  We present observations made with the 10m Heinrich Hertz Sub-Millimeter
Telescope of HCN (3-2) emission from a sample of 30 nearby galaxies ranging in
infrared luminosity from 10^10 - 10^12.5 L_sun and HCN (3-2) luminosity from
10^6 - 10^9 K km s^-1 pc^2. We examine the correlation between the infrared
luminosity and HCN (3-2) luminosity and find that the best fit linear
regression has a slope (in log-log space) of 0.74+/-0.12. Including recently
published data from Gracia-Carpio et al. tightens the constraints on the
best-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 dense
gas. Our results are consistent with predictions from recent theoretical models
that find slopes below unity when the line luminosity depends upon the average
gas density with a power-law index greater than a Kennicutt-Schmidt index of
1.5.
