  We present the first dynamical study of the optically selected Palomar
Distant Cluster Survey (PDCS). We show that eleven out of twelve PDCS clusters
we observed are real over-densities of galaxies. Most clusters have velocity
dispersions appropriate for clusters of galaxies. However, we find a fraction
(1/3) of objects in the PDCS which have velocity dispersions in the range of
groups of galaxies (200 +/- 100 km/s) but have richnesses appropriate for
clusters of galaxies.
  We measure the richness function, X-ray luminosity function (using both the
detections and upper limits), and the mass function derived from our velocity
dispersions. We confirm that the space density, as a function of richness, of
clusters of galaxies in the PDCS is ~5 times that of the Abell catalog.
Excluding the above fraction of 1/3 of objects with low velocity dispersions,
we measure a space density ~3 times that of the Abell catalog for equivalent
mass clusters of galaxies. Our space density estimates are in agreement with
other low-redshift, optically-selected cluster surveys such as the EDCC, APM
and EDCC2, which raises the possibility that the Abell catalog is incomplete.
Our X-ray luminosity function agrees with other measurements based on both
X-ray and optically selected samples, so we find that the PDCS does not miss
clusters of galaxies that would be found in an X-ray selected survey. Our
resulting mass function, centered around 10e14 Msun/h, agrees with the
expectations from such surveys as the Canadian Network for Observational
Cosmology cluster survey, though errors on our mass measurements are too large
to constrain cosmological parameters.
