introduces a complex selection as a function of density, but this selection is only relevant over a small range of densities. The HCG’s do not display this sharp cutoff because selection is based on angular rather than physical extent. These criteria lead to a range of HCG densities corresponding to a range of distances.

Hickson’s Criteria
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Unlike Hickson, we do not include isolation and luminosity criteria in our selection algorithm. Here we investigate the physical implications of the application of Hickson’s more restrictive criteria.

Population and Surface Brightness Criteria
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Hickson limited group membership to galaxies with $m \leq m_{1}+3$ because galaxies with similar magnitudes are more likely to be at the same redshift than galaxies with a broader magnitude distribution. This problem is irrelevant for groups selected in redshift space. Furthermore, faint galaxies are probably less massive and hence less important dynamically. This effect is relevant to very nearby groups in our sample. Seven of our groups (all with median velocities $\leq  1600\ {\rm km \ s}^{-1}$) contain fewer than three members in the interval \[$m_{1}$,$m_{1} +3$\]. Most of these groups are located in the outskirts of the Virgo cluster \[see, for example, Mamon (1989), who finds RSCG 