We show that the orbital variation in the UV P Cygni lines of the X-ray bin
ary LMC X-4 results when X-rays photoionize nearly the entire region outsid
e of the X-ray shadow of the normal star. We ht models to Goddard High Reso
lution Spectrograph (GHRS) observations of N v and C Iv P Cygni line profil
es. Analytic methods assuming a spherically symmetric wind show that the wi
nd velocity law is well fitted by v proportional to (1 - 1/r)P, where beta
is likely approximate to 1.4-1.6 and definitely less than 2.5. Escape proba
bility models can fit the observed P Cygni profiles and provide measurement
s of the stellar wind parameters. The fits determine L-X/M = 2.6 +/- 0.1 x
10(43) ergs s(-1) M-circle dot(-1), yr, where L-X is the X-ray luminosity a
nd M; is the mass-loss rate of the star. Allowing an inhomogeneous wind imp
roves the fits. IUE spectra show greater P Cygni absorption during the seco
nd half of the orbit than during the first. We discuss possible causes of t
his effect.