Using electron observations in the vicinity of, and over, auroral forms obtained from three rocket flights, we have found that the net downward electron energy flux generally varied as V2, where V is the magnetic-field-aligned electric potential difference inferred from the peak in the observed energy spectra of precipitating electrons. We show that this relation implies that V is proportional to the net downward number flux of electrons from the magnetosphere to the auroral ionosphere and thus that increases in V and increases in the net downward number flux of electrons are equally responsible for the enhanced electron energy deposition responsible for auroral forms. This also indicates a direct physical connection may exist between V and the net downward electron number flux.