  We use two existing molecular cloud catalogs derived from the same CO survey
and two catalogs derived from local dust extinction surveys to investigate the
nature of the GMC mass-size relation in the Galaxy. We find that the four
surveys are well described by $M_{GMC} \sim R^2$ implying a constant mean
surface density, $\Sigma_{GMC}$, for the cataloged clouds. However, the scaling
coefficients and scatter differ significantly between the CO and extinction
derived relations. We find that the additional scatter seen in the CO relations
is due to a systematic variation in $\Sigma_{GMC}$ with Galactic radius that is
unobservable in the local extinction data. We decompose this radial variation
of $\Sigma_{GMC}$ into two components, a linear negative gradient with Galactic
radius and a broad peak coincident with the molecular ring and superposed on
the linear gradient. We show that the former may be due to a radial dependence
of X$_{CO}$ on metallicity while the latter likely results from a combination
of increased surface densities of individual GMCs and a systematic upward bias
in the measurements of $\Sigma_{GMC}$ due to cloud blending in the molecular
ring. We attribute the difference in scaling coefficients between the CO and
extinction data to an underestimate of X$_{CO}$. We recalibrate the CO
observations of nearby GMCs using extinction measurements to find that locally
X$_{CO}$ $=$ 3.6$\pm$0.3 $\times$ 10$^{20}$ cm$^{-2}$ (K-km/s)$^{-1}$. We
conclude that outside the molecular ring the GMC population of the Galaxy can
be described to relatively good precision by a constant $\Sigma_{GMC}$ of 35
M$_\odot$ pc$^{-2}$.
