CHAP. VII] M.M.F. OF DISTRIBUTED WINDINGS 129 



due to phase 1, and gliding to the left, be denoted by LI, and that 

 due to phase 2 by L 2 . Let the corresponding waves gliding to the 

 right be denoted by R! and R 2 . Disregarding the higher har- 

 monics, the resultant m.m.f. is due to the combined action of the 

 four gliding waves L 1? L 2 , RI and R 2 . At the instant (=0 the 

 crest of the wave L! is at the point 0\; at the iristant t=T the 

 crest of the wave L 2 is at the center 2 of the coil 2. Consequently, 

 at the instant t=0 the crest of the wave L 2 is 90 electrical degrees 

 to the right of 2 , or it is at Oi. Thus, the waves LI and L 2 actu- 

 ally coincide in space, and form one wave of double the amplitude. 

 The crest of the wave R t is at the point Oi when t=0\ the en M 

 of Ro is at the point 2 when t= \T. Therefore, at t=0 the crest 

 of R 2 is 90 electrical degrees to the left of the point 2 , and the 

 waves RI and R 2 travel at a distance of 180 electrical degrees from 

 each other. But two such waves cancel each other at all points 

 and at all moments, so that there is no resultant R wave. Thus 

 the resultant fundamental wave of m.m.f. in a two-phase machine 

 is gliding. Its amplitude is twice as large as that of either of the 

 component gliding m.m.fs. of the two phases, which components 



,8 Armature ,2 A 





FIG. 356. A three-phase winding. 



are expressed by eq. (63). If the current in phase 12 were leading 

 with respect to that in phase 1, the L fluxes would cam-el each 

 other and the resultant flux would travel from left to riplit . 



Consider now a three-phase winding (Fig. 356) and call the 

 in.ni.fs. which glide to the left, and which are due to the separate 

 phases, by LI, L 2 , and L 3 respectively . l<t the waves which 

 travel to the right be denoted by R,, R L >, and R.I. Assume the cur- 

 in phase 2 to be lagging by 120 electrical degrees, or by J7\ 

 with respect to that in phase 1, and the current in phase 3 to be 

 ng by %T with respect to that in phase 2. By a reason in. u r 

 similar to that given for the two-phase winding above it can !>c 

 .-hnwn that the three L waves coincide in their position in space, 

 and : iv one lidini: wave of three times the amplitude of each 

 wave. UK time R waves are relatively displaced by 240 elec- 



