A perturbation treatment of the isotope effect has been developed which gives the change in the normal coordinates as well as the frequencies of vibration. The ratio rule is obtained from this treatment, and the conditions which are prerequisite to its application are clearly indicated. At present the lack of required experimental data limits the utility of this rule somewhat, and a more useful but generally less accurate form of it has been derived, which depends for its validity upon the ability to construct symmetry coordinates which approximate the corresponding normal coordinates. The application of these equations to experimental data has been illustrated. In particular the modified ratio rule has been tested on the molecules CD4, CH3D, CHD3, CDCl3, CD3Cl, ND3, B10F3, C2D4, and C2D6 and found to give generally good results.