We describe a new, deep photographic survey of the Virgo Cluster which uses multiple exposures on Tech Pan film with the United Kingdom Schmidt Telescope to probe the dwarf population to fainter surface brightness limits than previous surveys. We have identified galaxies having sizes (>= 3 arcsec scale length) and surface brightnesses (<= 24.5 R mag arcsec^-2) characteristic of those expected for dwarf spheroidal galaxies in the cluster. The survey is providing substantial samples of extremely low luminosity galaxies outside the environment of the Local Group and nearby groups for the first time. An initial study of two small areas has found dwarf spheroidal candidates in large numbers (500 deg^-2) which indicate a steep, continuously rising luminosity function at low luminosities.
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