88 Mr. Ivory on the figure requisite to maintain the equilibrium 
consequently, 
i dm i dm! 
r% f r' z ' f 
and as this is universally true of all the molecules, we have, 
V (r) V'(r') 
In this form the expression is inconvenient, because both 
the quantities become infinite when we suppose that the at- 
tracted point is placed in the origin of the co-ordinates. But 
the inconvenience is easily removed by substituting, for r 
and r', any other two homologous lines. Let r and r', pro- 
duced if necessary, meet the surfaces ; and let R and R' de- 
note the parts within the two bodies, intercepted between 
the surface and the origin of the co-ordinates : then it is 
manifest that — = ; and we shall therefore have 
r r 7 
V (r) _ V'(r') 
R a — R' * • 
If, therefore, we suppose a series of such bodies as we 
have been describing, which increase in magnitude from 
zero to infinity, while they constantly preserve the same pro- 
portions in their lineal dimensions, and the same densities of 
the parts similarly situated ; the quantity will have 
constantly the same value in all the bodies, supposing that 
the attracted points are alike placed in them all. It is mani- 
fest, therefore, that will depend only on what is com- 
mon to all the bodies in the series ; or it will be a function 
of the quantities that remain unchanged in passing from one 
of the bodies to another. But as these quantities are not the 
same in all positions of the attracted point, it will be proper 
to distinguish several cases. 
