The coefficients of capacity and the mutual attractions or repulsions of two electrified spherical conductors when close together

In connection with spark systems of wireless telegraphy, a knowledge of the electrostatic energy stored between spherical electrodes at the instant of the disruptive discharge is of great value to the engineer. In order to increase this energy, without unduly increasing the applied potential difference, the electrodes have been placed in compressed or highly rarefied gases and in oils or other liquid dielectrics having great electric strength. In these cases the least distance between the electrodes may only be a small fraction of the radius of either, and so the computation of the electrostatic energy by the ordinary formulæ is so laborious that it is practically prohibitive. By extending a mathematical theorem first given by Schlömilch, the author has succeeded in greatly simplifying the computation of this energy. The formulæ given below are very easily evaluated when the spheres are close together, and hence, in conjunction with Kirchhoffs final modification of his own formulæ, they give the complete practical solution of this important historical problem.