A method for measuring stable isotope ratios using Raman scattering has been developed. This method consists of simultaneously counting photons scattered out of a high-intensity laser beam by different isotopically-substituted molecules. A number of studies of isotopic diatomic molecules have been made. The Q-branches of the Raman spectra of the isotopic molecules /sup 14/N/sup 15/N and /sup 16/O/sup 18/O were observed at natural abundance in nitrogen and oxygen samples. Comparison of the ratios of the intensities of the Q-branches of the major nitrogen and oxygen isotopic molecules with mass spectrometric determinations of the isotopic compositions yielded scattering cross sections of /sup 14/N/sup 15/N relative to /sup 14/N/sup 14/N and /sup 16/O/sup 18/O relative to /sup 16/O/sup 16/O. These cross section ratios differ from unity, a difference which can be explained by considering nuclear mass effects on the Franck-Condon factors of the molecular transitions. The measured intensities of the /sup 14/N/sup 15/N and /sup 16/O/sup 18/O Q-branches provided the baseline data needed to make the previously-mentioned extrapolation. High-resolution (approximately 0.15 cm/sup -1/) spectra of the Q-branches of /sup 14/N/sup 14/N and /sup 16/O/sup 16/O yielded a direct determination of ..cap alpha../sub e/ (the difference between the rotational constant in the ground …