164 THE LAWS OF 



for the value of the total repulsion upon a particle p of positive 

 fluid situate within the sphere A and exterior to B. We thus 

 see that when P' is positive the particle p is always impelled 

 by a force which is equal to zero at B's surface, and which 

 continually increases as p recedes farther from it. Hence, if 

 any particle of positive fluid is separated ever so little from jB's 

 surface, it has no tendency to return there, but on the contrary, 

 it is continually impelled therefrom by a regularly increasing 

 force ; and consequently, as was before observed, the equilibrium 

 can not be permanent until all the positive fluid has been 

 gradually abstracted from B and carried to the surface of A 9 

 where it is retained by the non-conducting medium with which 

 the sphere A is conceived to be surrounded. 



Let now q represent the total quantity of fluid in the inner 

 sphere, then the repulsion exerted on p by this will evidently 

 be qr"", when r is supposed infinite. Making therefore r infinite 

 in the expression (15), and equating the value thus obtained to 

 the one just given, there arises 



-47rV7r.P'a 2 r \, n ,_ ,=p 



q = - - 7 - - - r- f ft dx . x n (1 an 2 . 



When the equilibrium has become permanent, q is equal to 

 the total quantity of that kind of fluid, which we choose to con- 

 sider negative, originally introduced into the sphere A ; and if 

 now ^ represent the total quantity of fluid of opposite name 

 contained within A, we shall have, for the determination of the 

 two unknown quantities P' and 6, the equations 



and = 



21 



and hence we are enabled to assign accurately the manner in 

 which the two fluids will distribute themselves in the interior 

 of A q and q lt the quantities of the fluids of opposite names 

 originally introduced into A being supposed given. 



9. In the two foregoing articles we have determined the 



