The limb-darkening observations of Venus made by the 19-mm channel of the United States spacecraft Mariner 2 are here analyzed in a hot-surface context. The observed peak brightness temperatures T3 near the center of each scan (dark side, terminator, bright side) at 19 mm are compared with the predictions of five different opacity models: pressure-induced transitions of CO2 and N2, continuously distributed throughout the atmosphere; non-resonant and resonant absorption by water vapor, similarly distributed; an aerosol of absorbing dust, arbitrarily distributed; an isothermal absorbing cloud layer, near the top of the atmosphere; and an aerosol of scattering particles, arbitrarily distributed with altitude. The CO2-N2, the water vapor, and the absorbing dust models in which these materials are the sole sources of microwave opacity are inconsistent with the Mariner 2 results. If the low radar cross-section at 3.8 cm is attributed to a low dielectric constant of 1.45 for the surface, the absorbing cloud model can account for the Mariner 2 data and offer no inconsistencies with the radar results. On the other hand the scattering model fails for this situation. An upper limit on the surface pressure of between 16 and 150 atm, depending on the CO3 mixing ratio, is derived from the failure of the CO2-N2 opacity model, and similarly an upper bound of 640 gm cm-2 is placed on the water-vapor content of the atmosphere. Finally sizable longitudinal temperature gradients are indicated, which are consistent with those inferred from the 3- and 10-cm phase effects. If the low radar cross-section at 3.8 cm is derived in good measure from atmospheric attenuation, then a model having both continuously distributed opacity, as well as either an absorbing cloud or scattering layer, would be required to explain both this datum and the Mariner 2 observations. Liquid water droplets are the most probable source of opacity for an absorbing cloud layer. In the scattering models the opacity is perhaps best realized by dust continuously distributed through the atmosphere; but hailstones or large raindrops are also possible. For all scattering models, particle radii very close to 0.5 mm are required. Such particles have terminal velocities of several tens of miles per hour.