Comparison between the column density ratios N₂∕N₁ and N₃ ∕N₂ of MF (triangles), DE (squares), F (star), and EC (circles) in the sources 18089–1732 (black data points), G24.78+0.08 (green), and G31.41+0.31 (red). The dashed coloured lines are the power regression fits to the data of each source, and identify the related β (see text). The horizontal blue lines correspond to different opacities at 2 mm. The dashed grey line represents the case N₂∕N₁ = N₃∕N₂ (i.e. β = 1). For further details on this plot see Appendix E.2.