AbstractThe double dilution method has many important advantages. For any element to be determined, let us say A, It enables us to control or calculate the matrix factor (sum of the absorption end enhancement effects) for the sample being Investigated towards A radiation, and it furnishes corrected Intensities which are strictly proportional to A concentration. Thus the results are exact, whatever the general composition of the sample, their accuracy depending only on the quality of measurement and preparation. Another major practical advantage is that the method does not require systematic calibration but only a few permanent standards consisting of a pure compound or of an accurately known sample.The procedure has been tested successfully for accurate determination of rare earth elements using, for solid materials such as ores and oxide mixtures, the borax fusion technique. It also can be readily applied to liquids. All the rare earth elements can be titrated by that method, as well as yttrium, thorium and, if necessary, all the elements relevant to X-ray fluorescence analysis. The concentration range considered for solids is of one comprised between 0.5 and 100 % and, with a lesser accuracy, between 0.1 and 0-5 % Examples are given relative to the analysis of various ores. Finally it rcust be pointed out that the method is universal and applies to the analysis of every solid, especially ores, provided that they can be converted to solid or liquid solutions. It appears that most industrial analyses can be worked on In this way.