CURRENT ON CLOSING. 521 



The differential of the latter equation 



dV E / ft , P'/\ 



= ( pe - pe ) 



dt 2 Ra V / 



shows that, in the secondary circuit C', the induced current, which 

 is always negative, since we have p>p in absolute value, starts 

 from zero, without its initial differential being zero, passes through 

 a maximum, and then decreases to zero. 



It will be seen that the inducing current commencing at zero, 



-p 

 increases progressively to its maximum value relative to the 



R 

 permanent state. 



If we suppose the two circuits C and C' identical, the formulae 

 reduce to 



_ Ef i/Jk --*_ 

 I = i - - ( e L+M - e L-M 



(37) 



E r _^_ _RL_-I 



I'= e L+M-<? L-M . 



2 R|_ 



If, further, the two circuits are in contact, the coefficients L 

 and M are very slightly different, and we have sensibly 



E r i _Rfi 



i --e SL 



4 J 



I' = -- e SL . 



2R 



In this latter case the strength of the direct current produced 

 on opening the circuit (533), is 



(39) r, = -*:'. 



The two currents attain their maximum, for / = 0, and this 

 maximum is twice as great for the direct as for the inverse current. 



544. Two CIRCUITS WITH VARIABLE ELECTROMOTIVE FORCE. 

 Suppose we have 



