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We present observations made with the 10m Heinrich Hertz Sub-MillimeterTelescope of HCN (3-2) emission from a sample of 30 nearby galaxies ranging ininfrared luminosity from 10^10 - 10^12.5 L_sun and HCN (3-2) luminosity from10^6 - 10^9 K km s^-1 pc^2. We examine the correlation between the infraredluminosity and HCN (3-2) luminosity and find that the best fit linearregression has a slope (in log-log space) of 0.74+/-0.12. Including recentlypublished data from Gracia-Carpio et al. tightens the constraints on thebest-fit slope to 0.79+/-0.09. This slope below unity suggests that the HCN(3-2) molecular line luminosity is not linearly tracing the amount of densegas. Our results are consistent with predictions from recent theoretical modelsthat find slopes below unity when the line luminosity depends upon the averagegas density with a power-law index greater than a Kennicutt-Schmidt index of1.5.

The Star Formation Rate - Dense Gas Relation in Galaxies as Measured by HCN (3-2) Emission