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 Xs at the surface of a smooth wire necessary to start the corona increases very greatly as the radius of the wire decreases. As an illustration of this increase it is found that the coronal gradient Xs at the surface of a wire of 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 no move in toward the wire from the place at which they cross a region where the gradient is X0 = 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 ?? = the number of ions that one ion produces in a cm., then fb ?? dx n = no e a The ?? 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.