A reasonable heuristic extrapolation of a theory given by Buckingham is used to estimate the frequency-and temperature-dependence of the second refractivity virial coefficient. The calculations are carried out for the atoms He, Ne, Ar, Kr, Xe and the small molecules H 2 , N 2 , 0 2 , HCl, C0 2 , N 2 0, NH 3 , CH 4 , C 2 H 4 , and SF 6 . In some cases the frequency-dependence of B R (co, T) is compared with experimental values, showing sometimes considerable deviations between experiment and the heuristic approach used in this work.