  We present a new analysis of the motion of broad line region (BLR) clouds in
active galactic nuclei (AGNs) taking into account the combined influence of
gravity and radiation pressure force. We calculate cloud orbits under a large
range of conditions and include the effect of a changing column density as a
function of location. The dependence of radiation pressure force on the level
of ionization and the column density are accurately computed. The main results
are: a. The mean cloud location r(BLR) and the line widths (FWHMs) are combined
in such a way that the simple virial mass estimate, r{BLR} FWHM^2/G, gives a
reasonable approximation to the black hole mass M even when radiation pressure
force is important. The reason is that L/M rather than L is the main parameter
affecting the planar cloud motion. b. Reproducing the observed mean radius,
FWHM and intensity of H-beta and CIV 1549 requires at least two different
populations of clouds. c. The cloud location is a function of both L^{1/2} and
L/M. Given this we suggest a new approximation for r(BLR) which, when inserted
into the BH mass equation, results in a new approximation for M. The new
expression involves L^{1/2}, FWHM and two constants that are obtained from a
comparison with available M-sigma mass estimates. It deviates only slightly
from the old mass estimate at all luminosities. d. The quality of present black
hole mass estimators depends, critically, on the way the present M-sigma AGN
sample (16 objects) represents the AGN population, in particular the
distribution of Eddington ratios.
