The Jahn-Teller effect in aromatic ions (and radicals) is studied, using a model in which the total energy is regarded as due to that of the original neutral molecule (or charged radical) for which no such effect arises, together with the energy of the odd electron in the degenerate orbital. It is shown that a general formula exists for the potential energy, analogous to, but more general than, that of Moffitt and Liehr. Three configurations of minimum energy, and three saddle-points, exist, and formulae are derived which make possible the calculation of the corresponding energies and bondlength changes. Numerical applications to benzene and triphenylene show excellent agreement with direct full-scale Roothaan-type calculations by Colpa.