The stability of Conelte flow and flow due to an azimnthal pressure gradient between arbitrarily spaced concentric cylindrical surfaces is investigated. The stability problems are solved by using the Calerkin method in conjunction with a simple set of polynomial expansion functions. Results are given for a wide range of spacings. For Couette flow, in the case that the cylinders rotate in the same direction, a simple formula for predicting the critical speed is derived. The effect of a radial temperature gradient on, the stability uf Couette flow is also considered. It is found that positive and negative temperature gradients are destabilizing and stabilizing, respectively. © 1964 by ASME.