  Gas in galactic disks is collected by gravitational instabilities into giant
atomic-molecular complexes, but only the inner, molecular parts of these
structures are able to collapse to form stars. Determining what controls the
ratio of atomic to molecular hydrogen in complexes is therefore a significant
problem in star formation and galactic evolution. In this paper we use the
model of H_2 formation, dissociation, and shielding developed in the previous
paper in this series to make theoretical predictions for atomic to molecular
ratios as a function of galactic properties. We find that the molecular
fraction in a galaxy is determined primarily by its column density and
secondarily by its metallicity, and is to good approximation independent of the
strength of the interstellar radiation field. We show that the column of atomic
hydrogen required to shield a molecular region against dissociation is ~10 Msun
pc^-2 at solar metallicity. We compare our model to data from recent surveys of
the Milky Way and of nearby galaxies, and show that the both the primary
dependence of molecular fraction on column density and the secondary dependence
on metallicity that we predict are in good agreement with observed galaxy
properties.
