A general formula is derived by assuming that the free electron is moving in a central field. The approximate initial and final free state wave functions are chosen so that they have exact asymptotic forms, the phases being obtained by extrapolating the quantum defects of the observed energy levels into the continuum. The relevant free–free transition integrals have been computed and, from the tables given, the free–free absorption cross section for an electron in the field of a positive ion can be readily calculated, provided that the experimental data permits a reliable extrapolation to positive energies. Use is made of the tables to compute cross sections for Helium, and it is shown that the simple hydrogenic approximation can be considerably in error.