\begin{table}%t2 \caption{\label{tab2}Correlation coefficients between the 4~quantities based on the tilt angle and the strength ($S$), amplitude ($A$) and length~($L$) of the same cycle.} %\centerline { \begin{tabular}{c c c c c c c c c c c c c c} \hline\hline \noalign{\smallskip} & \multicolumn{6}{c}{Mount Wilson} & \multicolumn{6}{c}{Kodaikanal} \\ Parameter & \multicolumn{2}{c}{$S$} & \multicolumn{2}{c}{$A$} & \multicolumn{2}{c}{$L$} & \multicolumn{2}{c}{$S$} & \multicolumn{2}{c}{$A$} & \multicolumn{2}{c}{$L$} \\ & $r_{\rm c}$ & $P$ & $r_{\rm c}$ & $P$ & $r_{\rm c}$ & $P$ & $r_{\rm c}$ & $P$ & $r_{\rm c}$ & $P$ & $r_{\rm c}$ & $P$ \\ \hline\noalign{\smallskip} $\langle \alpha \rangle$ & $-$0.59 & 0.30 & $-$0.60 & 0.28 & $-$0.29 & 0.64 & $-$0.77 & 0.04 & $-$0.69 & 0.09 & $-$0.58 & 0.17 \\ $\langle \alpha_{\omega} \rangle$ & $-$0.48 & 0.41 & $-$0.48 & 0.41 & $-$0.46 & 0.44 & $-$0.46 & 0.30 & $-$0.66 & 0.11& $0.19$ & 0.68 \\ \hline\noalign{\smallskip} $\langle \alpha \rangle/\langle \lambda \rangle$ & $-$0.95 & $1\times10^{-3}$ & $-$0.83 & 0.02 & $-$0.40 & 0.37 & $-$0.93 & $2\times10^{-3}$ & $-$0.82 & 0.02 & $-$0.48 & 0.30 \\ $\langle \alpha_{\omega} \rangle/\langle \lambda \rangle$ & $-$0.81 & 0.03 & $-$0.91 & $4 \times 10^{-3}$ & $0.08$ & 0.86 & $-$0.80 & 0.03 & $-$0.91 & $4 \times 10^{-3}$ & $0.03$ & 0.95 \\ \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.} \vspace*{-2mm} \end{table}