We present four years of observations of the disk-averaged H Ly &agr; emission from Uranus performed with the IUE Observatory. A detailed analysis of the uncertainties of these measurements is discussed based both on known calibration uncertainties and on a new analysis of the uncertainty in out customized extraction procedure. On the basis of roughly 30 observations we derive an average brightness of 1400 Rayleighs. The larger data base now available has allowed us to perform a more detailed analysis of the character of this emission and its functional relationship with other parameters. The observed extent and time scales of the variability of the emission are presented, and no evidence for correlation with the solar H Ly &agr; variations is found, implying a largely self-excited emission. Limits are derived from the minimum observed brightness and from a modeling of the atmosphere of Uranus for the possible contribution by reflected solar H Ly &agr; emission, which we estimate to be roughly 200 Rayleigh. We therefore interpret the remaining self-excited emission as being produced by charged particle excitation, i.e., an aurora. Studies of possible correlations between the self-excited component of the H Ly &agr; emission and the density and velocity of the local solar wind are presented, based on comparisons with solar wind measurements performed in the vicinity of Uranus from the Voyager 2 and Pioneer 11 spacecraft. No evidence is found for any correlation between the solar wind density and the H Ly &agr; brightness. We estimate an upper limit to the energy of the precipitating particles based on the lack of observed H2 band emission (which sets a lower limit to the ratio H Ly &agr;/H2) and by analogy to the auroral precipitation on Jupiter. Finally, an estimate of the total power in the precipitating particles is on the order of 1012 watts (comparable to the aurora on Saturn), and the disturbance of the upper atmosphere by the deposited energy is discussed.