134 Dr. 0. J. Lodge on Intermittent Currents 



we will suppose M to be the coefficient of mutual induc- 

 tion between the primary and secondary. The coils shall be 

 fixed in position so that M is constant ; then a current j 

 will be developed in the secondary circuit whenever the pri- 

 mary changes from E to S; and this will react on the primary 

 current i, the equations for determining both being 



L l +M f +Si=E • • • • < 17 > 



and 



1% + M§ + , i= 0, .... (18) 



with the conditions ^=p~ and^O when £=0. 



Differentiating these (E being supposed constant), we easily 

 separate the variables and obtain 



., (K-M0g+(Lr+SZ)| + Sn=E, . . (19) 



and 



(LZ-M 2 )g+(Lr + S0f +S,i=0. • • (2Q) 



. Now the solution of (20), remembering the initial condition, 

 is 



^We-^sinh/ft ......... (21) 



or 



where 



*-2{U-W) and ^-- pifj - ( 22 > 



[ le - « 2 -^ = l5mJ' 



and where J is a constant which has yet to be determined. 

 It is well to notice that neither a nor /S can vanish or be- 

 come imaginary ; but they can become infinite simultane- 

 ously. 



To obtain the' value of the primary current i, we can either 

 write down the solution of (19), viz. 



i= | +e-'(C 1 <F + CierV); . , , . (23) 



or, what is practically more convenient as determining all arbi- 

 trary constants directly, we can combine equations (17) and 



