\begin{table}%t3
%\centering
\par
\caption{Analytical expression for \cite{r:alter59} solution of
the gravito-elastic deformation equations, generalized for a
three-layer Earth.\label{tab3}} 
{\begin{tabular}{llll}
 \hline\hline
 & Earth & Core & Inner core
\\ \hline
  $y_1$ &
$\frac{C_1}{r^n}+\frac{C_2}{r^{n+2}}+C_3r^{n+1}+C_4r^{n-1}$
& $y_5/g_n$ &  $G_3r^{n+1}+G_4 r^{n-1}$\\
$y_2$ & $\frac{-2\mu C_1(n^2+3n-1)}{(n+1)r^{n+1}}
-\frac{2C_2(n+2)\mu}{r^{n+3}}+\frac{2}{n}C_3\mu (n^2-n-3)r^n$ &  /
& $\frac{2}{n}\mu_gG_3\left(n^2-n-3\right)
r^n+2\mu_gG_4(n-1)r^{n-2}$
\\ & $\; \; \; \hspace{1cm} +2\mu
C_4(n-1)r^{n-2}-\rho_my_5+g\rho_my_1$ &  & $ \; \;\;\hspace{1cm} -\rho_gy_5+g\rho_gy_1$\\
$y_3$ & $-\frac{(n-2)C_1}{n(n+1)r^n}-
\frac{C_2}{(n+1)r^{n+2}}+\frac{C_3(n+3)}{n(n+1)}r^{n+1}+\frac{C_4}{n}r^{n-1}$
& / &  $G_3r^{n+1}\frac{n+3}{n(n+1)}+r^{n-1}\frac{G_4}{n}$\\
$y_4$ & $ \mu C_1\frac{2(n-1)}{nr^{n+1}}+\mu
C_2\frac{2(n+2)}{(n+1)r^{n+3}}+\mu C_3 \frac{2(n+2)}{n+1}r^n $& 0
&
$2\mu_gG_3r^n\frac{n+2}{n+1}+2\mu_gG_4\frac{n-1}{n}r^{n-2}$\\
& $+\frac{2(n-1)}{n}\mu C_4 r^{n-2} $&  &\\
$y_5$ & $C_5r^n+\frac{C_6}{r^{n+1}}$ & $Cr^n+\frac{Dc}{r^{n+1}}$ & $G_5 r^n$\\
$y_6$ & $n C_5
r^{n-1}-C_6\frac{n+1}{r^{n+2}}-\frac{3g_0\rho_my_1}{a\rho_M}$ &
$nCr^{n-1}-\frac{Dc(n+1)}{r^{n+2}}-\frac{3g_0\rho_{\rm f}y_1}{a\rho_M}$&
$ G_5 nr^{n-1}-3\frac{g_0\rho_g y_1}{a\rho_M}$ \\
\hline
\end{tabular}}
\end{table}