  (Abbreviated) We present a detailed analysis of the space motions of 1203
solar-neighborhood stars with metal abundances [Fe/H] <= -0.6, on the basis of
a recently revised and supplemented catalog of metal-poor stars selected
without kinematic bias (Beers et al. 2000). This sample, having available
proper motions, radial velocities, and distance estimates for stars with a wide
range of metal abundances, is by far the largest such catalog to be assembled
to date. Unlike essentially all previous kinematically selected catalogs, the
metal-poor stars in our sample exhibit a diverse distribution of orbital
eccentricities, e, with no apparent correlation between [Fe/H] and e. This
demonstrates, clearly and convincingly, that the evidence offered by Eggen,
Lynden-Bell, and Sandage (1962) for a rapid collapse of the Galaxy, an apparent
correlation between the orbital eccentricity of halo stars with metallicity, is
basically the result of their proper-motion selection bias. However, even in
our non-kinematically selected sample, we have identified a small concentration
of high-e stars at [Fe/H] = -1.7, which may originate, in part, from infalling
gas during the early formation of the Galaxy. The implications of our results
for the formation of the Galaxy are also discussed, in particular in the
context of the currently favored CDM theory of hierarchical galaxy formation.
