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The effect of the change in moment of inertia part of the interaction between vibration and rotation on the intensities of parallel bands of linear polyatomic molecules has been determined to the first order. The results are quite similar to those of Herman and Wallis for diatomic molecules. The interaction term depends on among others a quantity, ξ k, different in general for each band. Perpendicular bands do not show a first-order correction. A ``sum rule'' for the ξ k has been determined.