of Bodies. 4-21 



several sounds, each of them exists in one or morejinite farts of 

 the surface, and appears to be perceptible there only ,- so that 

 the ear is affected as it would be by several separate surfaces, 

 ixhich should each give one only of the sounds in question. 



In this memoir, resting on new facts, which 1 first arrived 

 at theoretically and then demonstrated by experiment, I 

 attempted to bring the phaenomenon in question under another 

 class of phsenomena admitted without dispute, and which con- 

 sists in our perceiving simultaneously the sounds produced by 

 the vibrations of different points. These inductions were not 

 disputed by any physicist. M. Poisson himself, who was much 

 occupied with acoustics, raised no objection to them. It is to 

 this same class of phaenomena that I shall proceed now to refer 

 those under consideration ; but it will be by means of a more 

 simple and at the same time more general theory, which will 

 supply the voids and uncertainties which still existed, and 

 which induced me to engage anew in this subject. 



General explanation of the simultaneous sounds produced by 

 a single body. 



We admit that when several points of a medium have dif- 

 ferent vibratory movements, we hear, in general, the different 

 sounds which each of them would give if it alone were in 

 motion ; and we propose to refer to this phaenomenon that of 

 the perception of several simultaneous sounds produced by a 

 single point in motion. In other words, it has to be proved 

 that our organs are sensibly affected in the same manner by 

 several movements existing in distinct points of the surround- 

 ing medium, as by a single movement resulting from the com- 

 position of the several movements in a single point of this me- 

 dium. 



In the first place, when a point of the medium is not at a 

 very small distance from the ear, its movement produces in 

 all parts of our organ movements which do not differ percep- 

 tibly from those which would take place, if for the first point 

 of the medium any other were substituted not very distant 

 from it, and which was affected by the same movement. This 

 is easily demonstrated by calculation and experiment. 



This being settled, we know, by the principle of the super- 

 position of small movements, that in any system of material 

 points, homogeneous or not, but whose mutual actions depend 

 only on their distances ; if one or more of these points have 

 movements resulting from the composition of several others, 

 the displacement and velocity of every point of the system 

 may be considered at every instant as the resultant of the 

 composition of those which would be observed in them at the 



