\begin{table}%t1
\caption{The values of the stellar mass (in $M_{\odot}$) from spectroscopic 
and asteroseismic studies, and the values obtained in this work from three 
different methods.\label{tab1}}
\small
%\centerline
 {\begin{tabular}{lcccc}
\hline
\hline
\noalign{\smallskip}
Source &  PG~1159$-$035 &  PG 2131+066  & PG 1707+427 &  PG 0122+200 \\
\hline
\noalign{\smallskip}
Spectroscopy     &  $0.54 \pm 0.1^{(a)}$  & $0.55 \pm 0.1^{(a)}$   & $0.54 \pm 0.1^{(a)}$ &  $0.53 \pm 0.1^{(a)}$ \\ 
Asteroseismology  &  $0.59 \pm 0.01^{(b)}$ & $0.61 \pm 0.02^{(c)}$  & $0.57 \pm 0.02^{(d)}$ &  $0.69 \pm 0.04^{(e)}$\\ 
By comparing $\overline{\Delta  \Pi}$ with $\Delta \Pi_{\ell}^{\rm a}$ (this work) &  $0.575 \pm 0.005$  & $0.615 \pm 0.015$  & $0.595 \pm 0.015$  & $0.70 \pm 0.02$ \\ 
By comparing $\overline{\Delta  \Pi}$ with $\overline{\Delta \Pi_{k}}$ (this work) &  $0.555  \pm 0.005$  & $0.575  \pm 0.015$ & $0.565 \pm 0.015$  & $0.64 \pm 0.02$ \\ 
By means of $\chi^2 $ period fittings (this work)     &  $0.56 \pm 0.01$ & $0.60 \pm 0.01$  & $0.55 \pm 0.01$  &  $0.64 \pm 0.01$  \\
\hline
\end{tabular}}
\par
\smallskip
{References: 
$^{(a)}$ Dreizler \& Heber (\cite{Dreizler98}); 
$^{(b)}$ KB94; 
$^{(c)}$ Reed et~al. (\cite{Reed00}); 
$^{(d)}$ Kawaler et~al. (\cite{Kawaler04}); 
$^{(e)}$ O'Brien (\cite{OBrien00}).}
\end{table}