1919.] 
New Zealand Institute Science Congress. 
309 
the influence of the three-phase circuit may be readily determined by 
treating it as three independent circuits and neglecting the screening 
effect of one on the other. This, of course, does not give an exact result, 
but at the same time it is approximate enough for the present purpose. 
An attempt at greater exactness, whilst involving a good deal of extra 
work, is liable to be upset by unknown and uncertain factors which are 
not taken into account in the calculations, and the object of the experi¬ 
ment is to obtain a factor or coefficient which may be applied to the simplest 
form of equation which is capable of being applied to the conditions. As 
regards the telegraph or telephone circuit, it will be assumed that there 
is no apparatus connected thereto, and that the resistance to earth is 
infinite ; in other words, the line is entirely insulated. It is a compara¬ 
tively simple matter to take insulation resistance and also the resistance 
and inductance of the connected apparatus into account, but such is 
outside the scope of the present investigation. Let v a , v h , v c represent the 
difference of potential to neutral of the wires A, B, and C respectively and 
at the same instant of time : then at any time 
V a + V b -j- V c = 0. 
If v d be the instantaneous value of the voltage to earth of D when the 
voltages in A, B, and C are v a , v h , and v c respectively, we have 
where 
Vd — v a & a -j- v h k h -f- vJcq 
M d M d M d 
' - M a + C d ’ b M b + C d ’ c M c -f C d 
If we choose a particular instant when v a = V, the maximum value of the 
D.P. to neutral of the circuit, then 
= v ( - ! + j and v c = V ( - | —j 
Proceeding now to evaluate the equations: Let A, B, and C of 
fig. 2 represent the three conductors of the Lake Coleridge - Christchurch 
