1919 .] 
New Zealand Institute Science Congress. 
313 
The total number of lines through D due to the currents in A, B, and C is 
■°°ds 
'CD ^ 
2 —+2 i h f 
JXD ^ j Vbd s 
00 ds r 
-4-2 i / 
0 jyt 
these 
If we chose the instant when the phase of the current in A is at a 
maximum and call the value of it I, then at the same instant the current in 
B is I \ + j and in C it is I J — j Substituting 
values for i a , i h , and i c , and integrating, we have for the flux due to the 
three currents at the phase chosen 
’ BD .CD . /- CD 
0g A D 2 +1 V3 ° g 
BD 
The inductance of the line D with respect to A, B, and C is therefore 
, BD.CD , . CD 
log —-j- 'j V3 log cms. per centimetre. 
/ BD CD cD\ 
01 l0g —AT ) 2 -^ / ^3 log —-J X 10 -9 X 160934 henrys per mile. 
Call this L, then the flux per mile of line is IL, and the D.P. per mile is 
the time rate of change of the flux, which for sinuous alternations may be 
represented by jl'pL, where p = 2 nn and n is the frequency in cycles 
per second, which gives the D.P. per mile of line both in magnitude and 
phase. 
Fig. 4 shows the maximum induced voltage per mile in line D when 
the current in A is at its maximum and of the magnitude 100 amperes 
(maximum value). 
At a distance of 25 ft. it will be seen that the maximum induced E.M.F. 
amounts to 1*88 volts per mile, its phase relatively to that of A is 
