  We present an analysis of the intrinsic UV absorption in the Seyfert 1 galaxy
Mrk 279 based on simultaneous long observations with the Hubble Space Telescope
(41 ks) and the Far Ultraviolet Spectroscopic Explorer (91 ks). To extract the
line-of-sight covering factors and ionic column densities, we separately fit
two groups of absorption lines: the Lyman series and the CNO lithium-like
doublets. For the CNO doublets we assume that all three ions share the same
covering factors. The fitting method applied here overcomes some limitations of
the traditional method using individual doublet pairs; it allows for the
treatment of more complex, physically realistic scenarios for the
absorption-emission geometry and eliminates systematic errors that we show are
introduced by spectral noise. We derive velocity-dependent solutions based on
two models of geometrical covering -- a single covering factor for all
background emission sources, and separate covering factors for the continuum
and emission lines. Although both models give good statistical fits to the
observed absorption, we favor the model with two covering factors because: (a)
the best-fit covering factors for both emission sources are similar for the
independent Lyman series and CNO doublet fits; (b) the fits are consistent with
full coverage of the continuum source and partial coverage of the emission
lines by the absorbers, as expected from the relative sizes of the nuclear
emission components; and (c) it provides a natural explanation for variability
in the Ly$\alpha$ absorption detected in an earlier epoch. We also explore
physical and geometrical constraints on the outflow from these results.
