120 SYNCHRONOUS MOTORS 



Then, taking to as the origin, (*o=o), we will have 

 o2 sin (uj^t O} sin (oj\t 



= Cco 



2 Jo 



-^- f 

 2 Jo 



4 0* 



I 



sin 

 4 



Noting that 



the total value for the torque, at each instant, would therefore be 

 C= 



When wi is very near 0*2 the amplitude of the first term becomes 

 very high, and this is the case so long as a>i is not exactly equal to 01%. 

 At that moment, there is a discontinuity; and the term in question 

 vanishes. 



Under these conditions, the inertia is low compared with the enormous 

 torque which is developed, and the motion of the alternator can undergo 

 pulsating variations of speed which are considerable. The hypothesis 

 which forms the basis of our reasoning concerning the nature of the 

 motion is no longer fulfilled and the equations no longer have any value. 



Only one conclusion, therefore, can be drawn, i.e., it is necessary 

 to bring the motor, by some process, to a speed at least 'equal to that 

 of synchronism, before connecting it with the source of current-supply. 



A second method of starting a motor without load, and which can 

 be used with success every time there is only one power-transmission, 

 consists in starting simultaneously the generator and the motor. A 

 very weak impulse then suffices to make ^ 1 =o>2, at the moment of 



