  The disks that surround young stars are mostly composed of molecular gas,
which is harder to detect and interpret than the accompanying dust. Disk mass
measurements have therefore relied on large and uncertain extrapolations from
the dust to the gas. We have developed a grid of models to study the
dependencies of isotopologue CO line strengths on disk structure and
temperature parameters and find that a combination of 13CO and C18O
observations provides a robust measure of the gas mass. We apply this technique
to Submillimeter Array observations of nine circumstellar disks and published
measurements of six well studied disks. We find evidence for selective
photodissociation of C18O and determine masses to within a factor of about
three. The inferred masses for the nine disks in our survey range from 0.7-6
M_Jup, and all are well below the extrapolation from the interstellar medium
gas-to-dust ratio of 100. This is consistent with the low masses of planets
found around such stars, and may be due to accretion or photoevaporation of a
dust-poor upper atmosphere. However, the masses may be underestimated if there
are more efficient CO depletion pathways than those known in molecular clouds
and cold cores.
