CHAP. VIII] REACTION IN SYNCHRONOUS MACHINES 161 



active layer, and the wave form of the flux is very little affected by 

 the direct armature reaction. In the case of the transverse reac- 

 tion, however, the wave form of the flux produced by the actual 

 cross-magnetizing ampere-turns of the armature is entirely differ- 

 ent from that produced by the coil M t acting on the fictitious pole 

 (Fig. 39). Namely, the actual curve of the transverse flux has a 

 large " saddle " in the middle, due to the large reluctance of the 

 space between the real poles. The flux distribution produced by 

 the fictitious poles is practically the same as that under the main 

 poles, the two sets of poles being of the same shape. 



The addition of the vectors E t and E n in Figs. 40 and 41 is legit- 

 imate only when E t is induced by a flux of the same density dis- 

 tribution as E n , and this is the reason for representing the trans- 

 verse reaction as due to fictitious poles of the same shape as the real 

 poles. Therefore, for the purposes of computation, the flux dis- 

 tribution, produced by the actual distorting ampere-turns on the 

 armature, is resolved into a distribution of the same form as that 

 produced by the main poles and into higher harmonics. The m.m.f . 

 M t is calculated so as to produce the first distribution only. This 

 fundamental curve is not sinusoidal, but will have a shape depend- 

 ing on the shape of the pole shoes. The effect of the sinusoidal 

 higher harmonics on the value of E t is disregarded, or it can be 

 taken into account by correcting the value of the coefficient in 

 formula (81) from the results of tests. 



The first harmonic of the armature distortion m.m.f. is Af sin .r, 

 because this m.m.f. roaches its maximum between the real poles; 

 x is measured as before from the centers of the real poles. The 

 permeance of the active layer, with reference to the real poles, can 

 be represented as before by (Pf(x) . The flux density produced by 

 the transverse reaction of the armature at a point defined by the 

 abscissa x is therefore proportional to M sin x (Pf(x). The per- 

 meance of the active layer with reference to the fictitious poles is 

 tP/te + i*). The flux density under the fictitious poles follows 

 therefore the law M t (Pf(x + ^n). As is explained before, the two 

 ut ions of the flux density differ widely from one another, 

 and the real distribution is resolved into the fictitious distribution. 

 and higher sinusoidal harmonics; the prominent third harmonic is 

 clearly seen in Fig. 39. Thus, we have, omitting (P, 



M sin xf(x) =M t f(x + fr) +A 3 sin 3x + A& sin 5x+ etc. (91) 



