\begin{table}%t1
\caption{\label{tab1}The results of the $\Sigma-D$ and $L-D$ fits.}
\smallskip
%\centerline
{\small \begin{tabular} {llccccc}
\hline \hline \noalign{\smallskip}
No.& Sample$^{a}$& $\beta_{_{\Sigma - D}}^b$  &$r_{_{\Sigma- D}}^b$& $\alpha_{_{L-D}}^b$ & $r_{_{L{-}D}}^b$ & $N^b$\\
\noalign{\smallskip} \hline \noalign{\smallskip}
01 & SSV  $d<1.0$ & $2.61\pm0.21$ & $-0.97$ &  \p00.61$\pm$0.21 & $-0.67$ & \p013\\
02 & SSV  $1.0\leq d < 2.0$ & $1.89 \pm 0.43$ & $-0.78$ &  --$0.11\pm0.43$ & \p00.08 & \p015\\
03 & SSV  $d\geq2.0$ & $3.96\pm0.62$ & $-0.91$ &  \p01.97$\pm$0.61 & $-0.73$ & \p011\\
04 & SSV   &2.56$\pm$0.22 & $-0.89$ &  \p00.56$\pm$0.22 & $-0.40$ & \p039\\
05 & SSV + Ph02    $d\leq0.4$  & $1.47\pm0.40$ & $-0.74$ &  --$0.53\pm0.40$ & \p00.38 & \p013\\
\noalign{\smallskip}
06 & SSV + Ph02  $0.4<d\leq0.6$   &$2.18\pm0.22$ & $-0.91$ &  \p00.18$\pm$0.22 & $-0.17$ & \p023\\
07 & SSV + Ph02 $0.6<d\leq1.0$   &$2.37\pm0.20$ & $-0.95$ &  \p00.37$\pm$0.20 & $-0.43$ & \p018\\
08 & SSV + Ph02 $1.0<d\leq2.0$ & $2.64\pm0.40$ & $-0.88$ &   \p00.64$\pm$0.40 & $-0.41$ & \p015\\
09 & SSV + Ph02 $d>2.0$ & $4.44\pm$0.47 & $-0.96$ &   \p02.44$\pm$0.47 & $-0.90$ & \p0\p09 \\
10 & SSV + Ph02 & $2.40\pm0.17$ & $-0.86$ &  \p00.40$\pm$0.17 & $-0.27$ & \p078\\
\noalign{\smallskip}
11 & SSV + Ph02 $d\leq0.4$\dag    & $2.31\pm0.38$ & $-0.90$ &  \p00.31$\pm$0.38 & $-0.26$ & \p011\\
12 & SSV + Ph02 $0.4<d\leq0.6$\dag   & $2.33\pm0.15$ & $-0.96$ &  \p00.33$\pm$0.15 & $-0.44$ & \p022\\
13 & SSV + Ph02 \dag & $2.57\pm0.14 $ & $-0.92$ &  \p00.57 $\pm0.14$ & $-0.45$ & \p075\\
14 &  B\&L  & $ 2.31 \pm 0.11$ & $-0.90$ &  \p00.31~$\pm0.11$ & $-0.26$ & 109\\
15 & \cite{Zhang95} & $2.17 \pm0.14$ & $-0.80$ &  \p 00.17~$\pm0.14$ & $-0.10$ & 132\\
\noalign{\smallskip}
16 &\cite{Van95} &   $2.41 \pm 0.34$ & $-0.84$ &  \p 00.41~$\pm0.34$ & $-0.26$ & \p 023\\
17 & \cite{Van95} &  $2.24 \pm 0.09$ & $-0.92$ & \p 00.24~$\pm0.09$ & $-0.24$ & 132 \\
18 & \cite{Van95} (stronger criteria by B\&L)&  $2.21\pm0.09$ & $-0.94$ & \p 00.21~$\pm0.09$ & $-0.25$ & \p 088 \\
\hline
\end{tabular}}
\medskip
$^{a}$ SSV stands for \cite{Stanghellini08}, B\&L for  \cite{Bensby01} and Ph02 for  Phillips (2002). PNe from Ph02 are included in the sample sets (5--13) as additional,
if they were not extracted by the SSV in their sample; $d<1$   denotes that a set of PNe have distances less than 1~kpc, $1\leq d < 2$, between~1 and 2~kpc, etc.; $^b$ the parameters of the fit ($\beta$ and $\alpha$, respectively) and the correlation coefficient~$r$ are given for each sample. The number of PNe in the sample is given in the last column~($N$); \dag~ --~ 3 PNe (He~1--5, HDW~6 and HaWe~5)  are  removed (see text).
\end{table}