  We measure the galaxy luminosity function (LF) for the Virgo Cluster between
blue magnitudes M_B = -22 and M_B = -11 from wide-field CCD imaging data. The
LF is only gradually rising for -22 < M_B < -16. Between M_B = -16 and M_B =
-14 it rises steeply, with a logarithmic slope alpha ~ -1.6. Fainter than M_B =
-14, the LF flattens again. This LF is shallower (although turning up at
brighter absolute magnitudes) than the R-band LF recently measured by Phillipps
et al. (1998), who found alpha ~ -2.2 fainter than M_R = -13. It is similar,
however, to the LF determined from the Virgo Cluster Catalog by Sandage et al.
(1985). A few faint galaxies are found which Sandage, et al. missed because
their surface-brightness threshold for detection was too high, but these do not
dominate the luminosity function at any magnitude. Most of the faint galaxies
we find are dwarf elliptical, alternatively called dwarf spheroidal, galaxies.
The most important potential source of systematic error is that we may have
rejected some high surface-brightness galaxies from the cluster sample because
we think that they are background galaxies. This is quite different from what
has conventionally been regarded as the most serious source of systematic error
in this kind of study: that we are missing many LOW surface-brightness galaxies
because they are never visible above the sky.
