Dwarf spheroidal galaxies in the Virgo Cluster

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 deg(2), 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) similar or equal to -11 or about 5 x 10(-5) L*) is very steep, with a power-law slope alpha similar or equal to -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.