SINGLE-PHASE COMMUTATOR MOTORS 387
from (8) follows, by substituting (14) and rearranging:

h =

(15)

1 + Xi - X4S2
and, substituting (15) in (14), gives:
I =XI fa- J&4) (1 + Xi - X4/S2)+JSA - S2cQ- X4j£ (SA + jcp)

or, canceling terms of secondary order in the numerator:

•* /I O2N

T XT Co U — & )

44 = X4/2-

(16)

1 + Xi - X4S2
Equation (7) gives, substituting (10) and rearranging:

I2 (Z8 + Z') - IiZ7 - I4c0Z = e. (17)

Substituting (15) and (16) herein, and rearranging, gives:
Primary Current:

T e(l + \i -1S%) f .

12 __ ~~~ZK '

where:

X = (A3~jSc0)+Xi(A3+A)-X4(>S2A3-S2Co+co2--jSco), (19)
and:

A3 = ~|3J (20)

or, since approximately:

A, = Co2, . (21)

it is:

K = (A3 - jSco) + Xi (c02 + A) - X4c0 (c0 - jS). (22)

Substituting (18), (19), (20) in (15) and (16), gives:
Secondary Current:

\ . , JSCO . a I r, , .?Co\ 1

(23)

Brush Short-circuit Current:

_

(24)