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where n = 4.74. A stellar population with solar motion (U, V, W) and velocity dispersions (av,av,aw) has a characteristic transverse velocity, (VT}. Thus, a characteristic distance can be defined for the detection of members of that population in the survey:

^lim

The distribution with distance of stars selected by proper motion depends on the form of the velocity distribution. Given a Schwarzschild velocity ellipsoid (that is, Gaussian velocity distributions in each co-ordinate), 25% of the population members with r < rc are predicted to have p > plim, and these stars represent 80% of the contribution made by that population to the proper-motion survey (Figure 10.2). Hence, if a sample includes Ntot stars from a given stellar population, with known kinematics which provide a reliable estimate of rc, then,

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