circle which encloses all the galaxy centers in the RSCG. Figures \[fig:dens\]a and \[fig:dens\]b show the distribution of $\log(n)$ for both the HCG’s (solid line) and all RSCG’s (dotted line). Figure \[fig:dens\]a includes only groups with $N= 3$ and Figure \[fig:dens\]b includes only groups with $N \geq 4$. Table \[tab:dens\] lists the median, first and third quartiles of these distributions. As expected, the RSCG density distributions agree well with the HCG density distributions at high densities.

The density distributions of our compact groups fall off sharply below $\log(n) \approx 4$, where $n$ is in Mpc$^{-3}$, especially for groups with $N = 3$. This cutoff is an artifact of our search algorithm. Any galaxy in a compact group has a projected separation of at most $50\ {\rm kpc} = 0.05\ {\rm Mpc}$ from at least one other galaxy in its group. For a group of 3, the minimum density allowed is then 3 galaxies in a line, separated by 0.05 Mpc; the group radius is $R=0.05$ Mpc. The minimum group density is then $n= 5.7 \times 10^{3}$ Mpc$^{-3}$; $\log(n_{\rm min}) = 3.76$. A similar calculation for a group of 4 galaxies yields $\log(n_{\rm min}) = 3.35$. In general, the search algorithm 