The results are presented of laboratory experiments to investigate weak baroclinic waves which may occur in thermally driven flows in a rotating annulus beyond the Eady cutoff for baroclinic instability. In the system used for the experiments the Taylor number was large while the curvature ensured the presence of large gradients of potential vorticity. Stable axisymmetric flows, weak waves and strong baroclinic waves were observed depending on the values of the imposed parameters of the system. The horizontal and vertical profiles of mean zonal velocity were obtained both by measurement and from numerical simulations of the flows. The linear stabilities of flows approximating the observed flows were examined. Agreement between the laboratory observations and the linear analyses regarding the location in parameter space of the transition between different flow regimes and the structure of the flows was good, giving support to the hypothesis that the weak instabilities were due to potential vorticity gradients in the fluid.