Basic results of Biot and Hill concerning (i) the elastic moduli of initially isotropic materials and (ii) Cauchy symmetry for large deformation are combined. The result is a system of hyperbolic differential equations to be satisfied by the elastic potential as a function of the principal stretches. Imposing these restrictions, the elastic potential for any strain is shown to be a functional of the elastic potential for pure dilatation. The theory is to some extent corroborated by experimental results on foam rubber by Blatz & Ko (Trans. Soc. Rheol. 6, 223 (1962)).