  We present a fully sampled C^{18}O (1-0) map towards the southern giant
molecular cloud (GMC) associated with the HII region RCW 106, and use it in
combination with previous ^{13}CO (1-0) mapping to estimate the gas column
density as a function of position and velocity. We find localized regions of
significant ^{13}CO optical depth in the northern part of the cloud, with
several of the high-opacity clouds in this region likely associated with a
limb-brightened shell around the HII region G333.6-0.2. Optical depth
corrections broaden the distribution of column densities in the cloud, yielding
a log-normal distribution as predicted by simulations of turbulence.
Decomposing the ^{13}CO and C^{18}O data cubes into clumps, we find relatively
weak correlations between size and linewidth, and a more sensitive dependence
of luminosity on size than would be predicted by a constant average column
density. The clump mass spectrum has a slope near -1.7, consistent with
previous studies. The most massive clumps appear to have gravitational binding
energies well in excess of virial equilibrium; we discuss possible
explanations, which include magnetic support and neglect of time-varying
surface terms in the virial theorem. Unlike molecular clouds as a whole, the
clumps within the RCW 106 GMC, while elongated, appear to show random
orientations with respect to the Galactic plane.
