154 SYNCHRONOUS MOTORS 



where k% is a constant. But, 



R cos fy' = Ri cos fy AI cos Y) 

 where <J> is the phase difference between E\ and 7, and 



also A i is proportional to A (on the assumption of constant reluctance 

 in all directions through the armature, see " Diagram Transforma- 

 tions," page 149, etc., therefore 



P2 = K2(AiR\ cos fy A i 2 cos Y), .... (2) 



where K? is the new constant of proportionality. 



Referring now to Fig. 76, the isosceles triangle OA C is constructed 



on RI as base, with Y( =tan -1 - = tan -1 ) as the base angle. 

 \ Nt r r I 



The notation is the same as in the preceding figures. 



Locate the point B by the rectangular coordinates u and v measured 

 along the axes OC and OD (perpendicular to OC). Then u=-A\ cos <{, 

 and 



cos Y, ...... (3) 



2 j 



^+-=--. . (4> 



\ 2 COS Y / \COS Y/ L \ 2 / Kz \ 



This equation has exactly the same form as equation (See Ch. II, 

 near Eq. (19)) and its interpretation is likewise the same. The radius 

 - 



of the constant-power circles is 



T> J- i ARA 2 P 2 cos Y 



Radms= \[- (5) 



cos Y \ V 2 / Kz 



The general interpretation of Fig. 76 is identical to that of Fig. 27, 

 but the method of quantitative application is not quite so obvious. 

 The simplest method is as follows: 



Since A\, F, and RI are measured in ampere-turns, they may in 

 any given case be expressed in terms of the equivalent field amperes, 

 RI being the field current taken from the saturation curve at the 

 point corresponding to the impressed E.M.F. E\, F being the actual 

 operating field current, and AI the field current -taken from the 



