Ground-based polarimetric data taken near maximum elongation are presented. These data are analyzed on the assumption of an optically thin, Rayleigh-scattering atmosphere, and a surface whose polarization varies inversely as surface albedo. For Mars, the best fit to the data yields an estimate of surface pressure in the range 4-7.5 mb, if CO2 is the principal constituent. There is no need to postulate the existence of fine dust in the Martian atmosphere. For Mercury, the best fit to the data yields an upper limit on Rayleigh scattering equal to 0.001 of the Earth's atmosphere.