theoretically, such an initial shape to $d {\cal N}/dm$ may in fact be [*preserved*]{} during a Hubble time of dynamical evolution (Vesperini 1997). Thus, the intent here is not necessarily to argue for an explanation of present-day GCS mass spectra in purely evolutionary terms, but to show that even if such is adopted as an extreme possibility, the implied time dependence of total GCS masses is quite weak.

Given equations (\[eq:24\]) and (\[eq:25\]), then, straightforward integrations allow for comparisons of the present GCS population to the initial one: $${{{\cal N}_{\rm tot}^{\rm obs}}\over{{\cal N}_{\rm tot}^{\rm init}}} =
\left({{m_u}\over{m_*}}\right)^{\gamma_2-1}\,\left\{
{{1-(m_*/m_u)^{\gamma_2-1}+[(\gamma_2-1)/(1-\gamma_1)][1-(m_\ell/m_*)^
{1-\gamma_1}]}\over{(m_u/m_\ell)^{\gamma_2-1}-1}}\right\}\ ,
\label{eq:26}$$ and of the current total mass to its initial value: $${{M_{\rm gcs}^{\rm obs}}\over{M_{\rm gcs}^{\rm init}}} =
\left({{m_*}\over{m_u}}\right)^{2-\gamma_2}\,\left\{
{{(m_u/m_*)^{2-\gamma_2}-1+[(2-\gamma_2)/(2-\gamma_1)][1-(m_\ell/m_*)^
{2-\gamma_1}]}\over{1-(m_\ell/m_u)^{2-\gamma_2}}}\right\}\ .
\label{eq:27}$$ Values of $\gamma_1=0.4$ and $\gamma_2=1.7$ may be taken as representative of the typical situation in elliptical galaxies (Harris & Pudritz 1994; McLaughlin 1994, 1995; McLaughlin & Pudritz 1996). With $m_\ell=500\,M_\odot$, $m_*=1.6\times10^5\,M_\odot$, and $m_u=5\times10^6\,M_\odot$, it is then easily seen that $${{{\cal N}_{\rm tot}^{\rm obs}}\over{{\cal N}_{\rm tot}^{\rm init}}}=0.036
\ \ \ \ \ \ \ \ {\rm and}\ \ \ \ \ \ \ \ \ 
{{M_{\rm gcs}^{\rm obs}}\over{M_{\rm gcs}^{\rm init}}}=0.76
\label{eq:28}$$ in this simplistic scenario. Thus, [*even though dynamical 