On an Expression of the Electromagnetic Field due to Electrons by Means of Two Scalar Potential Functions

The object of the present paper is to show that when any number of electrons are moving in any manner, the functions which define the resulting electrodynamics field, namely, the three components of dielectric displacement in the aether and the three components of the magnetic force at every point of the field, can be expressed in terms of the derivates of two scalar potential functions. (Previous writers have expressed them in terms of a scalar potential function and a vector potential function, which are equivalent to four scalar potential functions.) These two scalar potential functions are explicitly evaluated in terms of the charges and co-ordinates of the electrons. It is then shown that from these results the general functional form of an electrodynamic disturbance due to electrons can be derived.