  Observational constraints on the primordial deuterium-to-hydrogen ratio (D/H)
can test theories of the early universe and provide constraints on models of
big bang nucleosynthesis (BBN). We measure deuterium absorption in
high-redshift, metal-poor QSO absorption systems and directly infer the value
of primordial D/H. We present two measurements of D/H, and find D/H = 3.3 $\pm
0.3 \times 10^{-5}$ at $z=3.572$ towards QSO 1937-1009 and D/H = 4.0 $\pm 0.7
\times 10^{-5}$ at $z=2.504$ towards QSO 1009+2956. Both measurements use
multiple-component Voigt profile analysis of high resolution, high
signal-to-noise spectra and determinations of the Lyman continuum optical depth
in low resolution spectra to constrain the column densities of deuterium and
hydrogen. The measurements are consistent with a single primordial value of D/H
= $3.4 \pm 0.3 \times 10^{-5}$. This is a relatively low value, which supports
homogeneous models of BBN and standard models of galactic chemical evolution.
With standard BBN, we find a cosmological baryon-to-photon ratio, $\eta = 5.1
\pm 0.3 \times 10^{-10}$, and a present-day baryon density in units of the
critical density, $\Omega_b h_{100}^2 = 0.019 \pm 0.001$.
