CHAP. XII] INDUCTANCE OF WINDINGS 237 



The number of simultaneously short-circuited coils varies 

 periodically with the position of the brushes. Thus, in Fig. 57 

 sometimes two and sometimes three coils are short-circuited 

 by one set of brushes. On the average 



s=(b-b')/a, ...... (159) 



where a is the width of one commutator segment including the 

 mica insulation. Thus, all the values which enter into the 

 formula (156) are determined, and the reactance voltage for a 

 given machine can be easily calculated. 



Formula (156) is used not only as a criterion of the commuta- 

 tion, but also for the calculation of the flux density, under the 

 interpoles where such are required. Namely, this flux density must 

 be such that the average voltage induced by the commutating 

 flux is approximately equal and opposite to the average reactance 

 voltage; see Art. 24. prob. 6. A still closer compensation for the 

 influence of the inductance is achieved by properly grading the 

 commutating flux, so as to compensate not only for the average 

 reactance voltage, but also to some extent for the instantaneous 

 induced e.m.fs. 



The average reactance e.m.f. induced in some other direct cur- 

 rent windings. With two-circuit wave windings two cases must 

 be considered, namely, (a) when the machine is provided with 

 only two sets of brushes, (6) when there are more than two sets 

 of brushes. In the first case eq. (156) is used, where 



/i = i/, ........ (160) 



and Lq is understood to comprise the short-circuited conductors 

 under all the poles, per commutator segment. Let there be 

 again q turns per coil, that is, per unit of winding per pair of 

 poles. Since the corresponding conductors under all the poles 

 .IK in series, we have that L^pLpp. The influence of the 

 ..I her simultaneously short-circuited coils is expressed as before 

 l)\ the factor 2, where is given by formula (159). Thus, for 

 a two-circuit winding with two sets of brushes 



L+-2p*p((Pi'li + tfVC + JtfVOXlO- 1 henrys. . (161) 



The frvcjurn, ;, 



When more than tun s.-N <>f l.ni-hi- :uv u-vd. tin- Wtfl <>f 

 equal polarity are connected in parallel by the stud connections 



