  Knowledge of the evolution of the low column density end of the Ly alpha
forest (12.8 < log N_HI < 16.0 cm^-2) can provide substantial insight for
models of structure formation and studies of the evolution of the ionizing
background. Here we describe the evolution of the b values and column densities
of forest clouds over the redshift range 2 < z < 4. While the distribution
function for clouds with column densities N_HI < 3 x 10^14 cm^-2 can be well
described by a single invariant power law fit with slope ~-1.5 over this range,
at higher column densities a break in this distribution function is seen, with
a deficiency of high column density clouds relative to the single power-law
fit, and with the break point moving to lower column densities for clouds at
lower redshifts. The median and cut-off (minimum) b values are seen to decrease
at higher redshifts.
