Radiometric measurements of the temperature of the south polar cap of Mars in winter have yielded values significantly below the expected 148 K. One proposed explanation for this result is a substantial reduction in the CO2 content of the atmosphere and a lowering of the mean molecular weight near the surface. We explore the meteorological consequences of this explanation by deriving a criterion for vertical static stability and a thermal wind law for an atmosphere of variable composition. The atmosphere proves to be statically unstable unless the anomaly in the CO2 mixing ratio extends to heights of tens of kilometers. The effect of varying molecular weight exceeds the effect of temperature gradient, in the thermal wind law, producing shears with height of reversed sign. The shears are baroclinically unstable, and this instability would eradicate the latitudinal gradient of molecular weight. This inconsistency can be resolved by invoking a reasonable elevation of the central polar cap and by imposing an adequate zonal wind. We conclude that if the explanation requiring a change in atmospheric composition is correct, it must be accompanied by other special circumstances to make it meteorologically consistent. No attempt is made to estimate the possible occurrence of barotropic instability.