Ion polarizabilities derived from low-frequency precision measurements of the dielectric constants of single crystals of more than 120 different oxides have recently been published but have proved difficult to interpret in terms of classical theory. The latter predicts that the polarizability of an ion should be proportional to the cube of its radius. We present a new approach to the analysis of the experimental data which clearly demonstrates a square law dependence, in agreement with the quantum mechanically based result expected for a purely electronic polarizability. There is then a demonstrable relationship between the low-frequency polarizability of an ion and the orbital angular momentum quantum number associated with its outermost, or most polarizable, electron subshell. The apparent absence of ion displacement contributions in oxides is explained as a consequence of the method though which polarizability data have been derived and the relative magnitude of the Szigeti charge. The new analysis offers, for the first time, the possibility of deriving a set of absolute values for the low-frequency `in crystal' polarizabilities of all ions for which there is a clearly established valence state. These should permit more reliable calculations of the properties of dielectric materials and a useful check for the modelling of their dynamical behaviour.