TRANSACTIONS OF SECTION G. 



877 



upon the vertical and the current i = l sin a can be represented by the projection 

 of 01 = I upon the vertical. In the diagram the maximum electromotive force of 

 self-induction is given by the line O El = Ei, and the maximum electromotive force 

 necessary to overcome the inert resistance of the circuit by the line OEp =Ep. 



Et = 27r«LI 

 Bp=rl 

 . , 2irnL 



tffCJ) = __ 



ET 



The work in time dt is fAV = _^ — sin (a + (p) sin ada, which integrated be- 

 tween the limits a = o and a — 'Jtt, and divided by the periodic time, gives the rate 

 of working — 



W = — cos (f>, 

 r 



Let e and i represent the measured values of electromotive force and current : 

 then we have also — 



W = ei cos (f). 



In a continuous current system (^ = o, and the measured volt-ampere capacity of 

 the plant is e;', all of which is available for doing work. In an alternate current 

 system the available work is reduced in the ratio of 1 to cos (f) ; hence cos (ft might 

 be called the plant efficiency. 



To make the work a maximum for a given E, I cos (f) must be a maximum. 

 From diagram 



El = E sin ^ ; 



K = 27r«LI, I = ^^,and 



and since 



'JjrnL, 



I cos (p ^ 



E sin (p cos ip 



which becomes a maximum, for (p = 45°. In this case 



Ep = E(. 



