HIGHER HARMONICS 153

Such a general or non-sinusoidal space distribution of magnetiz-
ing force and thus of magnetic flux, as represented "by F and F',
can be considered as the superposition of a series of sinusoidal
magnetizing forces and magnetic fluxes:

cos to #3 cos 3w as cos 5o:

/ K\ /« tf\

cos (w — a3 cos (3 a? 4 fls cos

2.

r COS 7 CO &9 COS 9 CO }

r cos (j co + 3 a9 cos f9 co - ~\ I (10)

\ £1 \ A/ }

The first component:

cos<

(10)

gives the fundamental torque of the motor, as calculated in the
customary manner, and represented by TI in Figs. 55 and 56.
The second component of space distribution of magnetizing
force:
0,3 cos 3
(11)
gives a distribution, which makes three times as many cycles
in the motor-gap circumference, than (10), that is, corresponds
to a motor of three times as many poles, This component of
space distribution of magnetizing force would thus, with the
fundamental voltage and current wave, give a torque curve
reaching synchronism as one-third speed; with the third harmonic
of the voltage wave, (11) would reach synchronism at one-ninth,
with, the fifth harmonic of the voltage wave at one-fifteenth of
the normal synchronous speed.
In (11), the sign, of the second term is reversed from that in
(10), that is, in (11), the space rotation is backward from that
of (10). In other words, (11) gives a synchronous speed of
S = — % with the fundamental or full-frequency voltage wave.
The third component of space distribution:
G&B cos 5 co, j
f& ^ (12)
fl&5 COS I 5 6) ~ r ) ,
gives a motor of five times as many poles as (10), but with same
space rotation as (10), and this component thus would give a
torque, reaching synchronism at S =