CONCATENATION

45

that is, corresponding to a twelve-polar motor again. That is,
as regards to the speed of the concatenated couple, it is immaterial
in which order the two motors are concatenated.

32. It is then, in a concatenated motor couple of pole ratio:

a =

if:

s = slip of first motor below full synchronism.

The primary circuit of the first motor is of full frequency.

The secondary circuit of the first motor is of frequency 5.

The primary circuit of the second motor is of frequency 5.

The secondary circuit of the second motor is of frequency s' =
s (1 + a) —a.

Synchronism of concatenation is reached at:

So =

1 + a

Let thus:

€o = voltage impressed of first motor primary;
YQ = g — jb = exciting admittance of first motor;"1
Y'o = g1 — jb' — exciting admittance of second motor;
Zo = r0 + J'XQ = self-inductive impedance of first motor

primary;
Z'o = r'o + jx'o = self-inductive impedance of second motor

primary;

Zl = n + j%i = self-inductive impedance of first motor second-
ary;
Z'\ = r'i + jx'f\ = self-inductive impedance of second motor

secondary.

Assuming all these quantities reduced to the same number of
turns per circuit, and to full frequency, as usual.

If:

e = counter e.m.f. generated in the second motor by its mutual
magnetic flux, reduced to full frequency.

It is then:
secondary current of second motor:

s'e

[s (1 + a) — a] e

T'I + js'v'i r'j + j [s (1 + a) - a] x\

7 = e(ai - ja2), (8)