to $S_N$ values that increase with radius inside the galaxies. Extending similar suggestions in the recent literature, it is argued that these trends in $S_N$ do not reflect any such behavior in the underlying $\epsilon_{\rm cl}$; rather, [*both*]{} of these problems stem from neglecting the hot, X-ray emitting gas in and around many large ellipticals, and both may be alleviated by including this component in estimates of $M_{\rm gas}^{\rm init}$.

    This claim is checked and confirmed in each of M87, M49, and NGC 1399, all of which have been thought to suffer from one or the other of these $S_N$ problems. Existing data are combined to construct GCS surface density profiles that extend over nearly the whole extents of these three galaxies, and a non-parametric, geometrical deprojection algorithm is developed to afford a direct comparison between the [*volume*]{} density profiles of their GCSs, stars, and gas. It is found, in each case, that $\rho_{\rm cl}\propto(\rho_
    {\rm gas}+\rho_{\rm stars})$ at radii beyond roughly a stellar effective radius, inside of which dynamical evolution may have depeleted the initial GCSs. The constant of proportionality is the same in all three galaxies: $\epsilon_{\rm cl}=0.0026\pm0.0005$. Taken together, these results suggest that GCSs generally should be 