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We have observed 150 regions of massive star formation, selected originallyby the presence of a water maser, in the J = 5-4, 3-2, and 2-1 transitions ofCS, and 49 regions in the same transitions of C$^{34}$S. Over 90% of the 150regions were detected in the J = 2-1 and 3-2 transitions of CS and 75% weredetected in the J=5-4 transition. We have combined the data with the J = 7-6data from our original survey (Plume et al. 1992) to determine the density byanalyzing the excitation of the rotational levels. Using Large VelocityGradient (LVG) models, we have determined densities and column densities for 71of these regions. The gas densities are very high (the mean log of the densityis 5.9), but much less than the critical density of the J=7-6 line. Small mapsof 25 of the sources in the J = 5-4 line yield a mean diameter of 1.0 pc. Themean virial mass is 3800 solar masses. The mean ratio of bolometric luminosityto virial mass (L/M) is 190, about 50 times higher than estimates using COemission, suggesting that star formation is much more efficient in the densegas probed in this study. The gas depletion time for the dense gas is roughly1.3 x 10^7 yr. We find no statistically significant linewidth--size ordensity--size relationships in our data. Instead, both linewidth and densityare larger for a given size than would be predicted by the usual relationships.We find that the linewidth increases with density, the opposite of what wouldbe predicted by the usual arguments. We estimate that the luminosity of ourGalaxy (excluding the inner 400 pc) in the CS J = 5-4 transition is 15 to 23L_sun, considerably less than the luminosity in this line within the central100 pc of NGC 253 and M82. In addition, the ratio of far-infrared luminosity toCS luminosity is higher in M82 than in any cloud in our sample.Comment: 26 pages, 6 postscript figures, 3 postscript tables. Uses AAS Latex  macros, accepted for Astrophysical Journa

Dense Gas and Star Formation: Characteristics of Cloud Cores Associated with Water Masers