382 ELECTRICAL APPARATUS

where nr with a fractional-pitch armature winding is the number
of series turns in the pitch angle, o>, that is:

nr = — nf

IT

n" being the number of turns in series between the brushes, since
in the space (TT — «) outside of the pitch angle the armature
conductors neutralize each other, that is, conductors carrying
current in opposite direction are superposed upon each other.
See fractional-pitch windings, chapter "Commutating Machine,"
" Theoretical Elements of Electrical Engineering/'
212. Let:
Eo, Jo, ZQ = impressed voltage, current and self-inductive
impedance of the magnetizing or exciter circuit of stator (field
coils), reduced to the rotor energy circuit by the ratio of effective
turns, Co,
Eiy Ji, Zi = impressed voltage, current and self-inductive im-
pedance of the rotor energy circuit (or circuit at right angles
to Jo),
Ez, J2, £2 = impressed voltage, current and self-inductive im-
pedance of the stator compensating circuit (or circuit parallel to
Ji) reduced to the rotor circuit by the ratio of effective turns, c2.
E3, h, Zi = impressed voltage, current and self-inductive im-
pedance of the exciting circuit of the rotor, or circuit parallel
tO IQj
J4, Z4 = current and self -inductive. impedance of the short-
circuit under the brushes, Ji, reduced to the rotor circuit,
J5, Z5 = current and self-inductive impedance of the short-
circuit under the brushes, J3, reduced to the rotor circuit,
Z = mutual impedance of field excitation, that is, in the direc-
tion Of Jo, 13, I*,
Zr = mutual impedance of armature reaction, that is, in the
direction of Ji, J2, Js-
Zr usually either equals Z, or is smaller than Z.
14 and JB are very small, Z& and Z5 very large quantities.
Let S = speed, as fraction of synchronism.
Using then the general equations 7 Chapter XIX, which apply
to any alternating-current circuit revolving with speed, S, through
a magnetic field energized by alternating-current circuits, gives
for the six circuits of the general single-phase commutator motor
the six equations: