THE INTERNAL CONSTITUTION OF BODIES. 453 



^^^ di dF ^ dG ^ dG, dG, dG. 



(0 d'y = -9d^ + 9 d^ + 9-0:^+9 d^ +^'rf]r+«^<^- 



de dF , dG , dG, , dGo . dG, , 



in which G^„ Go, • . . G^, &c. denote the quantities analogous to G 

 wliich correspond with the different molecules 1 , 2 . . . v, &c. 

 Let us likewise put 



gq' dx' dy' dz' 



~JTf{x^ 



T,= 



-M 



ya^d^td.yifdXM 



(0v-g)-^+(iv-i)'^+(?v-?;*}* 



where y denotes the force of repulsion existing among the molecules of 

 matter at the distance assumed as unity. 



The equations for the equilibrium of a molecule, if we take into 

 consideration the motion of its centre of gravity only, will be 



The sum S is to be extended to all the numbers v, that is to say, 

 to all the molecules except that one the equilibrium of which we are 

 considering ; the double integral is to be extended to the whole sur- 

 face of this molecule, and the triple integrals to its whole volume. 



4'. Let us begin by considering the equilibrium of the aether. The 

 elasticity possessed by the aether at any jjoint of space can be only the 

 result of the reciprocal action of the contiguous parts : hence we are 

 led, by considerations analogous to those employed by Laplace in re- 

 ference to the repulsion of caloric, in the 12th book of the Mecanique 

 (Celeste, to conclude that, in a fluid considered as a continuous mass, 

 the elasticity is proportional to the square of the density. If then k 

 represents a constant coefficient, we shall have e = ^kq'^, and by sub- 

 stituting this value in the equations (I) we shall derive the following : 



^dq ^_dF flG dG, dG^ dG, 



dx dx^ dx^ dx' "^ dx "^ dx '^^^^' 



