AbstractBetween adjacent major element absorption edges, background intensities at differing wavelength positions were found to be related linearly. Also, background intensity at any position is linearly related to the reciprocal of the mass absorption coefficient for any wavelength between the absorption edges.The method presented here allows for the determination of background, as well as mass absorption coefficient, by a single measurement at an interference‐free background position (which can be the Compton scatter ‘peak’). If the mass absorption coefficient is already known, backgrounds may be calculated directly.Tests on geological materials show that, while not as accurate as conventional methods of background determination, relative accuracies of two to five percent are obtainable with a very considerable saving in time, since intensity at only one background position need be measured. Use of low dispersion high reflectivity analysing crystals, e.g. LiF(200), is possible because it is no longer necessary to attain interference‐free background positions between peaks.Furthermore, the method is ideally suited to the determination of background intensities in energy dispersive systems where spectral resolution is a problem and in multi‐channel units where only one channel need be used for the determination of both mass absorption coefficient and backgrounds for a group of trace elements.The method has been used in the low cost determination of trace elements in large numbers of geochemical prospectin