We analyze $Chandra$ observations of the hot atmospheres of 40 early spiral and elliptical galaxies. Using new temperature, density, cooling time, and mass profiles, we explore relationships between their hot atmospheres and cold molecular gas. Molecular gas mass correlates with atmospheric gas mass and density over four decades from central galaxies in clusters to normal giant ellipticals and early spirals. The mass and density relations follow power laws: $M_{rm mol} propto M_{rm X}^{1.4pm0.1}$ and $M_{rm mol} propto n_{rm e}^{1.8pm0.3}$, respectively, at 10 kpc. The ratio of molecular gas to atmospheric gas within a 10 kpc radius lies between $3%$ and $10%$ for early-type galaxies and between $3%$ and $50%$ for central galaxies in clusters. Early-type galaxies have detectable levels of molecular gas when their atmospheric cooling times falls below $sim rm Gyr$ at a radius of 10 kpc. A similar trend is found in central cluster galaxies. We find no relationship between the ratio of the cooling time to free fall time, $t_{rm c}/t_{rm ff}$, and the presence or absence of molecular clouds in early-type galaxies. The data are consistent with much of the molecular gas in early-type galaxies having condensed from their hot atmospheres.
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