\begin{table}%t3
\caption{\label{tab3}Correlation coefficients between the 4 quantities based on the tilt angle and the length, $L$, of the next cycle.}
%\centerline
{\begin{tabular}{c c c  c c c}  % centered columns (7 columns)
\hline\hline                 % inserts double horizontal lines
  & \multicolumn{2}{c}{Mount Wilson}  &  \multicolumn{2}{c}{Kodaikanal} \\
%\hline                        % inserts single horizontal line
                      &  $r_{\rm c}$  &  $P$ &  $r_{\rm c}$  &  $P$  \\
\hline
$\langle\alpha\rangle$                               & $-$0.88  & 0.05 & $-$0.32 & 0.48\\
$\langle\alpha_{\omega}\rangle$   & $-$0.77 & 0.13 & $-$0.57 & 0.18 \\
\hline
$\langle\alpha\rangle/\langle\lambda\rangle$ & $-$0.46  & 0.30 & $-$0.37 & 0.41 \\
$\langle\alpha_{\omega}\rangle/\langle\lambda\rangle$  & $-$0.67 & 0.10 & $-$0.61 & 0.15 \\
\hline
\end{tabular}}
\medskip
\tablefoot{Correlation coefficients are represented by $r_{\rm c}$ and the probability that the correlation is due to chance by $P$ for both the MW and KK data sets.} 
\end{table}