THE ARMATURE REACTIONS OF ALTERNATORS 253 



mean line of the curve so obtained is then traced, which indicates 

 the zero of magnetic potential. The fluxes will be at every point 

 proportional to the ordinate of the curve from the zero point, and 

 inversely proportional to the reluctance per unit of surface correspond- 

 ing to the abscissa considered. For simplicity, the reluctance may first 

 be assumed constant, and account is only taken of its variations in 

 order to arrive at a definite correction for a second approximation. 

 To simplify the calculation, there is attributed to the maximum ampli- 

 tude of the polyphase currents an arbitrary value IQ, and it is supposed 

 that the currents follow a sinsuoidal law. Since the form of the curves 

 is reproduced for every one-sixth of a period in the three-phase cur- 

 rents (or for one-fourth of a period in two-phase currents), it suffices 

 to study them during such an interval, and then to outline the extreme 

 forms. 



Entrgj 



PhtM^S O 



Pb.* 1-H / 



FIG. 8. 



Let us take, for example, a three-phase machine with six slots in 

 the field, each containing N/6 wires, calling N the total number of 

 peripheral wires per double field (Fig. 8). The potential produced 

 by each is 0.271 (N/6)i, calling i the current which traverses the 

 winding, and it suffices to construct the curve of i, to which that of 

 the potentials should be proportional. We take two positions; one 



v7 



for which the current is nil in the slots i and 4 and equals - 7 



2 



in the others; the other position for which the current is equal to IQ 

 in the slots i and 4 and equal to (1/2) IQ in the others. The curves 

 proportional to the potential thus obtained are respectively represented 

 in Figs. 8 and 9. On these figures are added in position and in 

 magnitude the outlines of the field-magnet poles in the two positions; 

 in full lines the position corresponding to the watt current, that is to 

 say, a pole axis coinciding with the middle of the curve of potential; 



