356 ELECTRICAL APPARATUS mutator, as shown by Fig. 171 in its successive steps, in position: 1. There is current through brush, Bi] 2. There is current through both brushes, BI and Ł2, and the armature coil. A, is closed by the counter e.m.f. of coil, N, that is, the difference, A — N, is short-circuited; 3. There is current through brush jB2; 4. There is current through both brushes, BI and J52, and the coil, N, is short-circuited; 5. The current enters again by brush BI] thus alternately the coil, N, of half the voltage of the armature coil, A, or the difference between A and N is short-circuited, that is, the short-circuit current reduced to one-half. Complete elimination of the short-circuit current can be pro- duced by generating in the armature coil an opposing e.m.f. This e.m.f. of neutralization, however, can not be generated by the alternation of the magnetic flux through the coil, as this would require a flux equal but opposite to the full field flux travers- ing the coil, and thus destroy the main field of the motor. The neutralizing e.m.f., therefore, must be generated by the rotation of the armature through the commutating field, and thus can occur only at speed; that is, neutralization of the short-circuit current is possible only when the motor is revolving, but not while at rest. 200. The e.m.f. of alternation in the armature coil short-cir- cuited under the commutator brush is proportional to the main field, <Ł, to the frequency, /, and is in quadrature with the main field, being generated by its rate of change; hence, it can be rep- resented by e0 = 27r/10-8j. (17) The e.m.f., e\} generated by the rotation of the armature coil through a commutating field, <Ł', is, however, in phase with the field which produces it; and since e\ must be equal and in phase with e0 to neutralize it, the commutating field, <Ł', therefore, must be in phase with eQ, hence in quadrature with <Ł; that is, the com- mutating field, $', of the motor must be in quadrature with the main field, , to generate a neutralizing voltage, ei, of the proper phase to oppose the e.m.f. of alternation in the short-circuited coil. This e.m.f., ei, is proportional to its generating field, $', and to the speed, or frequency of rotation, /o, hence is: ei = 27T/o$'lO~8, (18)