  We measure the optical richness of galaxy clusters from the CNOC1 cluster
redshift survey using the galaxy-cluster center correlation amplitude B_gc. We
show that the B_gc values measured using photometric catalogs are consistent
with those derived from redshift catalogs, indicating that richness can be
measured reliably from photometric data alone, even at moderate redshifts of
\~0.6. We establish the correlations between optical richness and other
important attributes of a galaxy cluster, such as velocity dispersion, mass,
radius, and X-ray temperature and luminosity. We find that the scaling
relations of these quantities with richness are entirely consistent with those
derived by assuming a simple mass density profile at 0.5 Mpc of rho~r^{-1.8}.
The excellent correlations between B_gc and velocity dispersion and X-ray
temperature allow one to use richness, an easily measurable quantity using
relatively shallow optical imaging data alone, as a predictor of these
quantities at moderate redshifts. The B_gc parameter can be used to estimate
the velocity dispersion of a cluster to a precision of approximately 15%
(~+/-100 km/s), and X-ray temperature to about 20%. Similar correlations, but
with larger scatter, are also obtained between richness and the characteristic
radius and mass of the clusters. We compare the relative merits of B_gc, T_x,
and L_x as predictors of the dynamical mass, and find that they are comparable,
providing estimates at an accuracy of ~30%. We also perform similar analyses of
correlations between richness and velocity dispersion, T_x and L_x with a
sample of low-redshift Abell clusters and find consistent results, but with
larger scatter, which may be the result of a less homogeneous database, or
sample-dependent effects.
