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We present an analysis of the intrinsic UVabsorption 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 ofmore 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 (1) the best-fit covering factors for both emission sources are similar for the independent Lyman series and CNO doublet fits; (2) 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 (3) it provides a natural explanation for variability in the Lya absorption detected in an earlier epoch. We also explore physical and geometrical constraints on the outflow from these results.