A new efficient radiative transfer algorithm for inhomogeneous atmospheres has been used to simulate the limb to limb Lyman &agr; reflectivities observed with the Voyager ultraviolet spectrometer during the flyby of Uranus. It was shown that complete frequency redistribution should be adequate to describe the disc emissions. The model atmosphere used was derived using a combination of Voyager measurements and modeling. Atomic H densities calculated had sources derivable directly from solar FUV and EUV fluxes. To fit the observations, four contributions are evaluated: (1) the resonance scattering of solar Lyman &agr; radiation, (2) Rayleigh-Raman scattering of solar Lyman &agr; radition, (3) the resonance scattering of interplanetary Lyman &agr; radiation, and (4) a possible internal source of unknown origin. From comparison with the observations, and provided that the published Voyager calibrations are correct, it is shown that only atmospheres with low eddy diffusion coefficients (KH≤100 cm2 s-1) and an internal source could simulate both the shape and the strength of the measured disc emission. The main results are then that the direct solar Lyman &agr; scattering contribution (type 1 plus type 2) is of the order of 760 R, the scattering of interplanetary Lyman &agr; contributes about 320 R, and a small additional internal source providing about 100--500 R is needed to mach the measurements. Further, the analysis of the disc intensities suggests that there is no strong variation of K with latitude. ¿ American Geophysical Union 1991