42 PROFESSOR KELLANB, ON MOLECULAR EQUILIBRIUM. 



hence, the whole mutual attraction of a compound particle is 



S + ST + T + T 



= ^J*{BM+B'M'-(l + aa)e-<"'{AM + A'M')}- W-MJ 



-^e-« a l\A + A'\{e-" l (a + l+aal + ±) - e*' l .fa - I - aal + i) 

 + e- al ' (a + l')+ }]. 



Now for a single particle M = — , and there is no reason to 



suppose B different in other cases ; hence, the mutual attraction of the 

 compound particles is 



i^' - ^(AM + A'M')(1 + aa)e-°° 



-2mtf e ' aa{A + A '"> ^' al ' {a + l)+ - * 



Now if they are at a distance from each other, the quantity e~ aa is 



2 MM' 

 very small, and the force is ; — varying inversely as the square of 



the distance, which is the known law of gravitation. 



22. I shall not dwell longer on this point, as the difficulty is not 

 to obtain a portion of the expression which shall vary inversely as the 

 square of the distance; for this will be at once accomplished either by 

 the above method, or by supposing the attraction of M on P a little 

 greater than MP, as M. Mossotti has done, or by taking into the 

 calculation the caloric which is displaced by a particle, either by the one 

 attracting, or that acted on, which in accuracy ought to be done. But 

 the difficulty is to obtain an expression for the mutual action of two 

 particles, which shall express those facts of Boscovich's hypothesis 

 specified in the Introduction, and which are clearly essential to the 

 nature of a molecular action. 



To accomplish this object, I have supposed all the particles repul- 

 sive; which hypothesis requires that the density of the caloric within 



