136 
The N.Z. Journal of Science and Technology. 
[Mar* 
If g be the flux density at the surface of the wire, which is numerically 
equal to the potential gradient or the force when the specific inductive 
capacity is unity, the force at radius a due to the radial flux is 2Q /a, and 
for a system of wires in which the distance between wires is great 
compared with the radius this is also the force at the small distances 
which we are considering, and consequently g = 2Q /a and Q = g . a/ 2. 
Substituting, we have 
Y = g . a . log - 
a 
If V 0 be the voltage to neutral corresponding to a critical value g 0 of the 
disruptive potential gradient for air, we have 
y 0 - g 0 . a . log - 
a 
According to Peek, who experimented with alternating current under 
conditions obtaining in power-transmission systems, the value of g 0 is 
21,100 volts effective per centimetre at standard pressure and 25° C. At 
any other pressure and temperature the value of g 0 is 
g 0 x A x = 21100 x 8 
y b 0 T 
where b is the barometer pressure, b 0 is the standard barometric pressure 
(i.e., 76 cm. of mercury), T is the absolute temperature, and T 0 the 
datum temperature on the absolute scale (i.e., 273 + 25 — 298). The 
ratio T 0 /b 0 = 298/76 == 3 92, and the equation now becomes 
V 0 = 21100 to . 8 .a log - ...(9) 
a 
where V 0 is the effective voltage to neutral of a three-phase or single¬ 
phase system and where w is a factor expressing the surface condition of 
the wire, and which, according to Peek, is unity for smooth polished wire, 
and 0-98 to 0-93 for roughened or weathered wire, and 0-87 to 0*83 for 
seven-strand cable. 
Diagram D 52 shows the value of the disruptive critical voltages for 
different diameters and spacing. For a fully developed corona the 
potential gradient at the surface is, according to Peek, 
/ 0-301 \ 
21100 ( 1 + vt) 
and the effective voltage to neutral 
/ 0-301 \ , d 
Yi = 21100 to.8. (1 H- j=- ) a log ..(10) 
\ Va / a 
where to is a factor which varies from 1 to 0'93 according to surface 
conditions for single wires, and has a value of 0*82 for a seven-strand 
cable and for a fully developed corona, and 0-72 for localized corona 
effects. 
The loss due to corona is given by Peek in terms of the disruptive 
critical voltage and is as follows 
W = G,n (V - Vo) 2 X 10-6 ..(11) 
where W is the loss in kilowatts per mile of single line, V is the effective 
voltage between conductor and neutral, V 0 is the disruptive critical voltage 
to neutral, n the frequency, and C has the value | and k is a con¬ 
stant = 0*00552. 8 has the same significance as in equations (9) and (10). 
