  We acquired spectra for a random sample of galaxies within a 0.83 square
degree region centered on the core of the Centaurus cluster. Radial velocities
were obtained for 225 galaxies to limiting magnitudes of V < 19.5. Of the
galaxies for which velocities were obtained, we find 35% to be member galaxies.
Of the 78 member galaxies, magnitudes range from 11.8 < V < 18.5 (-21.6 < M_{V}
< -14.9 for H_o = 70 km s^-1 Mpc^-1) with a limiting central surface brightness
of \mu_o < 22.5 mag arcsec^-2. We constructed the cluster galaxy luminosity
function by using these spectroscopic results to calculate the expected
fraction of cluster members in each magnitude bin. The faint-end slope of the
luminosity function using this method is shallower than the one obtained using
a statistical method to correct for background galaxy contamination. We also
use the spectroscopy results to define surface brightness criteria to establish
membership for the full sample. Using these criteria, we find a luminosity
function very similar to the one constructed with the statistical background
correction. For both, we find a faint-end slope alpha ~ -1.4. Adjusting the
surface brightness membership criteria we find that the data are consistent
with a faint-end slope as shallow as -1.22 or as steep as -1.50. We describe in
this paper some of the limitations of using these methods for constructing the
galaxy luminosity function.
