  We present near-infrared spectroscopy of fluorescent molecular hydrogen (H_2)
emission from NGC 1333, NGC 2023, NGC 2068, and NGC 7023 and derive the
physical properties of the molecular material in these reflection nebulae. Our
observations of NGC 2023 and NGC 7023 and the physical parameters we derive for
these nebulae are in good agreement with previous studies. Both NGC 1333 and
NGC 2068 have no previously-published analysis of near-infrared spectra. Our
study reveals that the rotational-vibrational states of molecular hydrogen in
NGC 1333 are populated quite differently from NGC 2023 and NGC 7023. We
determine that the relatively weak UV field illuminating NGC 1333 is the
primary cause of the difference. Further, we find that the density of the
emitting material in NGC 1333 is of much lower density, with n ~ 10^2 - 10^4
cm^-3. NGC 2068 has molecular hydrogen line ratios more similar to those of NGC
7023 and NGC 2023. Our model fits to this nebula show that the bright,
H_2-emitting material may have a density as high as n ~ 10^5 cm^-3, similar to
what we find for NGC 2023 and NGC 7023. Our spectra of NGC 2023 and NGC 7023
show significant changes in both the near-infrared continuum and H_2 intensity
along the slit and offsets between the peaks of the H_2 and continuum emission.
We find that these brightness changes may correspond to real changes in the
density and temperatures of the emitting region, although uncertainties in the
total column of emitting material along a given line of sight complicates the
interpretation. The spatial difference in the peak of the H_2 and near-infrared
continuum peaks in NGC 2023 and NGC 7023 shows that the near-infrared continuum
is due to a material which can survive closer to the star than H_2 can.
