ALTHOUGH relations of the type where a is activity, n is number of moles, and the suffixes denote the components, are by no means new1, they have been little exploited. Further types such as and do not seem to appear in the literature at all, though they are sometimes more convenient to use than equation (1). Despite their neglect, these cross-differentiation relations provide a versatile tool in the study of three-component and more complicated systems, as the brief survey in this communication will indicate. They can be generalized by replacing the lna's by any partial molal quantities. Perhaps the most important conclusion is that, from measurements of the solvent activity only, it is possible to calculate the activities of all the other components.