Van der Waals's equation of state, with his original rules for relating his a and b to the composition of the mixture, is shown to lead to values of the thermodynamic excess functions for mixtures of spherical (or nearly spherical) molecules, which agree nearly as well with experiment as those obtained even with Leland, Rowlinson and Sather's greatly improved version of the more elaborate “pure-fluid based” theories of Prigogine, Kirkwood, Scott, Brown and others. Guggenheim's equation of state is shown to lead to excess functions which agree more closely with experiment than any previously published version of the more elaborate theories.