\begin{table}%t2
\caption{Significant periods detected in the combined data set of \pal.    \label{t:pal_period}}
%\centering
\par
\begin{tabular}{clll}
 \hline \hline\noalign{\smallskip}
      Signal & Period (min) & \multicolumn{2}{c}{Identification} \\
                &    &  case A  & case B\\
\noalign{\smallskip} \hline \noalign{\smallskip}
$P_{1}$  & 157.1725 & \multicolumn{2}{c}{$P_{\rm orb}$} \\
$P_{2}$  & 145.9688 & $P_{\rm spin}$          & $P_{\rm (\omega+\Omega)/2}$\\
$P_{3}$  & 136.2561 & $P_{\rm 2\omega-\Omega}$     & $P_{\rm spin}$ \\
  & 78.586   & \multicolumn{2}{c}{$P_{\rm orb}/2$} \\
  & 72.984   & $P_{\rm spin}/2$             & $P_{\rm (\omega+\Omega)}$ \\
  & 99.681   & $P_{\rm \omega+\Omega/2}$    & $P_{\rm \omega/2+\Omega}$  \\
  & 2043.576 & $P_{\rm beat,obs}$               & $2P_{\rm beat,obs}$  \\
  & 2047.752 & $P_{\rm beat,calc}$               & $2P_{\rm beat,calc}$  \\
   %  $P_{\rm beat, predicted}$  & 2047.752 \\
% $P_{\rm beat, observed}$  & 2043.576 \\
% $P_{\rm orb}/2$  & 78.586 \\
% $P_{\rm spin}/2$  & 72.984 \\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
      \end{tabular}\\
%   \noindent{\Ni\small $^{(2)}$ The letters after the date denote the
%   ROSAT detector: H = HRI, P = PSPC\\ 
%                       $^{(2)}$ Note  the lower sensitivity of the
%                                HRI at soft energies by a factor of 7.8.
%            }
   \end{table}