56 APPLICATION OF THE PRECEDING RESULTS 



the value of the total potential function belonging to p, the 

 centre of S. In like manner, the value of this function at p t 

 the centre of S', will be 



F being the part arising from 8, and Q the total quantity of 

 electricity on S'. But in consequence of the equilibrium of the 

 system, the total potential function throughout its whole interior 

 is a constant quantity. Hence 



Although it is difficult to assign the rigorous values of F 

 and F'; yet when the distance between the surfaces of the two 

 spheres is considerable, compared with the radius of one of them, 

 it is easy to see that F and F' will be Very nearly the same, 

 as if the electricity on each of the spheres producing them was 

 concentrated in their respective centres, and therefore we have 

 very nearly 



F=% and ^'=-f-\ 

 o o 



These substituted in the above, there arises 



Thus the ratio of Q to Q' is given by a very simple equation, 

 whatever may be the form of the connecting wire, provided it be 

 a very fine one. 



If we wished to put this result of calculation to the test of 

 experiment, it would be more simple to write P and P' for the 

 mean densities of the fluid on the spheres, or those which would 

 be observed when, after being connected as above, they were 

 separated to such a distance, as not to influence each other 

 sensibly. Then since 



Q = 4?ra 2 P and Q' 

 we have by substitution, etc. 



P _ a (b - a) 

 F~a'(1>-a' 



