Abstract: An X-ray spectrometer is provided with two channels for detecting characteristic lines of the X-ray source after being scattered by a sample undergoing analysis, in addition to means for detecting electric signals primarily representative of the concentrations of analytes in the sample. In this way, data is collected which facilitates corrections of the measurements corresponding to individual analytes for deviations from linearity of intensity caused by variations in interelement effects, and by variations in total-solids concentration, or density, of the slurry, or matrix, in which the analytes are distributed, and by variations in particle size of the total-solids in the sample. Correction of measurements of total-solids concentration and average particle size of the matrix for each other and for effects of analytes, may also be made.