BATTERY PLACED IN A CONDUCTING MEDIUM. 257 



269. The expressions for the current in the battery, and that 

 for the lateral current /, are 



(3) 



V 



t-^ ">] 



e-e 



In order to determine the potential V l of the ends, we must 

 estimate the current which flows through each of them. 



We have then, if R x is the resistance of the medium measured 

 from the ends, 



v, ir M- ? -fn 



''-sh; -- s-^' +e i 



e* -e * 



which gives 



I 



(5) 



If the external medium is an insulator, />' = oo and /3 = 0. The 

 second term of the current appears then in an indeterminate form, 

 but we get finally the ordinary expression, 



i= 



The total resistance of the battery, and of the medium, 



s 



