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$\begin{figure} \par\includegraphics[width=4.7cm,clip]{4611fg1a.eps}\includegraphics[width=4.7cm,clip]{4611fg1b.eps} \end{figure}$ Figure 1: $\chi ^2$ contours for fitting a substellar companion with fixed spectroscopic parameters to the Hipparcos Intermediate Astrometric Data of HD 38529 ( left panel) and HD 168443 ( right panel). The inclination i and ascending node $\Omega$ were free parameters in the fit, as were corrections to the standard five astrometric parameters in the Hipparcos Catalogue. The contours correspond to the confidence levels with probabilities of 68.3% (1 $\sigma$ ), 90% and 95% as appropriate for two parameters; the 1 $\sigma$ confidence intervals for only one parameter at a time are shaded in gray. The best fit solution is indicated with a cross. The small dots in each panel correspond to best fit solutions where errors in the spectroscopic parameters were taken into account. Note the small region in the parameter space taken up by the $\chi ^2$ contours, placing significant constraints on the astrometric orbits, especially for HD 168443c.
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