2 Sample selection and astrometric data

For our analysis we selected from the MSC database the outer subsystems of hierarchical multiple stars with periods from 500 to 10⁶ years. These periods were inferred from the projected separation $\rho$, the parallax and the total mass of the object. The physical status of these visual components is established by at least two independent criteria (such as the position at the colour-magnitude diagram, common proper motions or common radial velocities). We limited the study to primary components less massive than $5~M_{\odot}$. Too distant systems with parallax $\pi<0\hbox{$.\!\!^{\prime\prime}$ }003$ were not considered either. This gave an initial sample of 376 systems.

The vectors of the relative motion of the secondary outer components were derived from the change of position parameters $\rho$ and $\theta$ relative to the primary star between the first and the last observations of the system after correction for the precession. The first-epoch data were taken mainly from the Washington Double Star catalogue (Worley & Douglass 1996). In few cases the positions given in the CCDM (Dommanget & Nys 1994) were used (flag "c'' in Table 1, see below).

To get the most precise second epoch positions, we identified the components of our objects in the Hipparcos (ESA 1997) and Tycho-II (Høg et al. 2000) catalogues. The confusions in identification between different catalogues were resolved with the help of Digital Sky Survey images. For four systems in the output sample (flag "*'' in Table 1), the alternative solutions were accepted as given in Hipparcos Notes (HIP 17749/50, 24019/20), by Falin & Mignard (1999; HIP 64425) or Fabricius & Makarov (2000; HIP 76563/66). The identifications of components in WDS, CCDM, Hipparcos and Tycho catalogues are given in Table 2. Only a small fraction of objects with faint outer companions have no Hipparcos positions (flag "w'' in Table 1).

For twelve systems the difference of Tycho-II proper motions appeared to be more reliable for the determination of $\gamma$ than the change of the $\rho$, $\theta$ data (flag "m'' in Table 1).

Some companions of visual multiple stars which were treated as photocenters in WDS (e.g. systems like "AB-C'' in WDS) were resolved in Hipparcos observations. To compare consistently the position parameters provided by WDS and Hipparcos in this case, we computed the positions of the photocenter of inner subsystems for the second epoch using the $V_{\rm T}$- or Hp-band fluxes for weighting.