  We present an analysis of the first space-based far-IR-submm observations of
M 33, which measure the emission from the cool dust and resolve the giant
molecular cloud complexes. With roughly half-solar abundances, M33 is a first
step towards young low-metallicity galaxies where the submm may be able to
provide an alternative to CO mapping to measure their H$_2$ content. In this
Letter, we measure the dust emission cross-section $\sigma$ using SPIRE and
recent CO and \HI\ observations; a variation in $\sigma$ is present from a
near-solar neighborhood cross-section to about half-solar with the maximum
being south of the nucleus. Calculating the total H column density from the
measured dust temperature and cross-section, and then subtracting the \HI\
column, yields a morphology similar to that observed in CO. The H$_2$/\HI\ mass
ratio decreases from about unity to well below 10% and is about 15% averaged
over the optical disk. The single most important observation to reduce the
potentially large systematic errors is to complete the CO mapping of M 33.
