GENERAL PRINCIPLES OF SYNCHRONOUS MOTORS 17 

 This may also be written, 



P> Tf 



wherein tan/? = ^ ^- tan 0; 





a>L 

 tan r = -. 



In this equation /2=the phase-angle of the resultant E.M.F. and ?-=the 



supplemental phase-difference of the current measured from this E.M.F. 



In the simple particular case where EI =E 2 this expression reduces to 



2 ^j-^ 

 or, since 



. 



sm 

 2 

 iff cos coi+coL sin aJt\; 



R ajL 



T2 =sin r; 



we will have 



sin cos (cutr) 



._ 2 ' 



i.e., the current will have the effective value 



O 

 sn 



and will be out of phase by the angle 7- with respect to the resultant 

 E.M.F., which is itself out of phase with respect to the mean of e\ 



and 62. This result is easily interpreted in Fig. n, by drawing the 

 resultant curve ^1+^2, obtained by taking the difference of the ordinates 

 of the first two curves. It will be seen that the curve has actually a 



phase-difference equal to with regard to the mean of e\ and e^, and 



