  We present submillimeter continuum maps at 450 and 850 microns of a 12 x 8
arcminute region of the NGC 7538 high-mass star-forming region, made using the
Submillimeter Common-User Bolometer Array (SCUBA) on the James Clerk Maxwell
Telescope. We used an automated clump-finding algorithm to identify 67 clumps
in the 450 micron image and 77 in the 850 micron image. Contrary to previous
studies, we find a positive correlation between high spectral index, alpha, and
high submillimeter flux, with the difference being accounted for by different
treatments of the error beam. We interpret the higher spectral index at
submillimeter peaks as a reflection of elevated dust temperature, particularly
when there is an embedded infrared source, though it may also reflect changing
dust properties. The clump mass-radius relationship is well-fit by a power law
of the form M \propto R^(-x) with x = 1.5-2.1, consistent with theories of
turbulently-supported clumps. According to our most reliable analysis, the
high-mass end (approx. 100-2700 M_sun) of the submillimeter clump mass function
in NGC 7538 follows a Salpeter-like power law with index 2.0 +/- 0.3. This
result agrees well with similar studies of lower-mass regions rho Oph and Orion
B. We interpret the apparent invariance of the shape of the clump mass function
over a broad range of parent cloud masses as evidence for the self-similarity
of the physical processes which determine it. This result is consistent with
models which suggest that turbulent fragmentation, acting at early times, is
sufficient to set the clump mass function.
