Multi-transition spectra (histograms) of HCN line emission (HHT data from Bieging et al. 2000), overlaid by spectra from the best-fit model (solid lines; assuming a Guassian abundance distribution), towards top panels – the carbon star R For using a fractional HCN abundance f₀  =  4.0 × 10^-5 and an envelope size r_e  =  9.3 × 10¹⁵ cm. Middle panels – S-type AGB star W Aql using a fractional HCN abundance f₀  =  1.2 × 10^-6 and an envelope size r_e  =  1.3 × 10¹⁶ cm. Bottom panels – M-type AGB star TX Cam using a fractional HCN abundance f₀  =  3.5 × 10^-7 and an envelope size r_e  =  2.0 × 10¹⁶ cm are also shown (solid lines). The hyperfine splitting of the J = 1  →  0 transition significantly broadens the line. This effect is explicitly taken into account in the modelling. The calibration uncertainty in the observed spectra is  ≈±20%.