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The masses and emission-line region sizes of Active Galactic Nuclei (AGNs)can be measured by ``reverberation-mapping'' (measuring the lag of theemission-line luminosity after changes in the continuum). We use tis techniqueto calibrate similar size and mass estimates made by photoionization models ofthe AGN line-emitting regions. We compile a sample of 19 AGNs with reliablereverberation and spectroscopy data, twice the number available previously. Thedata provide strong evidence that the BLR size and the emission-line widthmeasure directly the central mass. Two methods are used to estimate thedistance of the broad emission-line region (BLR) from the ionizing source: thephotoionization method (available for many AGNs but has large intrinsicuncertainties), and the reverberation method (gives very reliable distances,but available for only a few objects). The distance estimate is combined withthe velocity dispersion, derived from the broad Hb line profile, to estimatethe virial mass. Comparing the central masses calculated with the reverberationmethod to those calculated using a photoionization model, we find a highlysignificant, nearly linear correlation. This provides a calibration of thephotoionization method on the objects with presently available reverberationdata, which should enable mass estimates for all AGNs with measured Hb linewidth. Comparing the BLR sizes given by the two methods also enables us toestimate the ionizing EUV luminosity which is directly unobservable. We find itto be typically ten times the visible (monochromatic luminosity at 5100A). Theinferred Eddington ratio of the individual objects in our sample are 0.001-0.03(visible luminosity) and 0.01-0.3 (ionizing luminosity).Comment: 27 pages Latex, 8 figures. Accepted for publication in the  Astrophysical Journa

Central Masses and Broad‐Line Region Sizes of Active Galactic Nuclei. I. Comparing the Photoionization and Reverberation Techniques