Derived temperature vs. the measured ratio p - H₂CO S_ν(3_2,1−2_2,0) /S_ν(3_0,3−2_0,2) for the dendrogram clumps. The big symbols represent leaves (compact clumps) and the small symbols represent larger and therefore lower-density ancestor structures. The temperature includes constraints from the assumed constant H₂CO abundance and the varying column density. The points are color coded by signal-to-noise in the ratio R₁, with gray S/N< 5, blue 5 <S/N< 25, green 25 <S/N< 50, and red S/N> 50. The black lines show the modeled temperature as a function of R₁ for three different assumed densities with a constant assumed abundance X_H2CO = 1.2 × 10^-9. While the measured values appear consistent with the n = 10⁴ cm^-3 curve, the systematic errors permit any density in the range 10⁴ cm^-3<n< 10⁵ cm^-3; this plot most importantly shows that n ~ 10³ cm^-3 is not plausible and that the temperature does not differ very much for a given value of R₁ over the plausible range of densities.