The axisymmetric accretion equations of Bondi and Hoyle are extended through the inclusion of a pressure gradient term and an energy equation. The equations are solved for the Mach number as a function of distance from the gravitating point mass, and two families of solutions are found, depending on the specific heat ratio ..gamma... For sufficiently small ..gamma.. the solutions remain subsonic in the outflowing region of the accretion wake. For larger ..gamma.., a supersonic transition occurs in the outflowing region. For all values of ..gamma.. the infalling flow is gravitationally accelerated to supersonic velocities. It is shown that the infall velocity solution is nearly independent of ..gamma.., a result with considerable practical significance for the solution of accretion problems involving realistic energy equations.