The theory of moment analysis of absorption band shapes is extended to include rotation-translation coupling in a linear solute molecule. It is shown that additional terms arise in the expressions for the even moments. In particular, the square of the average force acting on the solute contributes to the fourth moment because the center of gravity and the center of interaction are not coincident. The force and torque terms are compared quantitatively using a generalized KBM model. Experimental evidence in support of the theory is derived from the Raman spectral data of Perchard et al. [ Mol. Phys.23, 519 (1972)] on HCl and DCl solutions.