This paper considers some of the processes taking place in a simplified model of the plasma or positive column region of an electrical discharge through gas at low pressure. Particular attention is given the direct mutual interaction of the electrons, and the effect of this on the distribution of velocities.The first part deals with the question in a general way. To determine the velocity distribution function, two balance equations are set up. One expresses the conservation of energy, and the second the conservation of momentum parallel to the field. From these is derived one non‐linear integral equation.The geometry of the mutual scattering process is examined, and the necessary integrations are performed insofar as these depend only on this geometry. As an example the case of elastic sphere collisions is carried through to a point where integrations over the distribution function,f, become necessary.In the second part the cross section function σ is derived for electrone‐lectron scattering. As an interaction potential, the shielded Coulombvalue was used.In the third part an attempt is made to find functions which are solutions of the problem. Under the assumptions used, it is found that thefunctionis a fairly good approximate solution.It is found that experimental conditions can exist for which the theory predicts a value of the parametergnearly unity. This corresponds to a nearly maxwellian distribu