  We present a high spatial resolution submillimeter continuum survey of 24
circumstellar disks in the Tau-Aur and Oph-Sco star formation regions using the
SMA. In the context of a simple model, we use broadband SEDs and submillimeter
visibilities to derive constraints on some basic parameters that describe the
structure of these disks. For the typical disk in the sample we infer a radial
surface density distribution \Sigma ~ r^-p with a median p ~ 0.5, although
consideration of the systematic effects of some of our assumptions suggest that
steeper distributions with p ~ 0.7-1.0 are more reasonable. The distribution of
the outer radii of these disks shows a distinct peak at R_d = 200 AU, with only
a few cases where the disk emission is completely unresolved. Based on these
disk structure measurements, the mass accretion rates, and the typical spectral
and spatial distributions of submillimeter emission, we show that the
observations are in good agreement with similarity solutions for steady
accretion disks that have a viscosity parameter alpha ~ 0.01. We provide new
estimates of the spectral dependence of the disk opacity with a median spectral
index of ~0.7, corrected for optically thick emission. This typical value is
consistent with model predictions for the collisional growth of solids to
millimeter size scales in the outer disk. Although direct constraints on planet
formation in these disks are not currently available, the extrapolated density
distributions inferred here are substantially shallower than those calculated
based on the solar system or extrasolar planets and typically used in planet
formation models. It is possible that we are substantially underestimating disk
densities due to an incomplete submillimeter opacity prescription.
