High-resolution ultraviolet observations of the black hole X-ray binary Cygnus X-1 were obtained using the Space Telescope Imaging Spectrograph on the Hubble Space Telescope . Observations were taken at two epochs roughly one year apart ; orbital phase ranges around \phi _ { orb } = 0 and 0.5 were covered at each epoch . We detect P Cygni line features from high ( N V , C IV , Si IV ) and absorption lines from low ( Si II , C II ) ionization state material . We analyze the characteristics of a selection of P Cygni profiles and note , in particular , a strong dependence on orbital phase for the high ionization material : the profiles 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 Sobolev with Exact Integration method applied to a spherically symmetric stellar wind subject to X-ray photoionization from the black hole . Of the wind-formed lines , 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 ( normalized to the stellar radius ) according to v = v _ { \infty } ( 1 - r _ { \star } / r ) ^ { \beta } , with \beta \approx 0.75 and v _ { \infty } \approx 1420 km s ^ { -1 } . The microturbulent velocity was \approx 160 km s ^ { -1 } . Our fit implies a ratio of X-ray luminosity ( in units of 10 ^ { 38 } erg s ^ { -1 } ) to wind mass-loss rate ( in units of 10 ^ { -6 } M _ { \odot } ~ { } yr ^ { -1 } ) of L _ { X, 38 } / \dot { M } _ { -6 } \approx 0.33 , measured at \dot { M } _ { -6 } = 4.8 . The lines from the lower ionization species and the He II \lambda 1640 absorption are consistent with formation in the photosphere of the normal companion . 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 .