It has been recognized for some time that, when the discrete vibration rotation absorption bands connected with transitions to a certain final electronic state of a molecule overlap the continuous region for the transitions to another final electronic state, some of the discrete bands may be diffuse, i.e., the rotation lines may be broad and blur into each other. The broadness of the lines has previously been assumed to be connected with the short life period of a molecule in a discrete state, when there is the possibility of its making a radiationless transition to a state of dissociation. In this paper a calculation is made of the width directly. One starts with a wave equation which represents approximately the state of a molecule, and which has continuous and discontinuous groups of eigenfunctions. Then the extra terms in the exact wave equation may be treated in the usual manner as a perturbation, and the perturbed eigenfunctions may be expressed as a linear function of the unperturbed ones. The energy range over which the properties of a given discrete state may influence the properties of the perturbed eigenfunctions is determined in terms of the perturbation matrix components, and from this is found the width of the line and the total absorption over its width.

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