HE theoretical computation of absolute transition probabilities for electronic spectra of molecules has been attempted only recently, though T theoretical formulas for relative intensities of lines in a band, and methods for calculating theoretically the relative intensities of bands in a band-system, are well known. The quantum-mechanical calculations on absolute intensities are, for most molecules, necessarily approximate ; their usefulness is still being explored and the methods of computation improved. Fortunately, even very rough theoretical calculations prove to be valuable, since the transition probabilities vary over a range of several powers of ten. The methods of computation, and the results so far achieved in the actual determination of intensities and their interpretation in terms of molecular structure, form the principal subject matter of this Report. Applications to various other molecular properties such as dispersion, polarizability, and the interpretation of molecular refractivities, and to dyes and to the abundance of molecules in astronomical sources, are also discussed.I n the discussion of transition intensities in this Report, we shall consider, for the most part, only absorption spectra, since it is not feasible to obtain extensive experimental data on absolute transition probabilities in emission spectra. 9 2.