GENERAL PRINCIPLES OF SYNCHRONOUS MOTORS 19 



These variations constitute sine-functions having pulsations twice 

 as rapid as those of the current, which have for their axes the horizon- 

 tal lines (Pi, P2,) corresponding to the mean powers given by the first 

 terms within the brackets in the following equations: 



r\=- 



R 



E 2 



2 2 . /6 

 \=-= sin sin r-\ 



VR 2 +a?L 2 2 Y 



[cos (r+#)+cos rl; 



. o / e\ 



sin sin I r 

 2 V a/ 



E 2 



The very small difference between PI and P^ represents the loss 

 by resistance (Joule effect). The axis of the curve P\ is therefore 

 a little more above the axis of zero power than the axis of symmetry 

 of the curve P% is below it. 



The torque could be obtained, in each case, by dividing the power 

 by the angular velocity. These expressions show that the current 

 increases with 6 until equals TT, but the torques, which equal zero so 

 long as the lag #=zero, increase with only until the value 6 = ?; and 

 they then decrease. 



Stability will, therefore, exist only with < f having for its axis the 

 exact opposition of E.M.F.'s. 



The solution, in the case where E\ is different from 2, will be 

 obtained in an analogous manner, by forming the products e^e^i; 

 and it would still give pulsating values for pi and p 2 ; but, since these 

 caculations are uselessly complicated, we will pass them by and turn 

 to more simple methods. 



Case of Symmetrical Polyphase Motors. In the case of polyphase 

 motors the same considerations and equations remain applicable to each 

 of the symmetrical circuits, if only care be taken to include, in the 

 self-induction of these circuits, their mutual induction effects. By 

 reason of symmetry itself, the result is obtained by a simple in- 

 crease of the coefficient, L, in a ratio which depends on the number 

 of phases in the machine. 



The currents are, in general, approximately equal in effective values 

 in the different circuits, if there are no defects in construction. It 



