Observational data for Uranus are analyzed to derive a physically self-consistent model for the atmosphere. Quadrupole lines of H1 associated with vibration-rotation transitions in the 4-0 band yield a temperature of 118 + 40 K. The hydrogen abundance of 1450 km-atm derived on the basis of a reflectinglayer model indicates that Rayleigh scattering must play a role in line formation; a simple scattering model suggests that observed equivalent widths are consistent with a semi-infinite H2 atmosphere. The analysis implies that particulate matter is essentially absent in regions of Uranus's atmosphere probed by visual radiation. Continuum opacity sources in an atmosphere of pure H2 are reviewed, and results are applied to calculate geometrical albedos for both Uranus and Neptune. At short , only Rayleigh and Raman scattering are important, and geometrical albedos can be calculated to high precision. These calculations are combined with measured geometrical albedos in the ultraviolet to derive new values for the radii of Uranus and Neptune. The result for Neptune, 23600 km, is in good agreement with a value derived from a stellar occultation. The result for Uranus, 25300 km, is intermediate between values previously reported by Barnard and Kuiper. At longer wavelengths, pressure-induced absorption becomes significant. The analysis indicates that absorption associated with the far wings of lines in the fundamental band of H2 may be important in the red and near-infrared regions of the spectrum. A plausible model for the line profile gives results in agreement with observed UB VRI geometrical albedos for both Uranus and Neptune. More work, both laboratory and theoretical, is required before a definite analysis of the infrared spectrum can be performed. In particular, strong absorptions associated with CH4 bands are not considered here. Estimates are given for planetary brightness temperatures (defined as the temperature at optical depth 22) from 2000 A to 10 cm for Traf ton's pure-H2 model of the atmosphere of Uranus. Results are in good agreement with both the temperature deduced from the quadrupole lines and a brightness temperature observed at 20 . Brightness temperatures observed in the radio region of the spectrum are, however difficult to reconcile with this model. Reasons for the discrepancy are discussed.