据等温等压多相平衡Gibbs能最小原理并应用Lagrange未定乘数法导出多元系组元化学位和平衡成分关系式。由此给出三元系两相共存区边界上由一已知组元活度计算它组元活度的解析递推式。该结果被推广到K元K-1相平衡共存区相界。计算结果与实验值符合得较好。 According to the principle of isothermal equilibria and multiphase equilibrium Gibbs energy, Lagrange undetermined multiplicative method is used to derive the relationship between the multivariate elemental composition and the equilibrium composition. The analytic recursion of calculating the activity of a component from a known component activity is given on the boundary of the two-phase coexistence region of the ternary system. The result is generalized to K-K-1 phase equilibrium coexistence zone phase boundary. The calculated results are in good agreement with the experimental data.