The axial and azimuthal components of the shear rate on the wall of the outer fixed cylinder of a pair of concentric cylinders with the inner cylinder rotating was measured using a three-segment electro-diffusion probe. The axial distribution of the components was found by sweeping vortices past the probe by means of a small axial flow. A nonzero axial shear rate component indicated the onset of Taylor vortices. Azimuthal waves on the vortices caused fluctuations of both components. The instabilities were measured two geometries characterized by R(1)/R(2) = 0.84 and 0.7. The probe was calibrated ia the same apparatus with R(1)/R(2) = 0.94. The Stuart theory for the growth of vortex velocity with angular velocity agrees well with the amplitude of the fundamental mode measured with R(1)/R(2) = 0.84. Qualitative agreement was found with the numerical results of Fasel and Booz, especially between the axial shear rate component measured with R(1)/R(2) = 0.7 and the vorticity calculated for R(1)/R(2) = 0.5.