  We investigate 35 pre-stellar cores and 36 proto-stellar cores in the Perseus
molecular cloud. We find a very tight correlation between the physical
parameters describing the N2H+ and NH3 gas. Both the velocity centroids and the
line widths of N2H+ and NH3 correlate much better than either species
correlates with CO, as expected if the nitrogen-bearing species are probing
primarily the dense core gas where the CO has been depleted. We also find a
tight correlation in the inferred abundance ratio between N2H+ and para-NH3
across all cores, with N(p-NH3)/N(N2H+)= 22 +/- 10. We find a mild correlation
between NH3 (and N2H+) column density and the (sub)millimeter dust continuum
derived H2 column density for pre-stellar cores, N(p-NH3)/N(H2) ~ 10e-8, but do
not find a fixed ratio for proto-stellar cores.
  The observations suggest that in the Perseus molecular cloud the formation
and destruction mechanisms for the two nitrogen-bearing species are similar,
regardless of the physical conditions in the dense core gas. While the
equivalence of N2H+ and NH3 as powerful tracers of dense gas is validated, the
lack of correspondence between these species and the (sub)millimeter dust
continuum observations for proto-stellar cores is disconcerting and presently
unexplained.
