‘THE INTERNAL CONSTITUTION OF BODIES. 459 
fe) rT ©@ of 
= 5 if : , B (0) Vir!" El ade! 
bake 
° 7 o oO 
QO!.(7') V'. dr' 
+ de i Sie A es P,, sin 'di'dy'. 
17 
r= rT 
The functions 7", V', of this expression remain arbitrary; and, as 
the sum of an infinite number of these functions may be enrployed to 
represent any iuvction whaisoever, they w''l serve as two arbitrary 
functions which are to comleie the jotegral of the equation (1). 
When in some particular cases the integrations of the nreceding for- 
mula suall have been performed by substivvting ics expression in the 
equation (‘I}), the funciions 7’, and V, will be determined by com- 
paring them wiih those of the same order introdaced by means of the 
different expressions for G; so that this equation may become identi- 
cal. All being thus determined, the densivy g given by the formula (2) 
will be known. 
We have hitherto left our formule in all their generality, so that one 
may be ihe better able to judge of the restrictions to which we shall 
subject them while making the first applications of them. Jn the pre- 
sent state of our physical knowledge, the figure of the material mole- 
cules is totally unknown. We will therefore begin by considering the 
most simole case,—‘hat in which their form is spherical, and their den- 
sity uniform. We will, besides, assign to these molecules a very small 
volume, and suppose them in their state of equilibrium at a mutual di- 
‘stance, which is very considerab!e as compared with their dimensions. 
This manner of considering the constitution of bodies has been adopted 
‘by several philosophers as that which is most conformable to truih, and 
‘presents at the same time a considerable advantage in an analytical 
point of view. Tn adopting it we shall be able, by approximation, to 
consider the ether as if it were continuously diifused in all directions ; 
and to disregard, in the integration of the formula (5), the small spaces 
occupied by the material molecules. But as, by proceeding in this man- 
ner, we should include in the repulsion of the ether a surplus which is 
‘due to the actions answering to the points of space which are really 
occupied by the molecvles, we shall compensate for this surplus by add- 
‘ing to the action of each molecule an action equal and contrary to that 
of a quantity of ether of the same volume as the molecule, and of the 
same density as that which answers to the point of space which the 
molecule occupies. This is done by substituting ga +fq for ga in 
the expression for G (q representing the density which the zther would 
have at the point occupied by the molecule, and within so small a space 
we will suppose that density constant), and by extending the integrals 
Vor. I.—Part III. 21 
