The absorptivities of color elements in a mixture can be obtained by using Gauss elimination with selection of the principal element in the matrix to the stds. These values can be applied to the flexible tolerance simplex method to give the composition of samples. In the experimental design and data treatment, an effort was made to min. the errors of results according the principal of optimization. When the difference of absorptivities of color material is significant to the experimental error, the present method satisfies the accuracy for determing lanthanum, cerium, praseodymium, neodymium and samarium in their mixture If the difference is quite small, the present method only gives good results for lanthanum and the sum of cerium, praseodymium, neodymium and samarium. The relative error is less than 5% for determing more than 2 mg La2O3 and 3% for sum of other rare earths. In addition, the present method can give accurate results for the determination of total rare earths even though their composition differ greatly.

Key words: SPECTROPHOTOMETRY, COMPUTER APPLICATIONS, CERIUM, LANTHANUM, SIMULTANEOUS DETERMINATIONS, SAMARIUM, LIGHT RARE EARTH, ORTHOGONAL DESIGN, PRASEODYMIUM, CONTENTS