314 
The N.Z. Journal op Science and Technology. [July 
327° 13', whilst relatively to the earth the difference of potential is 
0-585 volts maximum, and its phase 169° 8'. If there be a return circuit 
at a distance of 26 ft. from the centre-line of the power circuit the 
induced E.M.F. is by computation 1-845 volts and its phase 328° 52', so 
that the induced potential difference between the two wires is 0-064 volts 
per mile and the phase 271° 22'. 
It is interesting to find the value of the electromagnetically induced 
E.M.F. in the wires of the twin service telephone circuit already referred 
to. Taking first the wire in the position for which the electrostatically 
induced E.M.F. has been calculated, we have 
BD.CD 6-71 X 7-625 1 1 
~AD~ (11*625)““ “ 2*64 ° g 2434 
5S = S = 1 ' 136 l»g 1-^ = 0-1275 
Vs X 0-1275 = 0-2208 
0-9708 
log 
BD.CD 
~4D^ 
-\-jVs log 
CD 
BD 
— 0-9708 + j 0-2208. 
Let the value of I be 100 amperes, and let n = 50 cycles per second ; 
then p — 27 m = 314-16, and the D.P. induced per mile of the wire D is 
j x 100 X 314-16 (— 0-9708 -j- j 0-2208) 160934 X 10~ 9 
= 5-056 (- 0-2208 - j 0-9708) 
= - 1*116 — j 4-907 
= 5-03 /257° IF volts. 
The maximum value of the electromagnetically induced E.M.F. is according 
to the above calculation 5-03 volts per mile, and its phase is 257° IF at 
the instant when the phase of the current in A is at its maximum. 
With regard to the other telephone conductor, inasmuch as the two 
are symmetrically placed with respect to the centre-line of the pole, the 
induced voltage will be the same, but the two induced voltages will be 
different in phase, so that there will be a potential difference between the 
two telephone-lines at any particular instant. Calculating the induced 
voltage as before, we obtain the following value—viz., 5-03 j 282° 49' volts 
per mile—the phase being relative to the phase of conductor A as a datum. 
There is thus a difference in phase between the two telephone conductors 
of 25° 38', which at any instant gives a difference between the two con¬ 
ductors of 2-1 volts and a phase of 155° relatively to A, so that the full 
specification of the potential difference between the two lines situated as 
above is 2-1 155°. 
The Effect of Low Power-factor from the Standpoint of Electric-power- 
station Operators, bv E. E. Stark. 
Along with the benefits of the alternating-current system are some 
inherent features which render the system less desirable than the original 
direct-current system. These objectionable features are due to the alter¬ 
nating current having to pass through a circuit surrounded by iron. This 
causes the current in a circuit to lag behind the electro-motive force by a 
time element which is sometimes expressed in degrees. 
When the current and voltage are not coincident there are portions of 
the period of each complete wave or phase in which the apparatus acts as 
