\begin{table}%t6
\caption{Parameters derived from the MFs of M~52.}
\label{tab6}
\small%\centerline
{
\begin{tabular}{ccccccccccccccc}
\hline\hline
&\multicolumn{2}{c}{Evolved}&&\multicolumn{4}{c}{Observed MS}&&
\multicolumn{6}{c}{$\rm Evolved\ +\ Observed\ MS\ stars$}\\
\cline{2-3}\cline{5-8}\cline{10-15}
Region&$N^*$&$m$&&$\chi$&&$N^*$&\mobs&&$N^*$&$m$&$\sigma$&$\rho$&&$\tau$\\
&(stars)&(\ms)&&&&($10^2$ stars)&($10^2\ms$)&& ($10^2$ stars)&($10^2~\ms$)&($\rm \ms~pc^{-2}$)&($\rm \ms~pc^{-3}$)\\
 (1)  & (2)   & (3)  &&(4)     && (5)    & (6)   && (7)    & (8)   &(9)     &(10)&&(11)\\
\hline
&\multicolumn{14}{c}{Before differential-reddening correction}\\
Core& -- & -- &&$0.73\pm0.11$& &$0.9\pm0.1$&$2.2\pm0.4$
&&$0.9\pm0.1$&$2.2\pm0.4$&$109\pm17$&$102\pm16$&&$97\pm26$\\
Halo&$3\pm1$ &$18\pm6$ &&$1.69\pm0.11$& &$4.7\pm0.6$&$9.7\pm1.2$
 &&$4.7\pm0.6$&$9.8\pm1.3$&$4.9\pm0.6$&$0.46\pm0.06$&&--\\
Overall& $3\pm1$&$18\pm6$ &&$1.53\pm0.09$& &$5.3\pm0.6$&$11.3\pm1.3$ 
&&$5.4\pm0.7$&$11.5\pm1.3$&$5.7\pm0.6$&$0.5\pm0.1$&&$2.2\pm0.5$\\
\cline{2-15}
&\multicolumn{14}{c}{After differential-reddening correction}\\
Core& -- & -- &&$0.89\pm0.12$& &$1.0\pm0.2$&$2.4\pm0.4$
&&$1.0\pm0.1$&$2.3\pm0.4$&$91\pm15$&$75\pm12$&&$78\pm20$\\
Halo&$3\pm1$ &$18\pm6$ &&$1.65\pm0.12$& &$4.6\pm0.6$&$10.0\pm1.4$
 &&$4.7\pm0.6$&$10.1\pm1.4$&$5.1\pm0.7$&$0.47\pm0.07$&&--\\
Overall& $3\pm1$&$18\pm6$ &&$1.48\pm0.09$& &$5.5\pm0.5$&$11.9\pm1.3$ 
&&$5.4\pm0.6$&$12.1\pm1.4$&$6.0\pm0.7$&$0.6\pm0.1$&&$2.2\pm0.6$\\ 
\cline{2-15}
&\multicolumn{2}{c}{}&&\multicolumn{4}{c}{}&&\multicolumn{6}{c}{$\rm Evolved\ +\ Observed\ +\ Extrapolated\ MS\ stars$}\\
Core& -- & -- &&$0.89\pm0.12$& &$1.0\pm0.2$&$2.4\pm0.4$
&&$8.3\pm5.4$&$4.8\pm1.1$&$184\pm41$&$152\pm34$&&$13\pm8$\\
Halo&$3\pm1$ &$18\pm6$ &&$1.65\pm0.12$& &$4.6\pm0.6$&$10.0\pm1.4$
 &&$82\pm60$&$34\pm11$&$17\pm6$&$1.6\pm0.5$&&--\\
Overall& $3\pm1$&$18\pm6$ &&$1.48\pm0.09$& &$5.5\pm0.5$&$11.9\pm1.3$ 
&&$88\pm64$&$38\pm12$&$19\pm6$&$1.8\pm0.6$&&$0.2\pm0.1$\\
\hline
\end{tabular}}
\medskip
Notes. MS mass range: $1.3{-}6.1$~\ms. Column~4: MF slope. Column~11: dynamical-evolution parameter 
$\tau={\rm age}/t_{\rm rel}$. 
\end{table}