  In a previous paper, we calculated numerical hydrodynamic models of the
interstellar medium in the Galaxy, which suggested that hot gas (T $\ge$ 3
$\times$ 10$^5$ K) has a filling factor near 50\% in the midplane (Rosen \&
Bregman 1995, ApJ 440, 634). Here we extend the work to examine the X-ray
emission characteristics of the best model and calculate a variety of
observable measures for comparison with the observed soft X-ray background. We
calculate the X-ray intensities, spectra, and hardness ratios in two soft X-ray
bands as Galactic latitude and cool gas column are varied, and make comparisons
with observational data. The observed distribution of N$_{H I}$ is similar to
that seen from one of the simulated bubbles, with the important exception that
the minimum hydrogen column in the model is too low. Also, there are clear
examples of anticorrelations between H I and X-ray emission as well as
correlations between H I and X-rays, which is caused by an increased emission
measure as a shock enters a cool gas region. Statistically, anticorrelations
are slightly more common than correlations. X-ray spectra are calculated from
the models and these reveal that for observations to have strong diagnostic
power in probing the hot ISM, a spectral resolution of E/$\Delta$E $>$ 30 is
required. This analysis demonstrates several shortcomings of our model, which
may be solved by future simulations that include magnetic fields.
