The scattering of electrons by gold, xenon and krypton atoms has been investigated using Dirac's equations. The polarization to be expected by double scattering at 90 degrees has been studied for an energy range 100 to 150,000 eV. The results agree substantially in the energy range 10,000-150,000 eV with those obtained by Mott for an unscreened gold nucleus. It is found, however, that for lower energies the effect of screening is more important. In particular, at energies for which the intensity of single scattering at 90 degrees is near a minimum, a large polarization is to be expected in the case of gold. For xenon the polarization never exceeds 4% and for krypton 2%. Modifications of the interaction between a nucleus and electron which would reduce the polarization are considered. As an example of a field as different as possible from the Coulomb type, the polarization produced in double scattering by a potential 'well' is investigated in detail.