32 SYNCHRONOUS MOTORS 



-P 2 = the electric power generated in the armature by the current, and 



counted positively in the same direction as the mechanical 



power obtained from the motor; 



0=the phase-angle between the E.M.F's. E\ and E 2 ; 

 0=the phase-angle between the current, /, and the E.M.F. E 2 , of 



the motor; 



^=the phase-angle between the current, 7, and the external E.M.F.,i. 

 f= an auxiliary angle representing the phase -angle existing between 



the current and the resultant E.M.F., e, which produces it in the 



circuit. It is defined by the known relation, 



sin f=-y, 

 aj+) v ^ 



(1) tan 7-=^ -=X; whence i 



-*^ R 



\cos r = y. 

 ( 6 



d=an analogous angle, obtained by neglecting the reactance of the 

 motor. It is defined by the relation, 



(2) tanfl=j. 



The standard diagram which has already been referred to is not 

 easy to apply, partly because a complicated construction is necessary 

 for each load to give the current-strength in magnitude and in phase, 

 and partly because the vectors of the current-strength become too 

 small, inasmuch as the E.M.F. may attain thousands of volts while the 

 currents are of a few amperes only. The geometrical constructions 

 deduced from this diagram by other authors are extremely complicated. 



The author devised, some years ago, 1 for the study of problems 

 of this kind, a so-called " bipolar " diagram, which avoids these two 

 objections and at the same time gives the theory an almost childlike 

 simplicity, and renders graphical calculation sufficiently accurate. 



Principle of Bipolar Diagrams. The principle of this method con- 

 sists in taking different axes of reference and different scales for the 

 currents and for the E.M.F's., instead of taking the same axis of 

 reference and the same scale for both, as is usually done. The axes 

 and scales may then be selected for the current in such manner that the 



1 Thtorie des moteurssynchroncs. Lahure, publ. 1895. L 1 Industrie Electrique, 

 Feb., 1895. 



