  We present results from the observations and modeling of seventeen Class I
cores with the Submillimetre Common Users Bolometer Array (SCUBA) on the James
Clerk Maxwell Telescope (JCMT). By modeling the transfer of radiation through
the envelope for nine cores, we find, for a power law distribution
n(r)=n_f(r/r_f)^-p, the average and standard deviation p=1.6 +/- 0.4 and a
median of p=1.8. However, the inclusion of a disk or other point-like component
can cause the derived p to be shallower by as much as 0.5. In addition, we test
the Shu collapse model for our sources and discuss the application of simpler
analyses that derive a density power law distribution directly from the slope
of the intensity radial profile. The total mass of the envelope in our sample
has a range from 0.04 to 5.0 M_sun, but these masses disagree with the virial
masses derived from molecular line observations. Finally, we discuss the nature
of these sources in light of various evolutionary indicators and find that
T_bol and L_obs/L_smm are often inconsistent in distinguishing Class 0 from
Class I cores.
