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We observed a 10x20 pc region of the molecular cloud M17 in the 12CO and 13COJ=3-2 and J=2-1 transitions to determine their global behavior and to assessthe reliability of using ratios of CO line intensities integrated over anentire cloud to determine the physical conditions within the cloud. Both the12CO/13CO J=2-1 and J=3-2 line ratios correlate with the 13CO integratedintensity, with smaller line ratios observed at locations with large integratedintensities. This correlation is likely due to variations in the column densityfrom one position to another within M17. The 12CO and 13CO (J=3-2/J=2-1) lineratios show no significant variation from place to place within M17, even onthe peak of the photon-dominated region. A Large Velocity Gradient analysis ofglobally averaged line ratios gives results in reasonable agreement with theresults obtained for individual lines-of-sight through the cloud, whichsuggests that the typical physical conditions in a molecular cloud can bedetermined using CO line ratios integrated over the entire cloud. There appearsto be a clear trend of increasing 12CO/13CO J=2-1 and J=3-2 line ratios as onemoves from Galactic molecular cloud cores to entire Galactic molecular cloudsto normal galaxies. The most likely explanation of the high line ratios fornormal galaxies is a significant contribution to the CO emission by low columndensity material, such as diffuse molecular clouds or the outer envelopes ofgiant molecular clouds.Comment: 26 pages, 6 figures, 2 tables. Accepted for publication in Ap

The Large‐ScaleJ = 3 → 2 andJ = 2 → 1 CO Emission from M17 and Its Implications for Extragalactic CO Observations