MUTUAL INDUCTION OF TWO LONG COILS. 139 



and the potential energy of the base B' by 



The potential energy of the base A' is in like manner 



which gives for the coefficient of mutual induction 

 M = XiS'[4** + PJ* - x) + PJ* + V) - 



772. If, lastly, the coils are of equal lengths and concentric, # = 

 and h' = h ; we have then 



M = 4 7r 1 'S f - 2 1 iS'[P TO (0) - P 

 'S' - 2^^'S' [P m (0) - 



In order to calculate the potential P m (0), we may utilise the 

 former of these equations (25), which gives, making 0= -, 



2 



From this follows by the ordinary rule, and making r=a\ 



In order to get the value of P m (//), we might develope the 

 ent 

 (736) 



potential of a circle as a function of the ratio - , taking the expression 



27T 



