In the de Hoffmann--Teller reference frame, defined so that the bulk velocities are aligned with the magnetic field in the uniform media on either side of a shock transition, the cross--shock electric field is simply the thermoelectric field responsible for preserving charge neutrality. As such, it gives information regarding the heating and dissipation occurring within the shock. The total cross--shock potential can be determined by integrating a weighted electron pressure gradient through the shock, but this requires knowledge of the density and temperature profiles. Here we exploit a recently proposed alternative approach relying on particle dynamics to provide an independent estimate of this potential. We apply both determinations to slow mode shocks which form the plasma sheet boundary in the deep geomagnetic tail as observed ISEE 3. The two methods correlate well. There is no indication of the expected transition from resistive to viscous shocks, although the highest Mach number shocks show the highest potentials. We have not found any strong dependence on the various shock parameters, but this may be due in part to the relatively uniform sample of shocks, all of which lie close to the switch--off limit, and in part to the lack of definitive thermal ion data. We discuss the implications of these results for the electron dissipation mechanisms and turbulence at the shock. ¿American Geophysical Union 1987