We have analyzed the properties of low column density Ly alpha forest
clouds (12.8 less than or equal to logN(HI)less than or equal to 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 clo
uds, f(N-HI), fits an empirical power law with a typical slope of -1.3
5-->-l.55 for clouds with N(HI)less than or equal to 10(14.3)cm(-2) an
d changes extremely slowly with redshift over this N-HI range. (2) The
deviation of f(N-HI) from this power-law distribution at higher colum
n densities depends on redshift: for higher redshifts, the departure f
rom a power-law distribution occurs at higher N-HI, which means that h
igher column density clouds rapidly disappear with decreasing redshift
. This may be consistent with an invariant shape for the different col
umn 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 linewidths of the forest clouds in
crease as redshift decreases. (4) The correlation strength of the fore
st clouds seems to increase as redshift decreases. We discuss these re
sults in terms of the evolution of the IGM comparing the results to mo
dels and analytic descriptions of the evolution of structure in the ga
s. (C) 1997 American Astronomical Society.