  The Milky Way's million degree gaseous halo contains a considerable amount of
mass that, depending on its structural properties, can be a significant mass
component. In order to analyze the structure of the Galactic halo, we use
XMM-Newton Reflection Grating Spectrometer archival data and measure OVII K
alpha absorption-line strengths toward 26 active galactic nuclei, LMC X-3, and
two Galactic sources (4U 1820-30 and X1735-444). We assume a beta-model as the
underlying gas density profile and find best-fit parameters of n_o =
0.46^{+0.74}_{-0.35} cm^-3, r_c = 0.35^{+0.29}_{-0.27} kpc, and beta =
0.71^{+0.13}_{-0.14}. These parameters result in halo masses ranging between
M(18 kpc) = 7.5^{+22.0}_{-4.6} x 10^8 M_sun and M(200 kpc) = 3.8^{+6.0}_{-0.5}
x 10^{10} M_sun assuming a gas metallicity of Z = 0.3 Z_sun, which are
consistent with current theoretical and observational work. The maximum baryon
fraction from our halo model of f_b = 0.07^{+0.03}_{-0.01} is significantly
smaller than the universal value of f_b = 0.171, implying the mass contained in
the Galactic halo accounts for 10% - 50% of the missing baryons in the Milky
Way. We also discuss our model in the context of several Milky Way observables,
including ram pressure stripping in dwarf spheroidal galaxies, the observed
X-ray emission measure in the 0.5 - 2 keV band, the Milky Way's star formation
rate, spatial and thermal properties of cooler gas (~10^5 K) and the observed
Fermi bubbles toward the Galactic center. Although the metallicity of the halo
gas is a large uncertainty in our analysis, we place a lower limit on the halo
gas between the Sun and the Large Magellanic Cloud (LMC). We find that Z >~ 0.2
Z_sun based on the pulsar dispersion measure toward the LMC.
