142 SYNCHRONOUS MOTORS 



to polyphase motors, but it can also be accomplished, although with 

 more difficulty, in the case of single-phase motors. The phenomenon 

 was first observed as early as 1874, by Siemens of London, who found 

 that he could suppress the excitation of a single-phase motor without 

 stopping it. The explanation is simple if we refer to the use already 

 made of the theorem of Leblanc, i.e., that the alternating field of the 

 armature-reaction can be replaced by two fields, each of half the strength, 

 rotating in opposite directions, one of which remains in front of the 

 field-poles and magnetizes them, the other being a useless parasite 

 current, rotating with twice the speed of the poles and producing no 

 effect (except eddy currents). 



Another explanation can also be given, based on the variation of 

 the coefficient of self-induction of the armature at each period during 

 its rotation. In consequence of this variation the reaction-flux li is 

 a maximum when the armature coils are exactly in front of the poles. 



This position is therefore that which the armature would tend to 

 take if a direct current were passing through it. Hence, if the machine 

 is driven by hand, it will be sufficient that the motion may continue, 

 as in certain toys, to break or to weaken the current each time that the 

 coils move away from a pole, or that it may close the circuit, or 

 strengthen the current, each time that they approach the next pole. 

 Now this effect is precisely produced with an alternating current 

 (because the direction of the current is of no importance here) as soon 

 as the maximum of the periodic current is made to lead in phase 

 with respect to the maximum of /, as can be easily seen. The sum 

 of the effects which attract the armature in the direction of motion 

 during a period is then greater than the sum of the contrary effects. 



The motion therefore continues, and it is easy to see that it may 

 be steady, because every acceleration of the motion tends to diminish 

 the phase-angle between i and /, and, consequently, tends to diminish 

 the dissymmetrical action, while retardation increases the phase-angle, 

 and, consequently, increases the useful action of the current. 



These considerations can be easily verified by calculation by referring 

 to the equation 



,di 



ue nujl-^-. 

 at 



in which we will let =o, to take into account the fact that there is 

 no excitation. The alternator having a variable self-induction 



l=l' + X COS 20)t, 



