A method of approximation applicable to some experimental investigations is based on the inversion for $\mu \left(\nu \right)$ of the integral equation $A\left(x\right)=\int 0^{\infty }(1-e^{-\mu \left(\nu \right)x})d\nu$ The general nature of the interdependence of $A\left(x\right)\mathrm{}$ and $\mu \left(\nu \right)$ is described and a practicable method of characterizing certain types of $\mu \left(\nu \right)$ is developed in sufficient detail to permit of immediate application of the results. The author's previously published data for the HCl fundamental band lines has been approximated by line patterns based on the hypothesis of (a) a Doppler broadening or error curve structure, (b) a Stark broadening due to the molecular force field set up by neighboring molecules, and (c) an interrupted absorption process or dispersion curve type. The modifications attendant on recognizing the isotopic doubling of the lines are predictable from the calculation for a doublet structure of infinite component separation. The values of the line intensities and breadths and the Einstein coefficients $A_{01}$ and $B_{01}$ are given for each of the assumed structures. Kinetic theory considerations make it improbable that the Doppler effect is the primary determining influence as regards line shape. The Lorentz line with a possible Doppler broadening superposed would seem to reproduce the experimental data satisfactorily. The results are in keeping with an atomic binding for HCl and if the atomic character of the dissociation products be accepted it appears that the dielectric constant measurements lead indirectly to the order of magnitude of our values for $\int 0^{\infty }\mu \left(\nu \right)d\nu$. This lends further support to Van Vleck's criticism of that explanation of the discrepancy between the extrapolated optical and direct measurements of the dielectric constant of HCl which depends on an appeal to the infra-red vibration bands. Some aspects of the recent work on the coupling effect in gases are examined and Badger's data in the pure rotational spectrum of HCl have been studied on the assumption of a line structure derived on the basis of such "coupling" pressure broadening. The value for the line intensity found here is in slightly better agreement with the new quantum theory but the discrepancy is still excessive.

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