The globular cluster M79 was observed with the Hopkins Ultraviolet Telescope (HUT) during the Astro-l space shuttle mission in 1990 December. The cluster's far-UV integrated spectrum shows strong absorption in the Lyman lines of atomic hydrogen. We seek to use this spectrum, together with optical photometry, to constrain the stellar mass distribution along its zero-age horizontal branch (ZAHB). We find that a Gaussian distribution of ZAHB masses, with a mean of 0.59M(.) and standard deviation 0.05M(.), is able to reproduce the cluster's (B,V) color-magnitude diagram when subsequent stellar evolution is taken into account, but cannot reproduce the cluster's far-UV spectrum. Model stellar spectra fit directly to the HUT data indicate a surprising distribution of atmospheric parameters, with surface gravities (and thus implied masses) significantly lower than are predicted by canonical HE evolutionary models. This result is consistent with the findings of Moehler et al. [A&A, 294, 65 (1995)] for individual HB stars in M15. Further progress in understanding the mass distribution of the HE must await resolution of the inconsistencies between the derived stellar atmospheric parameters and the predictions of HE evolutionary models. Improved stellar spectral models, with higher spectral resolution and non-solar abundance ratios, may prove useful in this endeavor. (C) 1996 American Astronomical Society.