Elastic scattering of electrons in the energy range 0-25 eV by mercury atoms is investigated by applying a perturbation method to the (nonrelativistic) Schrodinger equation. Relativistic correction to the potential is treated using two models: a Pauli approximation and a second-order Dirac potential. The nonrelativistic Hartree-Fock wavefunction is used to describe the target in the zeroth order approximation. Electron exchange is found to be important in the collision. The relativistic correction due to mass variation makes a significant contribution, in particular to p-wave scattering which is dominated by a low energy shape resonance. Phase shifts for s-, p-, d-and f-wave scattering are presented. An analytic expression for the momentum transfer cross section for relativistic scattering is obtained. The total cross section, momentum transfer cross section, differential cross section and spin polarization are calculated and compared with experiment.