  Much of the interstellar medium in disk galaxies is in the form of neutral
atomic hydrogen, H I. This gas can be in thermal equilibrium at relatively low
temperatures, T < 300 K (the cold neutral medium, or CNM) or at temperatures
somewhat less than 10^4 K (the warm neutral medium, or WNM). These two phases
can coexist over a narrow range of pressures, P_min < P < P_max. We determine
P_min and P_max in the plane of the Galaxy as a function of Galactocentric
radius R using recent determinations of the gas heating rate and the gas phase
abundances of interstellar gas. We provide an analytic approximation for P_min
as a function of metallicity, far-ultraviolet radiation field, and the
ionization rate of atomic hydrogen. Over most of the disk of the Galaxy, the H
I must be in two phases: the weight of the H I in the gravitational potential
of the Galaxy is large enough to generate thermal pressures exceeding P_min, so
that turbulent pressure fluctuations can produce cold gas that is thermally
stable; and the mean density of the H I is too low for the gas to be all CNM.
Our models predict the presence of CNM gas to R = 16-18 kpc, somewhat farther
than previous estimates. We also examine the potential impact of turbulent
heating on our results and provide expressions for the heating rate as a
function of Galactic radius.
