522 PARTICULAR CASES OF INDUCTION. 



and that the second circuit is closed without containing any electro- 

 motive force. 



When the permanent state is attained, the two currents are still 

 periodic, and as in (355), we may write 



I = A sin 27T ( 6 ) 



(40) V T / 



Putting 



M2R ' 



T 2 



/=L _4, l! _M ! L_ 



T 2 47T 2 



R'2 + 1_ L '2 

 T 2 



the condition that the differential equations are satisfied for any 

 given time by their values of E, I, and I', gives 



A2 _ 

 (41) 



27T/ 



tan 27rd> = -- . 

 Tr 



These expressions have the same form as above (535). It will 

 be seen that the effect of the presence of the second circuit is to 

 increase the apparent resistance of the first, and to diminish the 

 apparent coefficient of self-induction. 



We shall find, in like manner, for the second circuit, 



(41) 



tan 27T</>' = 



27T LV + R7 



