Experiments are described in which a radial temperature gradient is applied to the lower horizontal boundary of a rotating annulus containing a thermally convecting fluid; the vertical sidewalls and upper horizontal boundary are nominally insulating. Comparison is made with the non-rotating experiments of Rossby and the same general asymmetric flow is observed i.e. that of a weakly stratified interior of slowly descending fluid occupying most of the annular gap, overlying a thin thermal layer of large vertical temperature gradients, stable over the cold part of the base and statically unstable over the warmer part; the circulation is completed by a narrow region of rising motion at the warm end of the base. The relevant governing parameter is shown to be a quantity, Q, defined such that Q is the square of the ratio of the (non-rotating) thermal layer scale to the Ekman layer scale. Thus for small Q the flow is only weakly modified by rotation but as Q increases past unity rotation tends to thicken the thermal layer and reduce the heat flux. The experiments were carried out in the region of Q order unity. Above a certain critical value of Q baroclinic waves are seen; these waves have finite velocities throughout the total depth of fluid. The instability transition is only weakly dependent on the overall depth and geometry. It is believed that the essential features of such a system driven in this way have some bearing on certain natural systems, such as the influence of latitudinal variation of incoming solar radiation on the large-scale ocean circulation.