Mean PDF of the column density for an ensemble of isothermal self-gravitating cylinders with a variety of gravitational states or overpressures q^-1, but fixed inclination angle i. The probability distribution of the overpressures is given by Eq. (53) with fixed q₀, k₁ = 2, and γ = 2 where q₀ is either 1/14.04 (left-hand figure) or q₀ ≫ 1 (right-hand figure). The power index k₂ is assumed to be 1.5, 2, and 3. The cylinders are pressurized by a medium with p_ext/k = 2 × 10⁴ K cm^-3. The black dashed lines are asymptotes at low and high mass surface densities (Appendix E.2). For comparison, the PDF of a single cylinder with overpressure q^-1 = 14.04 is shown (gray line). The gray dotted line is the asymptotic PDF as defined in Eq. (43), and the gray dashed lines are the corresponding asymptotes at low (Eq. (47)) and high (Eq. (51)) mass surface densities.