SINGLE-PHASE COMMUTATOR MOTORS 389
it is, substituting (31), (32) in (30), and expanding:

P! = ^f {[x (1 - Scoa") - nScoa'] + (1 - Sc0r") [s(X'i - X'4)

- r (X"i + X"4)] -rSc0a; [r (X'i - X'4) + a? (X"i + X/74)]

- a? (X'4S2 - X'4Sc0a" + X"4Sc0a:') + r (\'*ScQa'

K (33)

after canceling terms of secondary order.
As first approximation follows herefrom:

c / „ r A 1

— ^CQ QJ" ^- _ aM L

V x / I '

Se*xll - ScJa" +~a'
I \ x

,o (1 + S")
hence a maximum for the speed S, given by:

or:

-So - ^l + Co2 (a" + T- «') 2 - Co (a" + I of) , (35)
and equal to:

The complete expression of the power of the main circuit is,
from (33) :
, (37)
where 60, &i, 6Vare functions of X'i, X'^, X'4, X;/4, as derived by
rearranging (33).
The Power produced in the brush short-circuit is:
P4 = [#'4, /'J«;