Theory of the corona

The theory of the corona developed in this paper explains the coronal discharge by the application of the known laws of the discharge of electricity through gases. The experiments of Dr. Whitehead and Mr. F. W. Peek and others have shown that the surface gradient X
s
at the surface of a smooth wire necessary to start the corona increases very greatly as the radius of the wires decreases. As an illustration of this increase it is found that the coronal gradient X
s
at the surface of a wire 0.5 cm. radius is 46,000 volts per cm., while a gradient of 97,000 volts per cm. is required for a wire of 0.02 cm. radius. The phenomenon is due to ionization by impact. The ions n
0
move in toward the wire from the place at which they cross a region where the gradient is X
0
= 26,600 volts per cm. up to the wire. They produce other ions, and n ions arrive at the wire. The condition for the corona is that n shall be a constant. If α = the number of ions that one ion produces in a cm., then
$n = n_{0} e^{\int^{b}_{a} \alpha^{-}dx}$
The α is a function of X at every point. This function is expressed in terms of x. It is introduced into the above equation, and on integration the equation for the corona is obtained. The equation also contains a term for the density of the air. The equation thus takes account of changes of pressure such as altitude and temperature effects. The equation when plotted in a curve for the variation of X
s
with the radius of the wire, agrees with the experimental results of Whitehead and Peek with as great accuracy as the experimental results would warrant.