We present measurements of the phase-separation temperature (T-ph(phi,alpha)) as a function of overall protein volume fraction (phi) and protein composition (alpha) for ternary aqueous (W) solutions of calf gamma(IIIa) (A) and gamma(IIIb) (B) crystallins. Additionally, we have determined the binodal curve describing coexisting points (phi(I),alpha(I)) and (phi(II),alpha(II)) in the phase diagram at 20 degrees C. We propose a mean-field form of the ternary Gibbs free energy G(phi,alpha,T) which contains three interaction energy parameters : E(net)(A,W), E(net)(B,W), and E(net)(A,B), which determine the magnitude of the quadratic (phi(2)) mixing energy contribution to G. Using a lattice model it is possible to express each of these interaction parameters in terms of the mean individual protein-water, protein-protein and water-water bond energies. In the limit where the two proteins are not too dissimilar, as applies in our system, we find quite generally that the ternary solution can be regarded as a binary solution with an interaction energy dependent upon the initial composition (alpha) of the solution. We have used this finding to predict the entire coexistence surface T-ph(phi,alpha) and the positions of coexisting points along the binodal curve. The interaction energy parameters were determined and we show that, within experimental error, this theory accurately describes the full range of our experimental results.