The ionospheric configuration of the vertical Birkeland currents associated with an auroral arc is calculated from a model based on the assumption that the auroral electrons constitute a net current into the ionosphere. It is further assumed that the return vertical current out of the ionosphere is impeded along the field lines which connect the arc to the magnetosphere. The magnitude, location, and structure of the return Birkeland current calculated from the model agree well with measurements of these parameters by a rocket-borne experiment.