1919.J 
Departmental Reports. 
131 
this paper is 37/12, which has a diameter of 0-728 in. (or 1-849 cm.), and 
a radius of 0-9245 cm. Substituting this for a the value of a 4 is 0-732 and 
the value of R 1 ^ 1 022R, an augmentation of 2J- per cent, in the resist¬ 
ance. For half the diameter the increase in resistance is one-sixteenth of 
this, or approximately i per cent. ; so that on the whole the increase may 
be regarded as negligible, especially as the augmentation of resistance in 
the case of even the largest size is but little more than the variation in 
ordinary resistance allowed by the Engineering Standards Committee 
of Great Britain to meet the exigencies of manufacture. 
Inductance. 
The inductance per phase per mile is herein denoted by L, whilst the 
value of the inductance per mile between any conductor and the neutral 
of a three-phase system for different values of d/a is shown in D 72, 
where d is the distance between any two conductors of a symmetrically 
arranged three-phase system and a is the radius. 
These values are calculated from the formula 
L = (2 log ~ + 0-5^ x 30-48 x 5280 x 10~ 9 
= 0-000161 (2 log i + 0-5^ 
The bracketed term is the inductance in C.G.S. lines per centimetre 
of length. The two factors 30-48 x 5280 convert the inductance to 
C.G.S. units per line of conductor, which is brought to practical units by 
dividing by 10 9 . The same formula gives also the inductance between 
either conductor of a single-phase system and the neutral plane, but in 
this case the induced voltage is one-half the voltage between conductors, 
whilst in the case of the three-phase lines it is 1/ v/3 times the voltage 
between conductors. 
Reactance. 
The reactance is derived from the inductance by taking its time-rate 
of variation— i.e., _pL, where p = 27 rf is the angular speed in radians and 
/ the frequency in cycles per second, the values being calculated in ohms 
per mile. . 
Impedance. 
Given the resistance R and the reactance pL, the electromagnetic 
impedance per phase per mile of circuit is R -j- ipLi ohms. 
Leakance. 
The term “ leakance,” or “ leakage factor,” or “ leakage conductance,” 
is herein denoted by K. The amount of leakage from high-tension trans¬ 
mission-lines is quite infinitesimal under ordinary working-conditions, but 
not negligible. There is always present in the air some electrons and ions 
which become carriers from one conductor to the other, but the principal 
path is over the surface of insulators, the amount of leakage depending 
upon weather conditions. This, of course, is not sufficient to enable any 
appreciable amount of current to pass over any single insulator, but the 
effect of a large number of insulators in parallel is appreciable enough 
to make it desirable to take the leakage into account in our calculations. 
A large number of insulation tests on the Lake Coleridge system were made 
for the Department by Mr. Burbidge, who summarized the results thus : 
