SINGLE-PHASE COMMUTATOR MOTORS 361

advantage of the series-repulsion motor type is the possibility
which this type affords, of securing the proper commutating
field at all speeds down to that where the speed is too low to
induce sufficient voltage of neutralization at the highest available
commutating flux.

VI. Motor Characteristics

202. The single-phase commutator motor of varying speed or
series characteristic comprises three circuits, the armature, the
compensating winding, and the field winding, which are connected
in series with each other, directly or indirectly.

. The impressed e.m.f. or supply voltage of the motor then con-
sists of the components:

1. The e.m.f. of rotation, ei, or voltage generated in the arma-
ture conductors by their rotation through the magnetic field, $.
This voltage is in phase with the field, <£, and therefore approxi-
mately with the current, i, that is, is power e.m.f., and is the
voltage which does the useful work of the motor. It is propor-
tional to the speed or frequency of rotation,/0, to the field strength,
$, and to the number of effective armature turns, MI.

el =

(23)

The number of effective armature turns, MI, with a distributed
winding, is the projection of all the turns on their resultant direc-
tion. With a full-pitch winding of n series turns from brush to
brush, the effective number of turns thus is:

i -«
77,1 = tn [avg cos] T = —m.

— •' IT

(24)

With a fractional-pitch winding of the pitch of r degrees, the
effective number of'turns is:

r r + i 2 . r

n\ = m ~ [avg cosj r = - m sin r'

(25)

2. The e.m.f. of alternation of the field, CQ, that is, the voltage
generated in the field turns by the alternation of the magnetic
flux, <i>, produced by them and thus enclosed by them. This vol-
tage is in quadrature with the field flux, <i>, and thus approxi-
mately with the current /, is proportional to the frequency of the