Abstract
A conductivity tensor is calculated for a partially ionized gas subject to electric fields which are harmonic in space and time, and to a uniform magnetic field. The collisions between charged particles and neutral molecules are included in the theory in an approximate way by means of a simplified form of Boltzmann's equation, as proposed by Bhatnagar, Gross and Krook. A simplified expression for the longitudinal component of the tensor is derived. Some applications of the results are mentioned, and will be described in detail in further papers.