14 SYNCHRONOUS MOTORS 



It will be observed that, when the current is in phase with the induced 

 E.M.F., the magneto-motive force of the armature-reaction has no 

 action on the inducing field, and can only produce a transverse dis- 

 tortion of the field; while, on the other hand, when the current is out 

 of phase one-fourth of a period in advance, or behind, the M.M.F. is 

 directly opposed to, or coincident with, that of the field. With regard 



to the sign, it can be easily seen that a phase-difference of in advance 

 of the induced E.M.F. produces a magnetizing reaction which is the 



same as in a generator, and that a phase-difference of - behind pro- 



2 



duces a demagnetizing reaction. It must not be forgotten, however, 

 that the internal E.M.F. is opposed to the external E.M.F. and that 

 the lag and lead are therefore transposed if they are referred to the 

 latter. 



Elementary Explanation of Single-Phase Synchronous Motors. 

 The phenomena are more complicated in single-phase motors. The 

 same explanation may nevertheless be retained by means of a simple 

 artifice of reasoning. 



The coils of the armature-winding, being excited by a single alternat- 

 ing current (Fig. 10), produce poles which no longer revolve, but are 

 stationary. These poles are alternately 

 positive and negative, and have a mag- 

 netic flux which varies periodically like 

 the current that produces it. There is, 

 therefore, no tendency to rotation; and 

 the motor can only be put in operation 

 by external means, as already seen. But 

 we may suppose it brought previously 

 to synchronism. 



M. Maurice Leblanc has enunciated a theorem which is an elec- 

 trical analogue of the following well-known optical theorem: A 

 vibration of luminiferous ether polarized rectilinearly may be replaced 

 by two circularly polarized vibrations of contrary sign having the same 

 frequency and having amplitudes equal to the half amplitude of the 

 rectilinear vibration. 



According to M. Leblanc's theorem, an alternating stationary mag- 

 netic field may be replaced by two fields revolving in contrary 

 directions, each having a flux half as large, and having equal velocities, 

 such that they advance a distance equal to that of two poles during a 



