1919,] 
Departmental Reports. 
135 
with the state of the air, and are small compared with the order of the 
uncertainty in regard to the actual effect of the capacity upon the circuit, 
which is due to the distortion of the current; so that the actual effect 
as distinct from the calculated effect is dependent to some extent upon 
the other constants of the circuit, more especially the inductance and 
also the form of the impressed w 7 ave of electromotive force. Under these 
circumstances it would be futile to strive after refinements in calculation. 
All that is required is a basic formula with a practical coefficient deter¬ 
mined by experiment, which condition is satisfied by the expression given 
for the capacity. 
Corona. 
High transmission-line voltages tend to destroy the insulating quali¬ 
ties of the air, manifested by the development of a luminous envelope 
around the conductor. The luminosity is produced by ionization, and 
ionization is the result of an excessive electrostatic stress which increases 
the energy of motion of the ions already existing in the air in compara¬ 
tively small numbers, and so produces more ions by collision. This 
ionization is accompanied by a loss of power which may become prohibi¬ 
tive, depending upon the diameter of the wire and the spacing of the 
conductors. It is a phenomenon which has to be guarded against, as the 
limits are quickly reached: for example, a 7/16 conductor with a 6ft. 
spacing between phases could not be used for three-phase transmission 
at 66,000 volts without serious loss, the amount depending upon the 
distance of transmission. Likewise, at 110,000 volts and 10 ft. spacing 
the smallest conductor which could be used with safety under all circum¬ 
stances is 19/13 S.W.G. The phenomenon has been studied by Russel,' 1 ' 
Whitehead,! and Peek,} and a number of others, Peek’s work being 
most valuable for engineers, as the conditions studied were those per¬ 
taining to transmission-lines. A bibliography of the subject is appended 
to Whitehead’s paper read before the American Institution of Electrical 
Engineers§ in 1910. 
Peek makes use of two critical potential differences, one which he 
calls the “disruptive critical voltage” and the other the “ visual critical 
voltage.” The first is the voltage which gives rise to a critical flux 
density or potential gradient at the surface of the wire, corresponding 
to the dielectric strength of the air, and the other the voltage which 
produces a corona, and he uses the first value as a basis for calculating 
the loss produced through ionization. The formulae which he uses are 
derived very simply from electrostatic principles. 
If Y be the potential difference, C the electrostatic capacity per unit 
length of wire, Q the quantity, we have Q — VC. The capacity to 
neutral per unit length of a single- or a three-phase system is approxi¬ 
mately 1/2 log - where d is the distance between centres of the conductors 
and a the radius of the wire. Consequently 
V = Q x 2 log - 
a 
* Alex. Russel, Dielectric Strength of Air, Proc . Phys . Soc ., vol. 20, p. 49, 1906. 
f I. B. Whitehead, The Electric Strength of Air, Proc . Am . Inst . Elect . 
Engineers , vol. 30, pt. 3, p. 1856, 1911. 
f P. W. Peek, Law of Corona, Proc . Am . Inst . Elect . Engineers , vol. 30, pt. 3, 
p. 1889, 1911. • - • • 
§ I. B. Whitehead, The Electric Strength of Air, Proc . Am . Inst . Elect . 
Engineers , vol. 29, pt. 2, p. 1189, 1910. 
