Absolute inelastic cross sections for rotational quantum state-to-state transitions have been measured in small angle grazing collisions of CsCl and KCl with the rare gas atoms. With CsCl the transitions (j,m) = (3,0)?(4,0) and with KCl the transitions (2,0)?(3,0) were studied. The cross sections for CsCl are similar in size to those reported previously for CsF by Borkenhagen, Malthan, and Toennies [J. Chem. Phys. 71, 1722 (1979)], whereas the cross sections for KCl are found to be considerably smaller. The cross sections are corrected for apparatus effects and analyzed in terms of the Born approximation and the long range anisotropic potential. A comparison of absolute center of mass differential cross sections reveals that the cross sections for CsCl and to a greater extent for KCl are considerably greater than expected for a pure induction potential. The relative size of the additional potential term is determined and is found to be somewhat smaller than the higher polarizability dispersion term predicted by Buckingham [J. Chem. Phys. 48, 3827 (1968)] using the Rittner model.