HYSTERESIS MOTOR 169

and the power of the motor is :

P = (1 - s) Z> = (1 - $) m$3> sin a,

where
s = slip as fraction of synchronism.
The apparent efficiency is :
-ft = (1 — s) sin a.
Since in a magnetic circuit containing an air gap the angle,
a, is small, a few degrees only, it follows that the apparent
efficiency of the hysteresis motor is low, the motor consequently
unsuitable for producing large amounts of mechanical power.
From the equation of torque it follows, however, that at
constant impressed e.m.f., or current — that is, constant 2F —
the torque is constant and independent of the speed; and there-
fore such a motor arrangement is suitable, and occasionally used
as alternating-current meter.
For s<0, we have a < 0,
and the apparatus is an hysteresis generator.
99. The same result can be reached from a different point
of view. In such a magnetic system, comprising a movable
iron disk, I, of uniform magnetic reluctance in a revolving
field, the magnetic reluctance — and thus the distribution of
magnetism — is obviously independent of the speed, and conse-
quently the current and energy expenditure of the impressed
m.m.f. independent of the speed also. If, now:
V = volume of iron of the movable part,
<B = magnetic density,
and
t\ = coefficient of hysteresis,
the energy expended by hysteresis in thS movable disk, I, is
per cycle:
W o = TfyB1-6,
hence, if / = frequency, the power supplied by the m.m.f. to
the rotating iron disk in the hysteretic loop of the m.m.f. is:
Po = /TW-6.
At the slip, sfj that is, the speed (1 — $)/, the power expended
by hysteresis in the rotating disk is, however:
Pi =