  (shortened) Spectroscopic observations of the fast X-ray transient and
superluminal jet source SAX J1819.3-2525 (V4641 Sgr) reveal a best fitting
period of P_spect=2.81678 +/- 0.00056 days and a semiamplitude of K_2=211.0 +/-
3.1 km/sec. The optical mass function is f(M)=2.74 +/- 0.12 solar masses. We
find a photometric period of P_photo=2.81730 +/- 0.00001 days using a light
curve measured from photographic plates. The folded light curve resembles an
ellipsoidal light curve with two maxima of roughly equal height and two minima
of unequal depth per orbital cycle. The secondary star is a late B-type star
which has evolved off the main sequence. Using a moderate resolution spectrum
(R=7000) we measure T_eff=10500 +/- 200K, log(g)=3.5 +/- 0.1, and
V_rot*sin(i)=123 +/- 4 km/sec (1 sigma errors). Assuming synchronous rotation,
our measured value of the projected rotational velocity implies a mass ratio of
Q=M_1/M_2=1.50 +/- 0.08 (1sigma). The lack of X-ray eclipses implies an upper
limit to the inclination of i<70.7 deg. On the other hand, the large amplitude
of the folded light curve (about 0.5 mag) implies a large inclination (i>60
deg). Using the above mass function, mass ratio, and inclination range, the
mass of the compact object is in the range 8.73 < M_1 < 11.70 solar masses and
the mass of the secondary star is in the range 5.49 < M_2 < 8.14 solar masses
(90% confidence). The mass of the compact object is well above the maximum mass
of a stable neutron star and we conclude that V4641 Sgr contains a black hole.
