  The real-space optical depth distribution along the line of sight to the QSO
Q1422+231 is recovered from two HIRES spectra. The first two moments of the
truncated optical depth distribution are used to constrain the density
fluctuation amplitude of the intergalactic medium (IGM).
  The $rms$ of the IGM density at $z\approx 3.25$ estimated from the first
spectrum is $\sigma = \sqrt{\exp{[(1.8 \pm 0.27)^2/\alpha^2]}-1}$, with $1.56
<\alpha <2$ for plausible reionization histories. This corresponds to $0.9 \la
\sigma \la 2.1$ with $\sigma(\alpha =1.7)= 1.44\pm 0.3 $. The values obtained
from the second spectrum are higher by $\approx 20 %$. If the IGM density
traces the dark matter (DM) as suggested by numerical simulations we have
measured the fluctuation amplitude of the DM density at an effective Jeans
scale of about a hundred to two hundred (comoving) kpc. For CDM-like power
spectra the amplitude of dark matter fluctuations on these small scales depends
on the cosmological density parameter $\Omega$. For power spectra normalized to
reproduce the space density of present-day clusters and with a slope parameter
of $\Gamma=0.21$ consistent with the observed galaxy power spectrum, the
inferred $\Omega$ can be expressed as: $\Omega= 0.61
(\alpha/1.7)^{1.3}(x_{_{\rm J}} /0.62)^{-0.6}$ for a flat universe, and
$\Omega= 0.91(\alpha/1.7)^{1.3} (x_{_{\rm J}}/0.62)^{-0.7}$ for a $\lambda=0$
universe. $x_{_{\rm J}}$ is the effective Jeans scale in (comoving) $\mpc$.
Based on a suit of detailed mock spectra the 1-$\sigma$ error is $\approx 25
%$. The estimates increase with increasing $\Gamma$. For the second spectrum we
obtain 15% lower values.
