When an electromagnetic field, derived from retarded potentials, is given it is generally possible to add to this a scalar field, derived from a retarded potential $\psi$, in such a way that the total radiation of energy to infinity is zero for each direction, the contribution of the scalar field being calculated with the aid of a tensor used in a former paper. The radiation of angular momentum to infinity is not zero for each direction unless the electromagnetic field is of a certain type. The approximate values of the field vectors at a great distance from the origin can be expressed in terms of a quantity $\alpha$ and when the field is of the type just mentioned $\alpha$ satisfies a certain partial differential equation. This result may be regarded as typical for attempts to solve the radiation problem in which the electromagnetic radiation in one of Bohr's stationary states is supposed to be balanced by radiation of a new type. Some remarks are made on the attempts which have been made to solve the problem with the aid of electromagnetic fields alone and a brief discussion is given of the radiation of angular momentum according to the classical theory.

• Received 12 February 1926

DOI:https://doi.org/10.1103/PhysRev.27.606