Formulas and graphs are given for the calculation of the propagation constants of an electromagnetic wave in weakly ionized, dry air at ionospheric temperatures in the presence of a magnetic field. Experimental studies of electron collision frequencies in nitrogen and oxygen are reviewed and used to obtain the magnitude and energy dependence of the electron collision frequency in air. The equations for the components of the conductivity tensor are developed taking into account the approximately linear dependence of the electron collision frequency on electron energy. Expressions derived on this assumption are found to be accurate except at low temperatures, high pressures, and low frequencies. The errors resulting from the use of an effective value for the energy independent collision frequency in the Appleton‐Hartree equations are evaluated. Procedures are given for the calculation of the propagation constants for electromagnetic waves propagated parallel to and perpendicular to the magnetic field. These results are then applied to the derivation of relations required to reanalyze the ionospheric collision frequency measurements reported by Kane. The use of an effective collision frequency is found to lead to errors comparable to the experimental errors in the ionospheric observations.