the results of these source extractions: the major and minor axes, aspect ratio, and position angle of each submillimeter source, calculated at both the the half-maximum and 2$\sigma$ contours.

2$\sigma$ Sizes {#2sig}
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Figure \[hist\] presents the distributions of the angular diameter at the 2$\sigma$ contour (defined to be $2\sqrt{ab}$, where $a$ and $b$ are the semi-major and semi-minor axes at the 2$\sigma$ contour, respectively), linear diameter at the 2$\sigma$ contour (defined simply as the angular diameter at the 2$\sigma$ contour multiplied by the distance to the core), distance between Barycenter and peak positions ($\delta_{pk}$), and aspect ratio ($\epsilon = a/b$) of each source. As seen in Figure \[hist\], the distribution of 2$\sigma$ linear diameters has a mean and median of 8.1 $\times 10^3$ and 7.2 $\times 10^3$ AU, respectively, while the distribution of 2$\sigma$ angular diameters has both a mean and median of 32 and a maximum of 57. The 2$\sigma$ diameters derived from SHARC-II are generally $1.5-3$ times smaller than those derived from 850 [$\mu$m]{} SCUBA data (Young et al. 2006). This discrepancy does not seem to correlate with the SHARC-II 2$\sigma$ angular diameter, it is observed in essentially all of the cores contained in both surveys regardless 