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To study the nature of low z Lya absorbers in the spectra of QSOs, we haveobtained high signal-to-noise UV spectra of H 1821+643 (z = 0.297) and PG1116+215 (z = 0.177) with the GHRS on the HST. The spectra have minimum S/N of70-100 and 3 sigma limiting equivalent widths of 50-75 mA. We detect 26 Lyalines with Wr > 50 mA toward H1821+643 and 13 toward PG1116+215, which impliesa density of 102+/-16 lines per unit redshift. The two-point correlationfunction shows marginal evidence of clustering on ~500 km/s scales, but only ifthe weakest lines are excluded. We have also used the WIYN Observatory tomeasure galaxy redshifts in the ~1 degree fields centered on each QSO. We find17 galaxy-absorber pairs within projected distances of 1 Mpc with velocityseparations of 350 km/s or less. Monte Carlo simulations show that if the Lyalines are randomly distributed, the probability of observing this many closepairs is 3.6e-5. We find that all galaxies with projected distances of 600 kpcor less have associated Lya absorbers within 1000 km/s, and the majority ofthese galaxies have absorbers within 350 km/s. We also find that the Lyaequivalent width is anticorrelated with the projected distance of the nearestgalaxy out to at least 600 kpc, but this should be interpreted cautiouslybecause there are potential selection biases. Statistical tests using theentire sample also indicate that the absorbers are not randomly distributed. Wediscuss the nature of the Lya absorbers in light of the new data.Comment: Accepted for publication in ApJ. 17 pages plus 11 tables and 17  figure

The Relationship between Galaxies and Low‐Redshift Weak Lyα Absorbers in the Directions of H1821+643 and PG 1116+215