312 
The N.Z. Journal of Science and Technology.. 
[July 
With respect to circuit C we have— 
CC' 
a, = 2 log — =16-5168 
a. 2 — 2 log = 17*9032 
r A 
DC' 
b x — b 2 — 2 log = 4-0666 
M d = 
6i 
bib $ ci\di 
b. 
M c = - , 
a x a. 2 — bfa 
= - 0-01457 
= + 0-01457 
C d = 
a x 
b x b 2 — a x a. 2 
- 0-05916 
M d 
K M c + C d 
= + 0-3267 
Proceeding to evaluate, we have— 
v& = v & Jc a + v h k h -f v c k c 
when 
«. = y = 38100 V2 = 53720 volts, 
% = V ( -1 +j = - 26860 +j 46521 
» e = V f - I —3 = - 26860 - j 46521 
(53720 x 0-2518) - (26860 x 0-3522) - (26860 X 0-3267) 
+ (j 46521 x 0-3522) - (j 46521 x 0-3267) 
== - 4780 + j 1200 = 4940 /165° 54' 
It will be seen that under normal working-conditions each telephone- 
wire in the position indicated is subject to a maximum voltage of 4,940 volts, 
hence the necessity of employing drainage coils and transformers insulated 
for a high voltage, insulating-platforms, and other devices for the security 
of the employees. 
Next, as regards electromagnetic induction, the effect is not nearly 
so great as in the case of electrostatic induction, and may be neglected 
except when the two circuits run for a considerable distance in parallel. 
The phenomenon depends upon the magnitude of the current and not 
the voltage, and as in high-tension transmission-lines the voltage is high 
and current small the relative importance of the two phenomena is of 
the same order. The nature of the induction is also different, and the 
D.P. due to electromagnetic induction varies as the length of conductor 
subject to induction. Moreover, in the case of twin telephone or telegraph 
circuits the induced E.M.F. on one wire will tend to balance the other, 
so that the net effect in practice is quite negligible. 
In fig. 2 let s be any distance in the direction AD, BD, or CD, and let 
i a , i b , i c be the instantaneous value of the current in A, B, and C respectively. 
2^ 2^ 2ft 
The flux-density at a point distant s from either is —- a , — b , — c . The flux in 
s s s 
an elementary length ds in the direction of s and of 1 centimetre length in 
ds ds ds 
the direction of the length of the conductor is 2 i & —, 2i h — , 2 i c — . 
