  We present a galaxy circular velocity function, Psi(log v), derived from
existing luminosity functions and luminosity-velocity relations. Such a
velocity function is desirable for several reasons. First, it enables an
objective comparison of luminosity functions obtained in different bands and
for different galaxy morphologies, with a statistical correction for dust
extinction. In addition, the velocity function simplifies comparison of
observations with predictions from high-resolution cosmological N-body
simulations.
  We derive velocity functions from five different data sets and find rough
agreement among them, but about a factor of 2 variation in amplitude. These
velocity functions are then compared with N-body simulations of a LCDM model
(corrected for baryonic infall) in order to demonstrate both the utility and
current limitations of this approach. The number density of dark matter halos
and the slope of the velocity function near v_*, the circular velocity
corresponding to an ~L_* spiral galaxy, are found to be comparable to that of
observed galaxies. The primary sources of uncertainty in construction of
Psi(log v) from observations and N-body simulations are discussed and
explanations are suggected to account for these discrepancies.
