Porster's theory of resonant transfer of energy has been used t o calculate the probability per unit time of transfer of energy from an excited singlet t o a triplet, raising the latter to a higher triplet. The magnitude of the effect is computed in applications to chlorophyll, rhodamine 6G, and anthracene, and in all cases it is found that the corresponding Forster radius RfT is of the order of 40 to 50 A. The rate con8tant k s~ for singlet-triplet exciton collisions resulting in quenching of the singlet is then calculated. It is found that the theoretical value of RfT, for the case of crystalline anthracene, which is much larger than that predicted by Babenko e t al., leads to better agreement with experiment and is to be preferred. Assuming 8 joint singlet-triplet diffusion constant of cm2/s, the rate constant kST for chlorophyll in solution is predicted to be 4.5 x LO-ll cm3/s.