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A high degree of relativistic beaming is inferred for the jets of blazars on the basis of several lines of evidence, but the intrinsic speed and angle of the jet to the line of sight for individual sources are difficult to measure. We have calculated inverse Compton Doppler factors for 3C 279 using the collection of VLBI data (including high-resolution space VLBI data at low frequencies) recently published by us (as Wehrle et al. and Piner et al.) and the collection of multiwavelength spectra recently published by Hartman et al. From the Doppler factor and superluminal apparent speed, we then calculate the Lorentz factor and angle to the line of sight of the parsec-scale relativistic jet. We follow the method previously used by Unwin et al. for 3C 345 to model the jet components as homogeneous spheres and the VLBI core as an unresolved inhomogeneous conical jet, using Konigl's formalism. The conical jet model can be made to match both the observed X-ray emission and the VLBI properties of the core with a suitable choice of Doppler factor, implying that the core makes a significant contribution to the X-ray emission, in contrast to the situation for 3C 345, where the jet components dominated the X-ray emission. The parameters of the Konigl models indicate that the jet is particle dominated at the radii that produce significant emission (from ~5 to 20 pc from the apex of the jet for most models) and is not in equipartition. At the inner radius of the Konigl jet the magnetic field is of order 0.1 G and the relativistic-particle number density is of order 10 cm-3. The kinetic energy flux in the jet is of order 1046(1 + k) ergs s-1, where k is the ratio of proton to electron energy, which implies a mass accretion rate of order 0.1(1 + k)/e M yr-1, where e is the efficiency of conversion of mass to kinetic energy. When all components are included in the calculation, then on average the core produces about half of the X-rays, with the other half being split between the long-lived component C4 and the brightest inner-jet component. We calculate an average speed and angle to the line of sight for the region of the jet interior to 1 mas of v = 0.992c (g = 8) and th = 4deg and an average speed and angle to the line of sight for C4 (at r [?] 3 mas) of v = 0.997c (g = 13) and th = 2deg. These values imply average Doppler factors of d = 12 for the inner jet and d = 21 for C4.