Molecular line ladders: the HCN and HCO⁺ line intensity ratios as a function of transition in normalized (equal) beams. Left to right: the HCN J = 2 − 1/J = 1 − 0, J = 3 − 2/J = 1 − 0, J = 4 − 3/J = 1 − 0, and the HCO⁺J = 3 − 2/J = 1 − 0 ratios as a function of ¹²CO J = 1 − 0 luminosity. Solid lines mark ratios of unity. Symbols are as in Fig. 3 but almost all data are from this paper. Fit parameters are listed in Table 8.