44 Mr green, ON THE LAWS OF THE EQUILIBRIUM OF FLUIDS. 



Now by adding the repulsion due to the inner sphere which is given 

 by the formula (16), we obtain, (since it is evidently indifferent what 

 variable enters into a definite integral, provided each of its limits re- 

 main unchanged) 



f'afdxCl -x") '' .{1 , , 



1 + w\ / 2-w \ •'^ ^ ' V (f ) 



\ 2 j ' 



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

 situate within the sphere A and exterior to S. We thus see that 

 when P' is positive the particle p is always impelled by a force whicli 

 is equal to zero at JS'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 2?'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, 

 Avhere 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 



q= — :: tclx-afil-x')'. 



2 J \ 2 



When the equilibrium has become permanent, q is equal to the total 

 quantity of that kind of fluid, which we choose to consider negative, 

 originally introduced into the sphere A ; and if now qi represent the 



