ALTERNATING-CURRENT MOTORS 307

are the reduction factors of the circuits to equal number of
effective turns, as discussed before.

Or circuits connected in series: ™ = — > etc.

Ci. Ck

When a rotating circuit is connected through a commutator,
the frequency of the current in this circuit obviously is the same
as the impressed frequency. Where, however, a rotating circuit
Is permanently closed upon itself, its frequency may differ from
the impressed frequency, as, for instance, in the polyphase in-
duction motor it is the frequency of slip, s = 1 — S, and the
self -inductive reactance of the circuit, therefore, is sx; though in
its reaction upon the stationary system the rotating system nee-
essarily is always of full frequency.

As an illustration of this method, its application to the theory
of some motor types shall be considered, especially such motors
as have either found an extended industrial application, or have

1 . at least been seriously considered.

1. POLYPHASE INDUCTION MOTOR
174. In the polyphase induction motor a number of primary
circuits, displaced in position from each other, are excited by
polyphase e.m.fs. displaced in phase from each other by a phase
angle equal to the position angle of the coils. A number of sec-
ondary circuits are closed upon themselves. The primary usu-
ally is the stator, the secondary the rotor.
In this case the secondary system always offers a resultant
closed circuit in the direction of the axis of each primary coil,
irrespective of its position.
Let us assume two primary circuits in quadrature as simplest
form, and the secondary system reduced to the same number of
phases and the same number of turns per phase as the primary
system. With three or more primary phases the method of
procedure and the resultant equations are essentially the same.
Let, in the motor shown diagrammatically in Fig. 148:
$0 and — j#o, /o and — j/o, ^o = impressed e.m.f., currents
and self-inductive impedance respectively of the primary system.
0, /i and •— j/i? Zi = impressed e.m.f., currents and self-in-
ductive impedance respectively of the secondary system, reduced
to the primary. Z = mutual-inductive impedance between
primary and secondary, constant in all directions.