98 ELECTRICAL APPARATUS

This inductive relation may be established outside of the motor
by an external phase-splitting device, or may take place in the
motor proper.

C. Monocyclic Devices. — An essentially reactive quadrature
voltage is produced outside of the motor, and used to energize
a cross-magnetic circuit in the motor, either directly through a
separate motor coil, or after combination with the main voltage
to a system of voltages of approximate three-phase or quarter-
phase relation.

D. Phase Converter. — By a separate external phase converter —
usually of the induction-machine type — the single-phase supply
is converted into a polyphase system.

Such phase converter may be connected in shunt to the motor,
or may be connected in series thereto.

This arrangement requires an auxiliary machine, running idle,

however. It therefore is less convenient, but has the advantage

of being capable of giving full polyphase torque and output to

the motor, and thus would be specially suitable for railroading.

64. If:

<i>o = main magnetic flux of single-phase

motor, that is, magnetic flux produced

by the impressed single-phase voltage,

and

$ = auxiliary magnetic flux produced by

starting 'device, and if
a? = space angle between the two fluxes, in

electrical degrees, and
<t> = time angle between the two fluxes,

then the torque of the motor is proportional to :

T = a$<!>o sin co sin <£; (13)

in the same motor as polyphase motor, with the magnetic flux,
$o, the torque is :

TQ = a$o2; (14)

thus the torque ratio of the starting device is:

T $

— . _ n <£ (15)
L o $0
or, if:
$' = quadrature flux produced by the starting device, that is,