  Techniques for the statistical analysis of the \Lya\ forest in high redshift
quasars are developed, and applied to the low resolution (25 \AA) spectra of 29
of the 33 quasars in the Schneider-Schmidt-Gunn (SSG) sample.We find that the
mean absorption increases with $z$ approximately as a power law
$(1+z)^{\gamma+1}$ with $\gamma = 2.46\pm 0.37$. The mean ratio of \Lya\ to
Lyman $\beta$ absorption in the clouds is $0.476\pm 0.054$. We also detect, and
obtain ratios, for Lyman $\beta$, $\gamma$, and possibly $\epsilon$. We are
also able to quantify the fluctuations of the absorption around its mean, and
find that these are comparable to, or perhaps slightly larger than, that
expected from an uncorrelated distribution of clouds. The techniques in this
paper, which include the use of bootstrap resampling of the quasar sample to
obtain estimated errors and error covariances, and a mathematical treatment of
absorption from a (possibly non-uniform) stochastic distribution of lines,
should be applicable to future, more extensive, data sets.

Astrophysics