The study of the vibrations of polyatomic molecules has recently turned into one of the most widespread and powerful methods of studying molecular structure. These vibrations ap- pear directly in the infrared absorption spectra and Raman spectra of gases, liquids, and solids. A measurement of the number of bands in addition to their positions (frequencies or wavelengths) offers the possibility of obtaining a great deal of important information regarding the geometric and mechanical properties of the molecules, the types of chemical bonds, and so forth. It is now quite difficult to list the...