  Emission-line variability data for Seyfert 1 galaxies provide strong evidence
for the existence of supermassive black holes in the nuclei of these galaxies,
and that the line-emitting gas is moving in the gravitational potential of that
black hole. The time-delayed response of the emission lines to continuum
variations is used to infer the size of the line-emitting region, which is then
combined with measurements of the Doppler widths of the variable line
components to estimate a virial mass. In the case of the best-studied galaxy,
NGC 5548, various emission lines spanning an order of magnitude in distance
from the central source show the expected velocity proportional to inverse
square root of the distance correlation between distance and line width, and
are thus consistent with a single value for the mass. Two other Seyfert
galaxies, NGC 7469 and 3C 390.3, show a similar relationship. We compute the
ratio of luminosity to mass for these three objects and the narrow-line Seyfert
1 galaxy NGC 4051 and find that that the gravitational force on the
line-emitting gas is much stronger than radiation pressure. These results
strongly support the paradigm of gravitationally bound broad emission-line
region clouds.
