A far ultraviolet rocket observation of an auroral arc has been analyzed by using laboratory measured emission cross sections and self-consistent models of the atmospheric composition and energetic electron flux. We find that the observed arc was produced by a precipitating electron flux of 5--8 erg cm-2s-1 energy content and 1.75- to 2.5-keV characteristic energy. The N2 Lyman-Birge-Hopfield spectral synthesis shows that the vibrational populations for the observed emissions are in agreement with laboratory electron impact spectra and the Franck-Condon factors to v'' = 0. This precludes any cascades process to the a1&Pgr;g state, which significantly changes the relative populations. Altitude profiles of the various bands can be reproduced by theory. Dissociation of N2 can account for N i lines at 1134, 1200, and 1493 ¿, and N ii 1085 ¿. Contrary to previous observations of auroras and the dayglow, there is no evidence of multiple scattering of 1200-¿ radiation by atomic nitrogen in the present observations. The atomic oxygen density required to explain the O i 1356, 1304, and 989-¿ emissions is 4¿1010 cm-3 at 120 km, a factor of 3.5 lower than the Jacchia (1971) model.