The elastic limit is ordinarily defined as the limit beyond which Hooke's Law no longer holds. In terms of the usual engineering tests the elastic limit is indicated by a permanent deformation. More accurate measurements show, however, that the ratio of stress to strain is not a constant even before the point of permanent deformation. Calculations based on the electrostatic theory of crystal lattices show that instead of the stress,f, being simply proportional to the strain, Δr(i. e., f = f′Δr), it is to be represented by an infinite convergent series of the formf = f0 + f′ Δr + 12! f″(Δr)2 + 13! f‴(Δr)3± …. Normallyf0is zero, so that Hooke's Law is to be regarded as only an approximation based on the neglect of terms of higher order thanf′Δr. It is therefore to be expected that Hooke's Law will fail for very refined measurements. The fact that it holds as well as it does up to the point of permanent deformation led Joffé to investigate the mechanism by which a permanent set is produced.