  Power law mass-size and linewidth-size correlations, two of "Larson's laws,"
are often studied to assess the dynamical state of clumps within molecular
clouds. Using the result of a hydrodynamic simulation of a molecular cloud, we
investigate how geometric projection may affect the derived Larson
relationships. We find that large scale structures in the column density map
have similar masses and sizes to those in the 3D simulation (PPP). Smaller
scale clumps in the column density map are measured to be more massive than the
PPP clumps, due to the projection of all emitting gas along lines of sight.
Further, due to projection effects, structures in a synthetic spectral
observation (PPV) may not necessarily correlate with physical structures in the
simulation. In considering the turbulent velocities only, the linewidth-size
relationship in the PPV cube is appreciably different from that measured from
the simulation. Including thermal pressure in the simulated linewidths imposes
a minimum linewidth, which results in a better agreement in the slopes of the
linewidth-size relationships, though there are still discrepancies in the
offsets, as well as considerable scatter. Employing commonly used assumptions
in a virial analysis, we find similarities in the computed virial parameters of
the structures in the PPV and PPP cubes. However, due to the discrepancies in
the linewidth- and mass- size relationships in the PPP and PPV cubes, we
caution that applying a virial analysis to observed clouds may be misleading
due to geometric projection effects. We speculate that consideration of
physical processes beyond kinetic and gravitational pressure would be required
for accurately assessing whether complex clouds, such as those with highly
filamentary structure, are bound.
