Simple mathematical transformations on the Gibbs excess function G(Em) permit the evaluation of many important thermodynamic quantities. It is therefore of considerable interest to be able to evaluate this excess function from experimental data. We extend the methods already developed for excess functions based on mole-fractions to derive appropriate partial differential equations which relate any pair of G(Em), the logarithm of an activity coefficient, or the osmotic coefficient phi. The derivation is general and does not depend on the experimental data conforming to any particular model. We illustrate the applications of these equations to experimental data from the literature. Equations and applications for other partial molar quantities are also discussed.