130 
The N.Z. Journal of Science and Technology. 
[Mar. 
If the line at the receiving end is open and pressure applied at the 
sending end the following relations are derived from equations (2) and (4) 
by making I r = o, viz :— 
Y s = V r cosh Im ...(5) 
I s = — sinh Im ..(6) 
n 
which latter is commonly called the charging-current of the line. 
Again, if the Hue at the receiving end is short-circuited the following 
equations are derived from equations (2) and (4) by making V r = o, 
viz. : — 
VJ = nl Y sinh Im .(7) 
Is 1 = I r cosh Im . (8). 
The open-circuit and short-circuit equations furnish a means of calculating 
the values of the constants m and n of the circuit from the observed 
values of Y s , YJ, I s , I s h 
Combining equations (5) and (6)— 
— = - tanh Im 
Y s n 
and combining (7) and (8)— 
= n tanh Im 
and again combining the two latter equations we get 
x YJ 
V s x Vg _ n2 an ^ I £ 
L 1 x I s 
V s x 
Is 1 
— tanh 2 Im 
It is to be noted that sinh Im, and consequently Im, and finally m, cannot 
be obtained from equations (6) or (8), as the relative phase of Y r and I s is 
not readily ascertainable under ordinary working-conditions. 
Having obtained m and n, the value of L may be calculated when the 
value of E is known from the relation 
E + 2 -pL = m . n 
whilst the value of S mav be calculated when the value of K is known 
«/ 
from the relation 
t / , • r>i THy 
K -f- tps == — 
n 
Eesistance. 
The resistance per mile of conductor is herein denoted by E, the 
values of which for copper and for the sizes selected are given in tables 
herewith. These values are taken from cablemakers’ lists for hard-drawn 
copper without any correction for the so-called “ skin effect,” which 
may be regarded as negligible for the selected sizes of conductor. The 
approximate value of the virtual resistance E 1 for a frequency of 50 
cycles per second is 
E 1 = E (1 + 0-03a 4 ) 
where a is the ra,dius of the conductor in centimetres* and E is the 
resistance to direct current. The largest-size conductor considered in 
* Lord Rayleigh, On the Self-induction and Resistance of Straight Conductors, 
Phil. Mag. S.S., vol. 21, No. 1B2, p. 387, May, 1886. 
