  Summary - By combining the 5634 redshifts from the ESO Nearby Abell Cluster
Survey (the ENACS) with another 1000 redshifts from the literature we are able
to study the distribution of velocity dispersions for a volume-limited sample
of 128 $R_{\rm ACO} \geq 1$ clusters, out to a redshift $z=0.1$, in a solid
angle of 2.55 sr centered on the South Galactic Pole. In deriving velocity
dispersions we apply a new, physically motivated method for removing fore- and
background galaxies. We discuss in detail the completeness of the cluster
sample for which we derive the distribution of cluster velocity dispersions.
The large apparent spread between velocity dispersion and richness must be
largely intrinsic. A consequence of the very broad relation between richness
and velocity dispersion is that all cluster samples complete in richness are
biased against low dispersions. For the richness limit of our sample this bias
operates below about 800 km/sec. Above 800 km/s, our distribution of global
velocity dispersions is free from systematic errors and biases, and agrees very
well with the most recent determination of the distribution of cluster X-ray
temperatures. Therefore, we conclude that X-ray temperature and velocity
dispersion distributions statistically measure the same cluster property. We
stress the need for model predictions that produce exactly the same information
as provided by the observations, for a sample of model clusters with a richness
limit that mimics that of the sample of observed clusters.
