340 Steady Currents in continuous Media [CH. x 



If E is the charge on this electrode in the analogous electrostatic problem, 

 we have, by Gauss' Theorem, 



so that the total flow of current is seen to be - . 



r 



If Pn , Pi2,p*2 are the coefficients of potential in the electrostatic problem 



so that 



If / is the total current, and R the equivalent resistance between the 

 electrodes, we have just seen that 



so that 



If we regard the two electrodes in air as forming a condenser, and denote 

 its capacity by (7, we have 



so that 



387. As instances of the applications of formulae (317) and (318) to 

 special problems, we have the following : 



I. The resistance per unit length between two concentric cylinders of 

 radii a, b (as, for instance, the resistance between the core of a submarine 

 cable and the sea), is, by formula (318), 



T . b 



27r log a- 



II. The resistance per unit length between two straight parallel 

 cylindrical wires of radii a, 6, placed with their centres at a great distance r 

 apart, in an infinite conducting medium, is, by formula (317), 



- ^: ( l g a - 2 log r + log b) 

 r r 2 



= TT- log -7 . 



STT 6 ab 



