  We describe a robust technique based on the ULySS IDL code for measuring
velocity dispersions of galaxies observed with the MMT's fiber-fed
spectrograph, Hectospec. This procedure is applicable to all Hectospec spectra
having a signal-to-noise >5 and weak emission lines. We estimate the internal
error in the Hectospec velocity dispersion measurements by comparing duplicate
measurements of 171 galaxies. For a sample of 984 galaxies with a median
z=0.10, we compare velocity dispersions measured by Hectospec through a 1.5
arcsec diameter optical fiber with those measured by the Sloan Digital Sky
Survey (SDSS) and Baryon Oscillation Spectral Survey (BOSS) through 3 arcsec
and 2 arcsec diameter optical fibers, respectively. The systematic differences
between the Hectospec and the SDSS/BOSS measurements are <7% for velocity
dispersions between 100 and 300 km/s, the differences are no larger than the
differences among the three BOSS velocity dispersion reductions. We analyze the
scatter about the fundamental plane and find no significant redshift dependent
systematics in our velocity dispersion measurements to z~0.6. This analysis
also confirms our estimation of the measurement errors. In one hour in good
conditions, we demonstrate that we achieve 30 km/s velocity dispersion errors
for galaxies with an SDSS r fiber magnitude of 21.
