A simple vibrational HΓΆnl-London-type formula for hot-band intensities is tested by measuring the intensities of a number of vibrational transitions, including many hot bands, for HCN. This vibrational intensity formula is based on one- and two-dimensional harmonic oscillator functions and a nonlinear electric dipole function that is expanded in a Taylor series with respect to the normal coordinates. It is shown that, when this formula is included, the observed transition dipoles for the bending hot bands differ by only a few percent from the transition dipoles for the same quantum number changes from the ground state. Infrared absorption intensity measurements are given for the transition dipoles for the transitions (01^{1} 0-00^{\circ} 0,02^{\circ} 0-00^{\circ} 0,03^{\prime} 0-00^{\circ} 0.04^{\circ} 0-) (00^{\circ} 0,10^{\circ} 0-01^{1} 0,12^{\circ} 0-00^{\circ} 0), and (20^{\circ} 0-00^{\circ} 0) and the accompanying hot bands involving the lower states (v_{2}=1,2), and 3 . This simple model is limited to well-behaved systems, but would be useful for estimating the intensities of some high-temperature spectra. For HCN the HermanWallis constants that are quadratic in (J) (or (\mathrm{m}) ) are shown to be determined principally by the effect of l-type resonance. (6) 1995 Academic Press. Inc.