We have used a small rotating-cylinder viscometer in which the inner cylinder rotates to measure the torque transmitted by fluid flow in the laminar and supercritical range of speeds. We find that when the radii of the cylinders are nearly equal, the torque is a unique function of the Reynolds number of the flow regardless of the manner in which the flow is established, provided only that sufficient time is allowed for equilibrium to be reached. In particular we find that the critical speed for transition to cellular flow is identical with the speed at which cellular flow reverts to laminar flow. When the gap between the cylinders is large a small hysteresis in the torque near the critical speed is observed. Some observations are reported which suggest that the transitions in hydromagnetic and spiral flow between rotating cylinders are also reversible.