Scattering of the electron beam by the residual gas in the vacuum chamber is calculated for the 1 Bev strong focusing Cornell Mesotron. It is shown that the elastic scattering by the nucleus and the inelastic scattering by the atomic electrons are the only important contributions to the loss due to the presence of gas. These two effects are calculated in detail. Radiation and space charge effects are not discussed. Because of the small scattering angles involved the details of the screening by the atomic electrons must be taken into account accurately. Multiple scattering is shown to be of little importance because of the damping of the beam oscillations as the energy increases. The calculations are carried out for two different injection conditions and little difference is found between them as far as the loss due to the scattering itself is concerned. The numerical results for the Cornell Mesotron show that about half of the beam gets lost at a vacuum of 5×10−6mm Hg. The scattering losses will depend on the field lattice of the synchrotron.