18 Prof. Poweirs Abstract o/M, Cauchy's 



de points materiels soUicites par des forces d'attraction ou de 

 repulsion mutuelle." In this paper he considers the subject 

 in a very general point of view. He supposes a great number 

 of molecules or material points arbitrarily distributed in space, 

 and subject to the influence of mutual attractive or repulsive 

 forces tending to put them in motion. He assumes these 

 forces to be proportional to the masses and some function of 

 the distance between any two molecules ; and hence proceeds 

 to deduce expressions which give rise to certain partial dif- 

 ferential equations representing the motions of the molecules 

 under the above conditions, referred to three rectangular axes. 

 The investigation pursued is of a high degree of generality ; 

 and expresses the equilibrium or motion of such a system of 

 particles. It is also closely connected with another inquiry, 

 which he has discussed in a separate memoir, — the interior 

 equilibrium or motion of a solid body, considered as a system 

 of distinct molecules. 



In the fourth volume (1829) of the same collection, p. 129, 

 liv. xlii., the author enters upon some further applications in 

 a memoir, entitled " Sur les equations difFerentielles d'equili- 

 bre ou de mouvement pour un systeme de points materiels sol- 

 licites par des forces d'attraction ou de repulsion mutuelle." 

 This investigation, relating chiefly to the " elasticity" of such 

 a system, turns upon the equations of motion deduced from 

 those in the former memoir, when simplified by certain con- 

 ditions, which reduces them to a less general character; but 

 which suffices for the object immediately in view. More pre* 

 cisely, the author has shown, that those equations of the former 

 memoir which include a great number of coefficients dependent 

 on the nature of the system, reduce themselves, in the case in 

 which the elasticity is the same in every direction, to other 

 formulas, including only a single coefficient: these, in fact, 

 coincide with expressions before obtained by the investigations 

 of M. Navier. In these equations given in the fourth volume, 

 the coefficients in question having disappeared, and the masses 

 of the molecules being supposed equal, two and two, and 

 distributed symmetrically on each side of a given point, on 

 straight lines passing through that point, the subject is much 

 simplified. In a subsequent article the author proposes to 

 show how the general integrals of these equations may be de- 

 duced, with a view to establishing the laws of the propagation 

 of sound in a solid body. 



But for the investigation of the theory of light, at least 

 when regarded as homogeneous, a more simple view of the 

 above analysis will suffice. It is not, as the author observes, 

 at all necessary to have recourse to these general forms of in- 



