The molecular gas in the Central Molecular Zone (CMZ) of the Galaxy has been studied using infrared absorption spectra of H$_3^+$ lines at 3.5-4.0 $mu$m and CO lines near 2.34 $mu$m. In addition to the previously reported spectra of these lines toward 8 stars located within 30 pc of Sgr A$^ast$, there are now spectra toward $sim$30 bright stars located from 140 pc west to 120 pc east of Sgr A$^ast$. The spectra show the presence of warm ($Tsim 200$ K) and diffuse ($n < 100 $cm$^{-3}$) gas with $N$(H$_3^+$) $sim 3 times 10^{15} $cm$^{-2}$ on majority of sightlines. Instead of our previous analysis in which only electrons from photoionization of carbon atoms were considered, we have developed a simple model calculation in which the cosmic ray ionization of H$_2$ and H are also taken into account. We conclude: (1) Warm and diffuse gas dominates the volume of the CMZ. The volume filling factor of dense gas must be much less than 0.1 and the CMZ is not as opaque as previously considered. The X-ray emitting ultra-hot 10$^8 $K plasma, which some thought to dominate the CMZ, does not exist over extended regions. (2) The cosmic ray ionization rate is $zeta sim 2 times 10^{-14} $s$^{-1}$, higher than in Galactic dense clouds and diffuse clouds by factors of $sim$1000 and $sim$100, respectively. If the equipartition law stands, this suggests a pervading magnetic field on the order of $sim$100 $mu$G.
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