706 INDUSTRIAL APPLICATIONS. 



When the ring turns in a magnetic field, we may propose to 

 determine the electromotive force in each coil, the position of the 

 brush which produces the maximum current, and the intensity of 

 this current. 



Let 4#z be the total number of coils, 



/ the number of windings of each coil, 

 P = ^mp the total number of windings, 

 n the number of turns in a second, 

 <j) = 2mr the angular velocity, 

 p the resistance of one winding, 

 r=pp the resistance of a coil, 

 / its coefficient of self-induction, 

 a the resistance of a ring-shaped coil, 

 R the total useless resistance, comprising the wires of the 

 machine and the connections. 



Fig. 253. 



When the brushes merely rest on a strip, the resistance of the 



coil is -2mr=mr=-i and when each rests on two successive 

 2 4 



strips - (2m - i) r= (P - 2/) -. We may, without appreciable error, 

 2 4 



replace this variable resistance by an intermediate constant value 



a = mr - - = (P -/) - . 

 4 4 



1263. We shall assume that the external field is symmetrical 

 with respect to a plane CD (Fig. 254) passing through the axis of 

 rotation ; we shall also assume that it is symmetrical to within a 



