  The excess numbers of blue galaxies at faint magnitudes are a long-standing
cosmological puzzle. We present new number-magnitude counts as a function of
galactic morphology from the first deep fields of the Cycle 4 Hubble Space
Telescope {\it Medium Deep Survey} project. From a sample of 301 galaxies we
define counts for elliptical, spiral and irregular/peculiar galaxies to $I=22$.
We find two principal results. Firstly the elliptical and spiral galaxy counts
both follow the predictions of high-normalisation no-evolution models at all
magnitudes, indicating that regular Hubble types evolve only slowly to $z\sim
0.5$. Secondly we find that irregular/peculiar galaxies, including
multiple-peaked, possibly merging, objects, have a very steep number-magnitude
relation and greatly exceed predictions based on proportions in local surveys.
These systems make up half the total counts by $I=22$ and imply the
rapidly-evolving component of the faint galaxy population has been identified.
