THE INTERNAL CONSTITUTION OF BODIES. 467 ■ 



then r, has a greater value than that whicli renders this expression 

 nail, the force represented by the last teimwill preponderate over that 

 represented by the first; and if r, be so great that this term may be 

 neglected as of no value, then the only remairing foice will be that 

 given by the last term. This term being negative, the force which 

 corresponds Avith 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- 

 vei"se rotio of the square of the distance, it will e::act);: lepresent the 

 universal gravitalio7i which takes place at finite distances. 



By diminishing rj we shall obtain a value that will satisfy the equa- 

 tion 



-ari 

 (6)yv(CT + q)v;(CT, ^q,) ( ^'^^^y^ -{g-y)vm.v,VT^^= 0. 



At this distance two molecules would remain in equilibrium, and as 

 the differentiation of this equation gives the result 



- 5- V (ot + q) v, (uTj + q,) ^l! 



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 («), 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 adhesion to form a whole, and we 

 should not be able to remove the one without at the same time remov- 

 ing the other. Thus these molecules present a picture in M'hich 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 

 ji'st now considering, and at a greater distance decreases as the square 

 of the distance of tlie 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 Mhen 



(c)-^v(CT + q)v,(t!7, +q,)(l +ar, + la,"v,")e~'''' + {g - y) 



vsr. V, to, = o; 

 that is to say, that it is at the distance r, we should find, bv (he resolu- 



