Relation between the FWHM and the central column density (Table 3, Cols. 4 and 6) for the four filaments in IC 5146 if the filaments are placed at the same distance D = 500   pc (black circles) closely consistent with the assumed effective emission coefficient and an assumed dust-to-gas ratio δ = 0.00588. For filaments b and d the values correspond to the fit with constrained distance. The curves of the relation shown are derived using the approximation (Eq. (32)) provided in Paper I. The grey shaded area shows the variation of the relation for a range of external pressures implied by the observed sizes and column densities of filaments in Polaris, IC 5146, and Aquila (Paper I). The external pressure is varied from 1.5 × 10⁴ to 5 × 10⁴   K   cm^-3 where for given central column density the FWHM is larger for lower pressure. The given mass ratios on the upper axis correspond to an external pressure 2 × 10⁴   K   cm^-3 shown as the solid black curve. Also shown are the observed properties if the effective emission coefficient is increased by a factor two (grey circles). The dashed curve shows the model relation for p_ext/k = 5 × 10³   K   cm^-3.