  We have analyzed the properties of low column density Lyman alpha forest
clouds (12.8 < log N_HI < 16.0) toward 5 QSOs at different redshifts, using
high signal-to-noise data from the HIRES spectrograph on the Keck I 10-m
telescope. The results are used to study the evolution of these clouds in the
interval 2.1 < z < 3.5. We find: 1) The differential density distribution of
forest clouds, f(N_HI), fits an empirical power law with a typical slope of
-1.35 to -1.55 for clouds with N_HI < 10^14.3 cm^{-2} and changes extremely
slowly with redshift over this N_HI range. 2) The deviation of f(N_HI) from
this power-law distribution at higher column densities depends on redshift: for
higher redshifts, the departure from a power-law distribution occurs at higher
N_HI, which means that higher column density clouds rapidly disappear with
decreasing redshift. This may be consistent with an invariant shape for the
different column density distributions, but with a shift to a lower column
density normalization for systems at different redshifts driven by the overall
expansion of the universe. 3) The line widths of the forest clouds increase as
redshift decreases. 4) The correlation strength of the forest clouds seems to
increase as redshift decreases. We discuss these results in terms of the
evolution of the IGM comparing the results to models and analytic descriptions
of the evolution of structure in the gas.
