We have made a device in which a one millimeter thick glass plate can rotate in a horizontal plane between two brass plates that are spaced about 1 mm from the glass plate. The glass plate is suspended by a double ended bifilar suspension of 5 mil nickel wire. It is placed on a standard Cenco pump plate under a bell jar and can be evacuated with a mechanical pump to a pressure of about 40 microns. A Stokes McLeod gauge is used to measure the pressure. The glass plate is set into rotation by rotating the whole pump plate assembly. The 1/e damping time is then measured at various pressures. The experiment is instructive because of the kinetic theory involved, and the fact that the viscosity does not vary with pressure until the spacings become comparable with the mean free path. The experiment thus also provides a rough determination of the value of the mean free path.