. REACTION MACHINES 263
that is, the sine wave of equal effective strength and equal power
with the distorted wave, is in advance of the wave of magnetism
by what is called the angle of hysteretic advance of phase a.
Since the e.m.f. generated by the magnetism, or counter e.m.f.
of self-induction lags 90° behind the magnetism, it lags 90° + a
behind the current; that is, the self-induction in a circuit contain-
ing iron is not in quadrature with the current and thereby
wattless, but lags more than 90° and thereby consumes power, so
that the reactance has to be represented by X — h + jx, where
h is what has been called the "effective hysteretic resistance/'
A similar phenomenon takes place in alternators of variable
reactance, or, what is the same, variable magnetic reluctance.
Operation of synchronous machines without field excitation
is most conveniently treated by resolving the synchronous
reactance, XQ} in its two components, the armature reaction and the
true armature reactance, and once more resolving the armature
reaction into a magnetizing and a distorting co'rnponent, and
considering only the former, in its effect on the field. The true
armature self-inductance then is usually assumed as constant.
Or, both armature reactance and self-inductance, are resolved
into the two quadrature components, in line and in quadrature
with the field poles, as shown in Chapters XXI and XXIV of
"Alternating-Current Phenomena/' 5'th edition.
150. However, while a machine comprising a stationary single-
phase "field coil," A, and a shuttle-shaped rotor, R, shown
diagrammatically as bipolar in Fig. 126, might still be interpreted
in this matter, a machine as shown diagrammatically in Fig.
127, as four-polar machine, hardly allows this interpretation.
In Fig. 127, during each complete revolution of the rotor, R,
it four times closes and opens the magnetic circuit of the single-
phase alternating coil, A, and twice during the revolution, the
magnetism in the rotor, R, reverses.
A machine, in which induction takes place by making and
breaking (opening and closing) of the magnetic circuit, or in
general, by the periodic variation of the reluctance of the
magnetic circuit, is called a reaction machine.
Typical forms of such reaction machines are shown diagram-
matically in Figs. 126 and 127. Fig. 126 is a bipolar, Fig. 127
is a four-polar machine. The rotor is shown in the position of
closed magnetic circuit, but the position of open magnetic circuit
is shown clotted,