considered as the Results of Vibratory Motion. 347 



originally vibrating. The vis viva of the system of all the 

 diapasons will by degrees diminish indefinitely, in consequence 

 of the waves which the medium propagates out of the system; 

 unless we suppose it to be inclosed within a sphere (une enceinte) 

 of diapasons kept in a state of vibration with a constant vis 

 viva, which we suppose, for example, to be inferior to that of 

 the part of the system originally vibrating. In that case, the vis 

 viva of that part and of the rest of the system tend to ap- 

 proach indefinitely that of the diapasons inclosed within the 

 sphere, without ever, mathematically speaking, being capable 

 of attaining it, because the diapasons within that sphere (en- 

 ceinte), which have a vis viva superior to its own, will lose a 

 part of it by the presence of the surrounding sphere commu- 

 nicating to it more than they receive; and that of those which 

 have less than the sphere will, oil the contrary, receive less 

 than they send out. 



If we consider the diapasons placed in a cylindrical enve- 

 lope of very small diameter to observe their propagation in 

 one dimension only, or placed between two planes to observe 

 the propagation in two dimensions, or merely placed in space, 

 we may suppose in the first case the length of the cylinder 

 occupied by these diapasons to be divided into a number of 

 slices equal in length and parallel to the bases of the cylin- 

 der; in the second, that the space comprised between the 

 two parallel planes is divided into circular zones of equal 

 magnitude, the centre of which is in that part, supposed to be 

 very little, where the diapasons had originally vibrated; in the. 

 third case, in which the space surrounding the same part is 

 divided into spherical layers of equal thickness ; and we 

 shall discover the vis viva in all those cases to be transmitted 

 from the diapasons of a division of a zone, or of a spherical 

 layer, to the diapasons of the consecutive slices, zones, or 

 spherical layers. This transmitted quantity will be found null 

 if their vis viva was equal ; we may therefore suppose, as a first 

 approximation, that the quantity of vis viva transmitted is 

 proportional to the difference of the vires viva? of the two 

 consecutive groups of diapasons. We then find necessarily, 

 with regard to the distribution of the vis viva in the dia- 

 pasons, the same equations as those found by Fourier, for 

 the distribution of heat in the three corresponding cases, 

 setting out from the same hypothesis, that the temperature or 

 transmitted heat, which here represents the transmitted vis 

 viva, is proportional to the difference of the respective values 

 of the temperatures. And supposing we apply to the trans- 

 mission of the vis viva between the diapasons other laws, — for 

 example, the laws which M. Libri or M. Babinet have pro- 



2 Y2 



