A set of theoretical formulae for calculating activities along the liq
uid surface in ternary phase diagrams has been presented. These formul
ae are rigorous since no assumption is made in the derivation. The exp
ressions are generalized and can be simplified to the forms presented
by Pelton, Chou, Elliott and Gokcen under certain conditions. In pract
ice, the activity of the components are desired at a fixed temperature
instead of a variable temperature like that along a liquid surface. U
nder this situation, with reasonable assumptions the equations can be
further simplified such that they do not contain any partial thermodyn
amic properties. Activities can then be readily calculated from phase
diagrams. The method presented in this paper is for a ternary system a
nd can be extended to multicomponent systems.