We discuss the kinematic properties of a sample of 1936 Galactic stars, selected without kinematic bias, and with abundances [Fe/H] less than or equal to -0.6. The stars selected for this study all have measured radial velocities, and the majority have abundances determined from spectroscopic or narrow-/intermediate-band photometric techniques. In contrast to previous examinations of the kinematics of the metal-poor stars in the Galaxy, our sample contains large numbers of stars that are located at distances in excess of 1 kpc from the Galactic plane. Thus, a much clearer picture of the nature of the metal-deficient populations in the Galaxy can now be drawn. Our present data can be well described in terms of a two-component kinematic model consisting of a thick disk, rotating at roughly 200 km s(-1) (independent of metal abundance), and an essentially nonrotating halo. The kinematics of these two components suggest a very broad overlap in metallicity; the thick disk is shown to possess an extremely metal-weak tail, extending to abundances even lower than previously reported, down to at least [Fe/H] approximate to -2.0. A ''minimal-assumptions'' maximum-likelihood model is used to show that below [Fe/H] = -1.5 roughly 30% of stars in the solar neighborhood can be kinematically associated with the thick disk. Over the metallicity interval -1.6 less than or equal to [Fe/H] less than or equal to -1.0, the thick-disk proportion rises to 60%. This fraction is only slightly smaller than contribution of thick-disk stars derived by Morrison, Flynn, and Freeman in the same metallicity interval (80%). Our confirmation that significant numbers of stars with thick-disk-like kinematics exist in the solar neighborhood at arbitrarily low metal abundance suggests that previous disagreements about the correlation of population rotation velocities and metal abundance (e.g., Sandage & Fouts vs. Norris) may be due primarily to the selection criteria employed, and the resulting different contribution of metal-weak thick-disk stars to the respective data sets. The non-Gaussian nature of the velocity distribution of extremely metal-poor stars ([Fe/H] less than or equal to - 1.5) in the directions of the Galactic poles reported by previous workers can also be understood as a consequence of the overlap between a cold metal-weak thick-disk population and a hot halo population. A maximum-likelihood technique has been developed in order to estimate the velocity ellipsoids of the thick-disk and halo components of the Galaxy. From the 349 stars in our sample with -1.0 less than or equal to [Fe/H] less than or equal to -0.6 and \z\ less than or equal to 1 kpc, the velocity ellipsoid of the thick disk is (sigma(U), sigma(V), sigma(W)) = (63 +/- 7, 42 +/- 4, 38 +/- 4) km s(-1) These values are in remarkably good accord with the predicted thick-disk velocity ellipsoid obtained by Quinn, Hernquist, and Fullagar from simulations of a satellite-merger formation scenario. Based on this velocity ellipsoid, a radial scale length for thick-disk stars of h(R) = 4.7 +/- 0.5 kpc is obtained, larger than reported by Morrison, and similar to the value obtained for the old-disk population. However, the apparent equality of sigma(V) and sigma(W) evidence that the thick disk is kinematically distinct from the old-disk population, where sigma(V):sigma(W) approximate to root 2:1. We find a substantially smaller asymmetric-drift velocity gradient for presumed thick-disk stars (delta V-rot/delta\z\ = -13 +/- 6 km s(-1) kpc(-1)) than reported by Majewski (delta V-rot/delta\z\ = -21 +/- 1 km s(-1) kpc(-1)). From 887 stars in our sample with [Fe/H] less than or equal to -1.5 the local velocity ellipsoid of the halo is (sigma(r), sigma(phi), sigma(theta)) = (153 +/- 10, 93 +/- 18, 107 +/- 7) km s(-1): that is, strongly radially peaked, as indicated by previous studies. We find little difference in the velocity ellipsoids of this sample when it is split into two roughly equal pieces with -2.2 less than or equal to [Fe/H] less than or equal to -1.5 and [Fe/H] less than or equal to -2.2, which indicates a lack of radial metallicity gradient in the halo, as found from studies of the Galactic globular cluster system. The velocity ellipsoid obtained from the small number of stars in our sample with Galactocentric distances r> 10 kpc (N = 61) is (sigma(r), sigma(phi), sigma(theta)) = (115 +/- 18,138 +/- 78,110 +/- 24) km s(-1), much less radially elongated than found for the local sample.
