A numerical solution is found for a fluid dynamical treatment of the accretion process in which a gravitating point source is moving through an adiabatic gas (having specific heat ratio sI ); the calculations being performed for Mach speeds , I 4 and 2A. Previous accretion theories were based on single particle orbits and would not be valid when collisions are important in the gas, as, for example, in the case of the Galaxy moving through a possible intergalactic plasma. The Mach speed of the Galaxy is probably of order unity and cooling can be neglected for a plasma temperature exceeding 5 x io 0K, so that our calculations could be relevant to this case although the internal pressure of the Galaxy may be sufficient to retard the inflow appreciably. Other possible applications include stars, star clusters, compact objects or `black holes ` moving through an ambient medium. The numerical method used involves time step iteration from a initial state until a steady state is achieved, which gives results accurate to about 4 per cent. The subsonic case shows density and temperature contours strikingly close to those of a stationary source. In the supersonic cases the source is preceded by a bow shock. The accretion rate for each case is calculted and found to be comparable with that derived from previous accretion theory.