Solution of the compressible Rayleigh problem involving an impulsively moved flat plate indicates that transverse velocities can be generated by a purely longitudinal shearing motion. It would be desirable to demonstrate the existence of these waves, and to do so was the motivation for the present investigation. However, the geometry for the Rayleigh problem is prohibitive; and since it was noticed that a similar behaviour should occur for the case of unsteady compressible Couette flow, this was considered for the present investigation. An experimental search for the existence of the transverse velocities was conducted using concentric rotating cylinders to generate the flow. Since these transverse velocities were too small to be measured directly, a temperature gradient was created across the annulus to take advantage of the much greater sensitivity of a hot-wire to temperature fluctuations produced by the fluctuation in the transverse velocity. The periodic temperature fluctuations noted were converted to equivalent transverse velocities. Experimental values obtained agreed qualitatively with the theory. Finally, the role of extraneous effects in the experimental apparatus was considered.