THE SYNCHRONOUS MOTOR. 



145 



That is, the power output of machine B is proportional to OQ 

 and the proportionality factor is the constant /i/R 2 -f X 2 . 



Equation (v) may be put into a more convenient form as 

 follows : The projection of A, Fig. 125, on the line ef is equal 

 to A cos (<t> 6) ; the projection of B on ef is B cos 6 ; and 

 OQ is the sum of these two projections. Therefore, substituting 

 A cos (</> &) -f B cos for OQ in equation (v), we have 



AB B 2 



P" 



S-COB - 



c 



Figure 126 is a construction essentially similar to Fig. 125, but 

 with the electromotive force A taken as the fixed reference axis : 



Fig. 126. 



both figures, 125 and 126, being constructed for the same value 

 of </>. From Fig. 1 26 it may be shown that 



(vi) 



from which an expression for P f may be derived corresponding 

 to equation (15) namely : 



ii 



