REACTION MACHINES 267
reactance, x, in the first case, the hysteretic cycle has been over-
turned so as to represent, not consumption, but production of
electrical energy, while in the second case the hysteretic cycle has
been widened, representing not only the electrical energy consumed
by molecular magnetic friction, but also the mechanical output.
152. It is evident that the variation of reluctance must be
symmetrical with regard to the field poles; that is, that the
two extreme values of reluctance, maximum and minimum, will
take place at the moment when the armature coil stands in front
of the field pole, and at.the moment when it stands midway
between the field poles.
The effect of this periodic variation of reluctance is a distortion
of the wave of e.m.f., or of the wave of current, or of both.
Here again, as before, the distorted wave can be replaced by
the equivalent sine wave, or sine wave of equal effective intensity
and equal power.
The instantaneous value of magnetism produced by the
armature current—which magnetism generates in the arma-
ture conductor the e.m.f. of self-induction-—is proportional to
the instantaneous value of the current divided by the instan-
taneous value of the reluctance. Since the extreme values of
the reluctance coincide with the symmetrical positions of the
armature with regard to the field poles—that is, with zero and
maximum value of the generated e.m.f., EQ, of the machine—
it follows that, if the current is in phase or in quadrature with
the generated e.m.f., jB0, the reluctance wave is symmetrical to
the current wave, and the wave of magnetism therefore sym-
metrical to the current wave also. Hence the equivalent sine
wave of magnetism is of equal phase with the current wave; that
is, the e.m.f. of self-induction lags 90° behind the current, or is
wattless.
Thus at no-phase displacement, and at 90° phase displace-
ment, a reaction machine can neither produce electrical power
nor mechanical power.
If, however, the current wave differs in phase from the wave
of e.m.f. by less than 90°, but more than zero degrees, it is un-
symmetrical with regard to the reluctance wave, and the re-
luctance will be higher for rising current than for decreasing cur-
rent, or it will be higher for decreasing than for rising current,
according to the phase relation of current with regard to generated
e.m.f., EQ.