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

The Mass-Size Relation and the Constancy of GMC Surface Densities in the Milky Way