The flow rates of hydrogen, helium, argon, nitrogen, carbon dioxide, krypton and water vapour through both glass and silver parallel-plate channels have been measured for values of the ratio of the plate separation to the mean free path between 0.02 and 0.5. An equation for the diffusive flow is derived which takes account of the mode of scattering at the channel surface, which when compared with the experimental results shows that the scattering off the silver surfaces is diffusive, whereas that off the glass surfaces is mainly diffusive but with some specular reflection.