Previous calculations of the drift motion of electrons moving through a gas under the combined action of electric and magnetic fields and concentration gradient have been based upon inexact averaging methods. For electrons which, like arc plasma electrons, have a Maxwell distribution to a first approximation, the first-order correction to the distribution function which arises from drift motion is now calculated. This permits exact averaging of component velocities to be carried out. The resulting equations are compared with Townsend's earlier results. Tonks' theorem that "the drift speed is the same as would occur if the components of concentration gradient and electric field perpendicular to it, as well as the magnetic field itself did not exist" is found to hold within 12 percent.