16 ELECTRICAL APPARATUS
is calculated in the usual way as described on page 318 of
" Theoretical Elements of Electrical Engineering." For any
value of slip, s, and corresponding value of torque, Ty the secondary
current is ii = e \/a^ +&22. To this secondary current corre-
sponds, by Fig. 6, the resistance, r, of the pyro-electric conductor,
and the insertion of r thus increases the slip in proportion to the
increased secondary resistance: --------> where 7*1 = 0.1 in the
present instance. This gives, as corresponding to the torque,
T, the slip:
,._ r+ TV
s " n '
where 5 = slip at torque, T, with short-circuited armature, or
resistance, TV
As seen from Fig. 7, very close constant-speed regulation is
produced by the use of the pyro-electric resistance, over a wide
range of load, and only at light-load the motor speeds up.
Thus, good coiistant-speed regulation at any speed below
synchronism, down to very low speeds, would be produced—
at a corresponding sacrifice of efficiency, however—by the use
of suitable pyro-electric conductors in the motor armature.
The only objection to the use of such pyro-electric resistances
is the difficulty of producing stable pyro-electric conductors, and
permanent terminal connections on such conductors.
B. Condenser Speed Control
11. The reactance of a condenser is inverse proportional to
the frequency, that of an inductance is directly proportional to
the frequency. In the secondary of the induction motor, the
frequency varies from zero at synchronism, to full frequency at
standstill. If, therefore, a suitable capacity is inserted into the
secondary of an induction motor, there is a definite speed, at
which inductive reactance and capacity reactance are equal and
opposite, that is, balance, and at and near this speed, a large
current is taken by the motor and thus large torque developed,
while at speeds considerably above or below this resonance speed,
the current and thus torque of the motor are small.
The use of a capacity,' or an-effective capacity (as polariza-
tion cell or aluminum cell) in the induction-motor secondary
should therefore afford, at least theoretically, a means of speed
control by varying the capacity.