Rocket observations of the far ultraviolet dayglow spectrum near solar cycle maximum are analyzed using laboratory cross sections, atmospheric composition models, and photoelectron production models. Photoelectron-excited emissions of N2 and O are used to derive a self-consistent description of the atmosphere at solar maximum. Spectral synthesis of the N2 Lyman-Birge-Hopefield bands shows a departure of a1&Pgr;g state vibrational populations from the direct excitation theory. Observations of the N2 second positive (0,0) 3371-¿ band and O I 1356-¿ emission indicate an exospheric temperature of 1600 K, 200 K higher than predicted by empirical models. The empirical models are also found to overestimate the O and O2 densities required to fit the data by a factor of 2 and 1.4, respectively. These results are compared to the results of an analysis of similar observations made in 1978 near solar minimum. The derived photoelectron flux at 290 km is a factor of 1.6 times larger than for the 1978 data.