REACTION MACHINES 289

The magnetism produced by this current is:

where n = number 'of turns.
Hence, substituted:

gin (0 __ 0) (L + 7 cos 2

n

or, expanded:
77"

1 - -M cos 6 sin 0 - 1 + ~ sin 0 cos

n

when neglecting the term of triple frequency as wattless.
Thus the e.m.f. generated by this magnetism is:

d*

e = —n -j-
dt

hence, expanded:

e = -2 7T/ZJ \/2 ! (l - ^) cos 0 cos 0 + (l + ^) sin ^ sin j
and the effective value of e.m.f. :

= 2T/U\/1 + ?- - 7 cos 26.
\ 4

Hence, the apparent power, or the volt-amperes:
Q = IE = 2 vfll\l + ^ - 7 cos 2 0

2-xfl-Jl + T — 7 cos 2 0
The instantaneous value of power is:
= -47T/7J2 sin (0 — 0) I /I — ^ cos 0 cos j3 +
sin 6 sin