540 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



Then the equation of the current x in A will be 



(4), 



;md that of y in B TJ = Sy + -7- ( MX + Ny] ............................ (5), 



where and 17 are the electromotive forces, x and y the currents, and R and <S 

 the resistances in A and B respectively. 



Induction of one Current by another. 



(29) Case 1st. Let there be no electromotive force on B, except that 

 which arises from the action of A, and let the current of A increase from 

 to the value x, then 



n tf 



whence Y = I ydt = -~ x, .............................. (6) 



Jo 



that is, a quantity of electricity Y, being the total induced current, will flow 

 through B when x rises from to x. This is induction by variation of the 

 current in the primary conductor. When M is positive, the induced current 

 due to increase of the primary current is negative. 



Induction by Motion of Conductor. 



(30) Case 2nd. Let x remain constant, and let M change from M to M', 

 then 



M'-M 



so that if M is increased, which it will be by the primary and secondary 

 circuits approaching each other, there will be a negative induced current, the 

 total quantity of electricity passed through B being Y. 



This is induction by the relative motion of the primary and secondary con- 

 ductors. 



