a) Probability density function of column density (N-PDF) in the Aquila cloud, derived from the 18.2′′-resolution column density image shown in Fig. 1. The left and right axes give the actual and normalized numbers of independent beams per logarithmic bin in the column density map, respectively. (The right axis thus provides an estimate of a proper N-PDF whose integral is 1.) A power-law fit to the high column density tail at A_V> 7 gives dN/dlog. The CO high-V_LSR area in the eastern corner of the field (see Sect. 4.3) has been excluded from this PDF. b) Normalized cumulative mass fraction as a function of column density for the Aquila cloud (excluding the CO high-V_LSR area – see Sect. 4.3), based on the Herschel column density map shown in Fig. 1. The dense material to the right of the dashed vertical line (equivalent to A_V ~ 7–8) represents only ~17% of the total cloud mass, while the majority of the mass (~83%) corresponds to lower-density gas. A power-law fit to the cumulative mass fraction for A_V> 7 gives . (Color figure is available in the online version.)