THE INTERNAL CONSTITUTION OF BODIES. 4.55 
dé dF dG dG, dG, dGy 
(1) dy=— Vay +4 dy t 9 dy +4 dy +1 ay tee 
wey dG, &Ge dG, ‘ 
az ~9 +952 dz S+q ae al Yds +q dz ets 
in which G,, G,,... G,, &c. denote the quantities analogous to G 
which correspond with the different molecules 1,2... ¥, &c. 
Let us likewise put 
' dx! dy! dz! 
‘ LLKi a Re —)2}4 
Lyre NiO TGA WEE enone vd © 
Poff} Corte rc © Cart Pitas Occ te 
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 
Sf ssc ff foiteess-af {fein 
(a), if sazat aff fog rianar—3f f fo FZ aganar 
S fren ff fer eee Eff fae tanas 
The sum = is to be extended to all the numbers », 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 ether. The 
elasticity possessed by the zther at any point 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, inthe 12th book of the Mécanique 
Céleste, 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 = 3k g?, and by sub- 
stituting this value in the equations (I) we shall derive the following : 
ag aR ae dG a dG, 
Ge de de ae. © ace +7, Fete. 
