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We present a complete morphologically classified sample of 144 faint field galaxies from the HST Medium Deep Survey with 20.0 < I <22.0 mag. We compare the global properties of the ellipticals, early and late-type spirals, and find a non-negligible fraction (13/144) of compact blue [(V-I) < 1.0 mag] systems with r^{1/4}-profiles. We give the differential galaxy number counts for ellipticals and early-type spirals independently, and find that the data are consistent with no-evolution predictions based on conventional flat Schechter luminosity functions (LF's) and a standard cosmology. Conversely, late-type/Irregulars show a steeply rising differential number count with slope (\frac{\delta log N}{\delta m}) = 0.64\pm 0.1. No-evolution models based on the Loveday et al. (1992) and Marzke et al. (1994b) {\it local} luminosity functions under-predict the late-type/Irregular counts by 1.0 and 0.5 dex, respectively, at I = 21.75 mag. Examination of the Irregulars alone shows that \sim 50% appear inert and the remainder have multiple cores. If the inert galaxies represent a non-evolving late-type population, then a Loveday-like LF (\alpha\simeq -1.0) is ruled out for these types, and a LF with a steep faint-end (\alpha\simeq -1.5) is suggested. If multiple core structure indicates recent star-formation, then the observed excess of faint blue field galaxies is likely due to {\it evolutionary} processes acting on a {\it steep} field LF for late-type/Irregulars. The evolutionary mechanism is unclear, but 60% of the multiple-core Irregulars show close companions. To reconcile a Marzke-like LF with the faint redshift surveys, this evolution must be preferentially occurring in the brightest late-type galaxies with z > 0.5 at I = 21.75 mag

The Contribution of Late-Type/Irregulars to the Faint Galaxy Counts from Hubble Space Telescope Medium-Deep Survey Images