Direct evidence for gravitational domination of the motion of gas within one light-week of the central object in NGC 4151 and the determination of the mass of the probable black hole

A practical method is demonstrated for determining the average direction of motion of broad-line region gas in quasars. Analysis of the variability of the blue and red wings of the C IV λ1549 and Mg II λ2798 lines and the UV continuum in the low-luminosity quasar in NGC 4151 reveals that the red sides of both lines lead to blue sides in their variations. Outflow of the high-velocity gas (v > 5000 km s^-1^) emitting the C IV and Mg II lines is excluded at the 99.5% confidence level. The dominant motion of the gas is most likely to be inward, although totally random or chaotic motions are excluded only at the 93% level. It is suggested that the gravitational domination of the motion of the broad-line region clouds at small radii is a consequence of their high densities (N_e_>10^11^ cm^-3^). The demonstration that the broad-line region has its motions dominated by gravity (versus domination by a wind or radiation pressure) puts black hole accretion models onto an observational footing and permits the first simple kinematic determination of the mass of the black hole in a galactic nucleus. The mass is 5 x 10^7^ M_sun_ if the gas is indeed inflowing.