  We present a 190-307 GHz broadband spectrum obtained with Z-Spec of NGC 1068
with new measurements of molecular rotational transitions. After combining our
measurements with those previously published and considering the specific
geometry of this Seyfert 2 galaxy, we conduct a multi-species Bayesian
likelihood analysis of the density, temperature, and relative molecular
abundances of HCN, HNC, CS, and HCO+. We find that these molecules trace warm
(T > 100 K) gas of H2 number densities 10^4.2 - 10^4.9 cm^-3. Our models also
place strong constraints on the column densities and relative abundances of
these molecules, as well as on the total mass in the circumnuclear disk. Using
the uniform calibration afforded by the broad Z-Spec bandpass, we compare our
line ratios to X-ray dominated region (XDR) and photon-dominated region models.
The majority of our line ratios are consistent with the XDR models at the
densities indicated by the likelihood analysis, lending substantial support to
the emerging interpretation that the energetics in the circumnuclear disk of
NGC 1068 are dominated by accretion onto an active galactic nucleus.
