\begin{table}%t3
%\centering
\par
\caption{Theoretical contributions (from W94, Williams (\cite{Williams95}) and MHB) 
to the precession rates, $r_{\psi}$ and $r_{\epsilon}$, of the equator used in 
the present~paper.\label{tab3}}
\begin{tabular}{|l|c||r|r|r||r|r|r|r}
\hline\hline
\ \ \ Source of the effect& $\epsilon$ dependence &
\multicolumn{3}{c||}{Contribution in longitude at J2000}  &
\multicolumn{3}{c|}{Contribution in obliquity at J2000} \\
\cline{3-8} & & $\mu$as/cy & $\mu$as/cy$^2$ & $\mu$as/cy$^3$ & $\mu$as/cy & 
$\mu$as/cy$^2$ & $\mu$as/cy$^3$\\
\hline
Luni-solar \& Planetary torque & & & & & & & \\
~~~~Luni-solar 1st order&$\cos\epsilon$ &$(r_0)_1$ &$-3395$ &$-6$& 0 & 0 & 0\\
~~~~Luni-solar 2d order(a)&$6\cos^2\epsilon-1$  &$-33~100$  & 0& 0 & 0 & 0 & 0\\
~~~~Luni-solar 2d order(b)&$3\cos^2\epsilon-1$  &$-13~680$  & 0& 0 & 0 & 0 & 0\\
~~~~Luni-solar $J_4$ & $\cos\epsilon\left(4-7\sin^2\epsilon\right)$ &$+2600$ & 0 & 0 & 0 & 0 & 0\\
~~~~Planetary 1st order &$\cos\epsilon$  &$+31~367$  & 0& 0 & $-1400$ & 0 & 0\\
$J_2$ and planetary tilts & & & & & & & \\
~~~~$J_2$ and planetary tilt(a) & $\cos2\epsilon/\sin\epsilon$ &$-269~430$ & $+1074$ 
& 0 & 0 & 0 & 0\\
~~~~planetary tilt(b)& $\cos\epsilon$ & 0 & 0 & 0 &$(u_0)_1$&$-44$&$+3$\\
Tides & & & & & & & \\
~~~~tides(a)&$\cos^2\epsilon$ &0&$-102$& 0 & 0 & 0 & 0\\
~~~~tides(b)&$\cos^3\epsilon$ &0&$-133$& 0 & 0 & 0 & 0\\
~~~~tides(c)&$\sin\epsilon \cos\epsilon$ &0 & 0& 0 & $+2400$ & 0 & 0\\
$J_2$ rate & $\cos\epsilon$ &0 &$-14~000$& 0 & 0 & 0 & 0\\
Non-linear effect &$1$ &$-21~050$ &0& 0 & 0 & 0 & 0 \\
Geodesic precession & $1$ &$-1~919~883$ &$+3$ &$+1$ & $-1$ &$0$ &$+5$\\
\hline
Total & & $(r_0)_1 - 2~223~176$ &  $-16~553$ & $-5$ & $(u_0)_1 + 999$ &
$-44$ & $+8$\\
\hline
\end{tabular}
\end{table}