Measurements of the geocoronal Balmer-alpha (H&agr;) brightness have been made at the Arecibo Observatory during 11 separate periods since 1983 using both a Fabry-Perot interferometer and a tilting filter photometer. The tilting filter photometer is calibrated for absolute sensitivity using a constant brightness source traceable to National Institute of Standards and Techniques (NIST) standards and is used to cross-calibrate the Fabry-Perot interferometer. Since the observational technique has not changed since 1983, and since the data analyses technique are uniform, these data provide a measure of the solar cycle variation of H&agr; brightness at Arecibo. Unlike earlier studies, we discern no systematic discrepancy between the H&agr; brightness and estimates of the solar Lyman-beta flux that pumps the resonant fluorescent H&agr; emission. Rather, we conclude that geocoronal hydrogen abundance is generally (but not always) larger than models suggest, although not systematically so. The largest H&agr; emission is measured during solar minimum conditions, when brightness is approximately 50% greater than during solar maximum conditions, for measurements at solar depression angles from 15¿ to 35¿. Above about 40¿ solar depression (corresponding to an illuminated column with a base at approximately 2000 km), no solar cycle variation is evident, and the brightness there is persistently greater than models. Intricacies of the Lyman-beta radiative transport problem make detection of an early morning maximum of hydrogen density near the exobase difficult using brightness data alone, although the H&agr; brightness is generally asymmetric with respect to local midnight, with brighter emission in the postmidnight sector. Studies of the semidiurnal (nighttime) variation demonstrate that the H&agr; brightness can vary by a factor of 2 over a period of days. ¿ 2001 American Geophysical Union