  (Shortened) Ultraviolet observations of the black hole X-ray binary Cygnus
X-1 were obtained using the STIS on HSTubble. We detect P Cygni line features
show strong, broad absorption components when the X-ray source is behind the
companion star and noticeably weaker absorption when the X-ray source is
between us and the companion star. We fit the P Cygni profiles using the SEI
method applied to a spherically symmetric stellar wind subject to X-ray
photoionization from the black hole. The Si IV doublet provides the most
reliable estimates of the parameters of the wind and X-ray illumination. The
velocity $v$ increases with radius $r$ according to
$v=v_\infty(1-r_\star/r)^\beta$, with$\beta\approx0.75$ and
$v_\infty\approx1420$ km s$^{-1}$.The microturbulent velocity was $\approx160$
km s$^{-1}$. Our fit implies a ratio of X-ray luminosity to wind mass-loss rate
of L$_{X,38}/\dot M_{-6} \approx 0.33$, measured at $\dot M_{-6}$ = 4.8. Our
models determine parameters that may be used to estimate the accretion rate
onto the black hole and independently predict the X-ray luminosity. Our
predicted L$_x$ matches that determined by contemporaneous RXTE ASM remarkably
well, but is a factor of 3 lower than the rate according to
Bondi-Hoyle-Littleton spherical wind accretion. We suggest that some of the
energy of accretion may go into powering a jet.
