Förster's theory of electronic excitation transfer between molecules in solution treats a donor-acceptor system of constant intermolecular distances. However, in most solvents, at room temperatures, the relative diffusion path of donor and acceptor over the time of excitation is of the order of magnitude of their average separation. It is shown how the change in intermolecular distances can be incorporated into Förster's theory. An expression is derived for the fractional decrease of donor fluorescence due to resonance transfer in dilute solution where the diffusional displacement does not exceed the average distance between donor and acceptor molecules. It is shown that the effect of Brownian movement, though not great, should be detectable by experiment.