In this paper the spectrum of radio-frequency radiation from a fully ionized ion-electron plasma is calculated, starting from the dependence of the dipole moment on the particle-particle Coulomb fields. These Coulomb fields are shielded according to the usual dielectric constant theory. The acceleration of a particle by others of like species gives rise to quadrupole radiation only; thus the second derivative of the dipole moment depends on the sum of ion-electron forces. It is simplest to find the total force acting on each ion due to all the electrons, and then to sum over the ions. Ion-ion correlation may be allowed for readily.

The final result agrees with calculations made by Dawson and Oberman and others whose approach was via the absorption coefficient and Kirchhoff's law. The present approach is rather simpler.