UNIPOLAR MACHINES

453

induced in a turn is proportional (or equal, in absolute units) to
the rate of change of the number of lines of magnetic force en-
closed by the turn, and a decrease of the lines of force enclosed
by the turn, induces a voltage opposite to that induced by an
increase. As the number of lines of force enclosed by a turn can
not perpetually increase (or decrease), it follows, that a voltage
can not be induced perpetually in the same direction in a turn.
Every increase of lines of force enclosed by the turn, inducing

FIG. 217.—Mechanical an-
alogy of bipolar induction.

FIG. 218.—Mechanical analogy*of
unipolar induction.

a voltage in it, must sometime later be followed by an equal
decrease of the lines of force enclosed by the turn, which induces
an equal voltage in opposite direction. Thus, averaged over a
sufficiently long time, the total voltage induced in a turn must
always be zero, that is, the voltage, if periodical, must be alter-
nating, regardless how the electromagnetic induction takes place,
whether the turn is stationary or moving, as a part of a machine,
transformer, reactor or any other electromagnetic induction
device. Thus continuous-voltage induction in a closed turn
is impossible, and the coil-wound unipolar machine thus a
fallacy. Continuous induction in the unipolar machine is pos-
sible only because the circuit is not a closed one, but consists of a
conductor or half turn, sliding over the other half turn. Mechan-
ically the relation can be illustrated by Figs. 217 and 218. If
in Fig. 217 the carriage, C, moves along the straight track of
finite length—a closed turn of finite area—the area, A, in front of
C decreases, that B behind the carriage, C, increases, but this
decrease and increase can not go on indefinitely, but at some time
C reaches the end of the track, A has decreased to zero, B is a