We present the results of an analysis of the rate of evolution of the Ly- \alpha absorption lines in the redshift interval 0.0 to \sim 1.5 based upon a sample of 987 Ly- \alpha absorption lines identified in the spectra of 63 QSOs obtained with the Faint Object Spectrograph ( FOS ) of the Hubble Space Telescope ( HST ) .
These spectra were obtained as part of the QSO Absorption Line Survey , an HST Key Project during the first four years of observations with the telescope .
Fits to the evolution of the number of absorbers per unit redshift ( dN / dz ) of the form dN / dz = A \times ( 1 + z ) ^ { \gamma } continue to yield values of \gamma in the range 0.1 to 0.3 , decidedly flatter than results from groundbased data pertaining to the redshift range z > 1.7 .
These results are consistent with our previous results based on a much smaller sample of lines , but the uncertainties in the fit have been greatly reduced .
The combination of the HST and groundbased data suggest a marked transition in the rate of evolution of the Ly- \alpha lines at a redshift of about 1.7 .
The 19 Ly- \alpha lines from an additional higher redshift QSO from our sample for which tentative line identifications are available ( UM 18 , z _ { em } = 1.89 ) , support the suggestion of a rapid increase at around this redshift .

We derive the cumulative distribution of the full sample of Ly- \alpha lines and show that the distribution in redshift can indeed be well represented by a power law of the form ( 1 + z ) ^ { \gamma } .
For this same sample , the distribution of equivalent widths of the Ly- \alpha absorbers above a rest equivalent width of 0.1 Å is fit quite well by an exponential .

Comparing samples of Ly- \alpha lines , one set of which has redshifts the same as , or very near to , the redshifts of ions from heavy elements , with another set in which no ions from heavy elements have been identified , we find that the Ly- \alpha systems with heavy element detections have a much steeper slope than the high rest equivalent width portion of the Lyman–only sample .
We argue that this result is not likely to be due to either line misidentification or incomplete spectral coverage .
Considering the insensitivity of the equivalent width to large changes in the column density for saturated lines , we suggest that this result is probably attributable to rapid evolution of the very highest column density systems , rather than real differences in metallicity .
We find evidence that the rate of evolution increases with increasing equivalent width .

We compare our results for the variation of line density with redshift to recent numerical simulations of Ly- \alpha absorbers , in particular , to those of [ Riediger et al .
1998 ] which extend to zero redshift .
We find fairly good agreement between these simulations and our results though the rapid evolution we find in the Ly- \alpha systems containing heavy element ions is not predicted in their models .
We speculate that these heavy element containing Ly- \alpha systems involve those clouds closely associated with galaxies , whose column densities are too high and whose sizes are too small to be included in the Riediger et al .
simulations .

Our results for Ly- \alpha lines at the high end of our equivalent width distribution are compatible with the recent analysis of the absorber–galaxy correlation by [ Chen et al .
1998 ] .
For the weaker lines however , our results suggest that whatever association exists between absorbers and galaxies is different from that for the stronger lines .
We conclude with some suggestions for further observations .