  We present a study of the smallest and faintest galaxies found in a very deep
photographic R band survey of regions of the Virgo Cluster, totalling over 3
square degrees, made with the UK Schmidt Telescope. The objects we detect have
the same physical sizes and surface brightnesses as Local Group dwarf
spheroidal galaxies. The luminosity function of these extremely low luminosity
galaxies (down to M_R =~ -11 or about 5 X 10^{-5} L*) is very steep, with a
power law slope alpha =~ -2, as would be expected in many theories of galaxy
formation via hierarchical clustering, supporting previous observational
evidence at somewhat higher luminosities in other clusters.
