\begin{table}%t5
   %\centering
\par
   \caption{Sample non-linear coordinate combinations, where
     $w$, the intermediate coordinate of Eq.~(\ref{eq:w}), has a
     different meaning for each of these equations  It has units given
     by the spectral coordinate type code as listed in
     Table~\ref{ta:codes}.}
   \begin{tabular}{llllll}
      \hline\hline
      \noalign{\medskip}
      \TT{FREQ-W2F} &
      \Ma{\nu  = \left( \frac{\nu\sub{r}}{\nu\sub{r}-w} \right)
                       \nu\sub{r}} \\
      \TT{VELO-W2V} &
         \Ma{v = c~ \frac{A^2_\lambda-1}{A^2_\lambda+1}} & \Wh &
         \Md{A_\lambda \equiv \frac{c^2-v\sub{r}^2+cw}
                              {(c-v\sub{r})\sqrt{c^2-v\sub{r}^2}}} \\
      \TT{VRAD-W2F} &
         \Ma{V = \frac{V\sub{r} (c-V\sub{r}) + cw}{c-V\sub{r} + w}} \\
      \TT{WAVE-F2W} &
         \Ma{\lambda = \left( \frac{\lambda\sub{r}}
                        {\lambda\sub{r}-w} \right) \lambda\sub{r}} \\
      \TT{VELO-F2V} &
         \Ma{v = c~ \frac{A^2_\nu-1}{A^2_\nu+1}} & \Wh &
         \Md{A_\nu \equiv \frac{c^2-v\sub{r}^2-cw}{(c+v\sub{r})
                          \sqrt{c^2-v\sub{r}^2}}} \\
      \TT{VOPT-F2W} &
         \Ma{Z = \frac{Z\sub{r} (c+Z\sub{r}) + cw}{c+Z\sub{r}-w}
         \label{eq:Zw}} \\
      \TT{ZOPT-F2W} &
         \Ma{z = \frac{z\sub{r} (1+z\sub{r}) + w}{1+z\sub{r}-w}
         \label{eq:zw}} \\
      \TT{WAVE-V2W} &
         \Ma{\lambda = \rsl\sqrt{\frac{1+B_\lambda}{1-B_\lambda}}} &
                       \Wh &
         \Md{B_\lambda \equiv \frac{\lambda\sub{r}^4-\rsl^4 +
              4\rsl^2\lambda\sub{r}w}{(\rsl^2+\lambda\sub{r}^2)^2}} \\
      \TT{FREQ-V2F} &
         \Ma{\nu = \rsn\sqrt{\frac{1-B_\nu}{1+B_\nu}}} & \Wh &
         \Md{B_\nu \equiv \frac{\rsn^4-\nu\sub{r}^4-4\rsn^2\nu\sub{r}
                                      w} {(\rsn^2+\nu\sub{r}^2)^2}} \\
      \TT{VOPT-V2W} &
         \Ma{Z = c \left(\sqrt{\frac{1+D_Z}{1-D_Z}} - 1 \right)}
                 & \Wh &
         \Md{D_Z \equiv \frac{Y_Z^4 - 1 + 4Y_Zw / c}{(1+Y_Z^2)^2}}
                 & \Wi &
         \Mc{Y_Z \equiv 1 + Z\sub{r} / c} \\
      \hline
   \end{tabular}
   \label{ta:Nonlincc}
\end{table}