THE INTERNAL CONSTITUTION OF BODIES. 467. 
then r, has a greater value than that which renders this expression 
null, the foree revresented by the last term will preponderate over that 
represented by the first; and ifr, be so great that this term may be 
neglected as of no value, then the only remaiving force will be that 
given by the last term. This term being negative, the force which 
corresponds with it tends to bring the molecules nearer to each other ; 
and as it is in the direct ratio of the product of the masses, and the in- 
verse ratio of the square of the distance, it will exactly represent the 
universal gravitation which takes place at finite distances. 
By diminishing r, we shall obtain a value that will satisfy the equa- 
tion 
—G@r) 
O)gv(wta)vi(a, rq) EF22)* _ _G—y vane, = o. 
1 1 
At this distance two molecules would remain in equilibrium, and as 
the differentiation of this equation gives the result 
a1; 
—9v(e +4) (@ +41) —— 
} 
which is always negative, the equilibrium will be permanently fixed. 
Should it be attempted, by the application of an external force, to 
bring the molecules nearer to each other, the repulsive force repre- 
sented by the first term of the expression (a), which would now in- 
crease in a greater ratio than the attractive force represented by the 
last term, would produce a resistance to such an approximation: on 
the other hand, if it should be sought to remove the molecules to a 
greater distance from each other, the repulsive force would decrease in 
a greater ratio, and the attractive would preponderate and prevent the 
separation. These two molecules would therefore be so placed rela- 
tively to each other as by mutual adhesioa to form a whole, and we 
should not be able to remove the one without at the same time remoy- 
ing the other. Thus these molecules present a picture in which the 
hooked atoms of Epicurus are as it were generated by the love and 
hatred of the two different matters of Empedocles. 
As the attractive force is null at the distance which we have been 
just now considering, and at a greater distance decreases as the square 
of the distance of the molecules, there must be an intermediate point 
at which it reaches its maximum. By the ordinary rules of the dif 
ferential calculus we find that the function (a) is a maximum when 
iGo y) 
= ayy 
(c) —gv (a7+q)v,(@,+q,) 0 +ar,+ serie 
V@.V, a, =0; 
that is to say, that it is at the distance r, we should find, by the resolu- 
