Measurements of the hydrodynamic stability of viscous flow between concentric cylinders have been made with a small rotating cylinder viscometer. The inner cylinder is rotated and the outer cylinder is freely suspended on a torsion fibre. The onset of instability is characterized by a discontinuity in the measured effective viscosity. The results for the case of a small annular gap between cylinders agree to within 1$\cdot $3% with the theory for an infinitesimal gap. The results for the case of a wide annular gap agree to within 0$\cdot $50% with the exact theory given by Chandrasekhar in the preceding paper. Detailed measurements of the torque above the onset of instability have been made in both cases.