\begin{table}%t2
\par
\caption {\label{tab:nodeshifts}Shift of the antinodes ($i$) of the first 5 eigenmodes ($k$) when expanded linearly in the stratification parameter.}
%\centerline
 {
\begin{tabular}{c|ccccc}\hline\hline
\multicolumn{6}{c}{Displacement:} \\
\hline %\hline
$k i$ & 1 & 2 & 3 & 4 & 5\\
\hline
1 & 0 &&&&\\
2 & --.020154 & 0.020154 &&&\\
3 & --.024759 & 0 & 0.024759 &&\\
4 & --.023445 & --.019519 & 0.019519 & 0.023445 &\\
5 & --.021226 & --.028299 & 0 & 0.028299 & 0.021226\\
\hline
\end{tabular}}
%\centerline
 {\begin{tabular}{c|ccccc}\hline\hline
\multicolumn{6}{c}{Compression:} \\
\hline
$k i$ & 1 & 2 & 3 & 4 & 5\\
\hline
1 & 0 &&&&\\
2 & --.0764 & 0.0764 &&&\\
3 & --.0554 & 0 & 0.0554 &&\\
4 & --.0418 & --.0271 & 0.0271 & 0.0418 &\\
5 & --.0334 & --.0358 & 0 & 0.0358 & 0.0334\\
\hline
\end{tabular}}
\par
\smallskip
The numbers are the coefficients of $\alpha_1$ in the expansion. Note the number of digits in the table for the compression. The terms in summation~(\ref{eq:antinodesum}) decay rather slowly with~$j$ and although 200~terms were used to compute the above values, they are only valid up to the third significant digit. For the displacement the contributions decay much faster 
with~$j$ and are almost entirely determined by the $(k+2)$th contribution.
\end{table}