Top: virial parameters derived for clumps identified in the Ophiuchus and Perseus clouds using thresholding at . In calculating the virial parameter, linewidths derived from ¹³CO data from the COMPLETE survey (Ridge et al. 2006a) were used. The dashed line shows the slope corresponding to the relation α ∝ M^−2/3, predicted for clumps confined by external pressure (Bertoldi & McKee 1992). A linear fit to the data points yields the slope −0.64 ± 0.13. The open circles show the modified virial parameters of the same clumps, , that take into account the external confining pressure (see Sect. 3.2 in text). The dotted line indicates the α = 1 (and ) level. Bottom: size-linewidth relation for the same clumps, shown for both ¹²CO (red) and ¹³CO (blue). The dotted line shows the σ ∝ R^0.5 relation (Solomon et al. 1987), not a fit to the data points.