The Distribution of Column Densities and B Values in the Lyman-Alpha Forest

We describe the properties of the Ly\ forest in the column density range \ \ 2\10^12 cm^-2 based on 1056 lines in the wavelength range 4300--5100\\\ measured in extremely high S/N, R=36, 000 spectra of four quasars. The column density distribution is well described by a -1. 5 power law to 2\10^12 cm^-2, below which limit confusion becomes too severe to measure a spectrum of individual clouds. The distribution of b values shows a well-defined lower envelope with a cutoff at b=20\ corresponding to a cloud temperature of 24, 000~K. There is only a very small fraction (less than 1\\%) of narrow line clouds which cannot be identified with metal-lines. From modeling the Ly\ absorption lines as complexes of clouds each with thermal broadening corresponding to bc we find the b distribution can be understood if there is a mean of 3. 25 clouds per absorption line with a spread in velocity centroids characterized by a dispersion of 10. 75\.