114 Trans. Acad. Sci. of St. Louis. 



The first term therefore represents the resistance which the 

 lines of the bound charge on the larger sphere would suffer, 

 if they proceeded radially to an infinite distance in the 

 absence of the other sphere. 



The second term on the other hand is the resistance which 

 these lines would suffer if they proceeded radially from the 

 smaller sphere. The sum of these two resistances, then, is 

 the resistance of the internal tube. 



If the first term of eq. (10) and the resistance 1^ as 

 determined in (9) be treated as resistances in multiple, their 



product divided by their sum, will be found to be -^—^ which 



is the resistance around the larger sphere when it is alone in 

 space and its lines are radial. The remaining term of (10) 

 gives the resistance around the other sphere under the same 

 conditions. 



If Qx = Q 2 then 

 R a = oo 



1 1 



2 4 - r x 4 t: r 2 



If now \\ = r 2 = r 

 1 



Ro — 



2 rr 



which is a very well-known result. The resistance offered to 

 the lines of either body is the same as it would be if the 

 other were absent and the lines were radial. 



It is evident that the two terms of (10) represent resist- 

 ances from the respective charges + Q 2 and — Q 2 within the 

 internal tube, to the surface of zero potential surrounding the 

 smaller charge — Q 2 , and which all the lines of this tube 



cross. If — = — * these terms become equal. 



If we now apply equation (8) to these two tubes of force 

 we have 



W = ^ r (llE 1 + lU ! ) (11) 



