The equations for the pulsed Townsend discharge involving two ions interacting through the &ggr; process have been solved for the ion densities as a function of time and position. The same mathematical approach yields equations for the single ion case, with or without diffusion, which are valid for all time. Negative ions are a special case in which &ggr;=0. Plots are presented of the rate of ion arrival at the electrode and of ion current, both of which are experimentally accessible. The temporal increase of ion flux in the neighborhood of Townsend's breakdown condition is shown.