The Equations of Motion in Electrodynamics

A formulation of the equations of motion of singularities in classical electromagnetic theory is obtained. The general method introduced by Einstein, Infeld and Hoffmann leads in a simple way, without any difficulty with "infinities," to the equations of motion obtained before by Dirac. It is shown further that Dirac's introduction of the inertial term into the equations of motion correspond in this method to the assumption of an energy-momentum tensor of matter. The attempt to remove this arbitrary assumption leads in a simple and natural way to the general theory of relativity, in which the equations of motion are obtained from the Einstein-Maxwell field equations.