Abstract: The invention is particularly useful for multi-element solutions wherein successive pairs of X-ray beams are generated and passed through the solution sample corresponding to each of the successive various elements the concentrations of which is to be measured, enabling the on-line concentration measurement of, for example, rare earth elements. Microprocessor control is provided of the presentation of successive X-ray emitting irradiated metal targets to the solution sample and with programming enabling on-line successive measurement of the concentration of each successive element, calibration and storage of such measurements and calculation to eliminate the contribution of other interfering elements from the successive elements to be measured, and display of the successive element concentrations. Applications of the invention may be found, also, in the fields of wet metallurgy for precious metals and less common metals, in the field of petrochemical industry and other chemical engineering applications.