This thesis presents a set of measurements of spin asymmetries from the heavy atoms krypton and rubidium. These investigations allow examination of the spin orbit interaction for electron scattering from the target atoms. These measurements utilise spin polarized electrons in a crossed beam experiment to measure the Sherman function from krypton and the A2 parameter from the 52P state of rubidium. The measurements utilise a new spin polarized electron energy spectrometer which is designed to operate in the 20-200 eV range. The apparatus consists of a standard gallium arsenide polarized electron source, a 180 degrees hemispherical electron analyser to detect scattered electrons and a Mott detector to measure electron polarization. A series of measurements of the elastic Sherman function were performed on krypton at incident electron energies of 20, 50, 60, 65, 100, 150 and 200 eV. Scattered electrons are measured over an angular range of 30-130 degrees. These measurements are compared with calculations of the Sherman function which are obtained by solution of the Dirac-Fock equations. These calculations include potentials to account for dynamic polarization and loss of flux into inelastic channels. At the energies 50, 60 and 65 eV, experimental agreement with theory is seen to be extremely dependent on the theoretical model used. Measurement of the A2 parameter from the combined 52P1/2,3/2 state of rubidium are performed at an incident energy of 20 eV. The scattered electrons are measured over an angular range of 30-110 degrees. This measurement represents the first such measurement of this parameter for rubidium. Agreement with preliminary calculations performed using the R-matrix technique are good and are expected to improve with further theoretical development.