The different emission lines in the spectrum of a QSO give systematically different redshifts, because line peaks are shifted with respect to the systemic velocity. These velocity shifts are not understood, and there is great disagreement over their magnitude, but they are likely to play an important role in the next generation of emission-line models, which will combine dynamical information from line profiles, with determinations of size, density, and ionization. We present a new method for determining mean line velocities which is an order of magnitude more accurate than past work. Using a large sample of 518 lines from 160 QSOs, largely from Barthel, Tytler, & Thomson, we find that each ultraviolet emission line has a well-determined mean velocity, with a surprisingly small QSO-to-QSO dispersion of under 200 km s-1. These velocities increase in order from O I at -50 +/- 69 km s-1, to Mg II, Ly-alpha, N V, O III], C IV, C III], to He II at -454 +/- 37 km s-1, where the negative sign indicates motion toward us. The errors on these mean velocities, 8-70 km s-1, are generally smaller than their differences, showing that the sequence order is well determined. It is roughly the order of increasing ionization, indicating that mean ionization and obscuration both vary continuously with velocity. Presumably velocities, ionization, and obscuration all correlate with distance from the continuum source, the agreement with current results and thinking on emission lines. We cannot determined whether the gas is falling in or flowing out, but our results are compatible with relevant models, which tend to favor infall. The Si IV + O IV] blend is an exception which appears out of order when use the predicted blend wavelength from the recent model of Rees, Netzer, & Ferland with Si IV about 4 times the strength of O IV]. We deduce that the mean flux ratio is actually 1.0 +/- 0.2, with a small QSO-to-QSO variance of under 12%, only 25% of the dispersion in the ratio of fluxes from other pairs of lines. The mean line velocities correspond to shifted rest-frame wavelengths, which statistically give the same redshifts as narrow and Balmer lines. These new shifted rest wavelengths can be used instead of laboratory values, giving improved, unbiased QSO redshifts. Published QSO redshifts derived from high-ionization emission lines, including most QSOs at z greater-than-or-equal-to 1.5, are systematically too low by about 260 km s-1. We find that all correlations between emission-line velocities and QSO properties, including those reported by Corbin, are explained by just three basic correlations. Both N V and Mg II tend to be at less negative velocities in radio-quiet versus radio-loud QSOs, and C IV lines with small equivalent widths are at more negative velocities, probably because of the line asymmetry. We find that the "Baldwin effect" is strong for ions such as N V, He II and C III], and for Ly-alpha, in addition to C IV. Except for Ly-alpha, the correlation is strongest for radio-loud QSOs. At a given luminosity, radio-quiet QSOs show stronger lines of C IV and Si IV + O IV] than radio-loud objects-a possible selection effect. We do not find any correlations between either FWHM, W(r), or line-shift velocity and radio core/total flux ratio, implying that the orientation of the emission-line region is not correlated with the radio axis, or that the region is not flat. We confirm Sargent, Steidel, & Boksenberg's finding that UV spectral index increases with UV luminosity, but we do not confirm their claim that radio-loud and radio-quiet QSOs have different indices.
