\begin{table}%t3
\caption{\label{table03}Internal estimation of the proper motion errors
binned by magnitude, including the number of stars per magnitude interval.}
%\centerline
 {\small \begin{tabular}{rrrr}
 \hline  \hline
 Mag. & $ \langle \sigma_{\mu_{\alpha} \cos\delta} \rangle $&
$ \langle \sigma_{\mu_{\delta}} \rangle$  & $N_{*'s}$ \\
      &\multicolumn{1}{c}{(mas/yr)} &\multicolumn{1}{c}{ (mas/yr) }& \\
 \hline
% \noalign{\smallskip}
7 &  1.2 & 1.2 &      7\\
   8 &  1.3 & 1.0 &    130\\
   9 &  1.1 & 1.0 &   1092\\
  10 &  1.1 & 1.1 &   5936\\
  11 &  1.1 & 1.1 &  20~405\\
  12 &  1.1 & 1.0 &  44~464\\
  13 &  1.1 & 1.1 &  77~505\\
  14 &  1.6 & 1.4 & 136~028\\
  15 &  2.9 & 2.6 & 202~416\\
  16 &  3.2 & 3.1 &  15~786\\
 \noalign{\smallskip}
 \hline
 \noalign{\smallskip}
 Total  & 2.0 & 1.9 & 503~769\\
\hline
\end{tabular}}
\medskip
Each bin $m$ includes stars whose magnitude is in the range of
$[m-0.5,m+0.5)$.
\end{table}