It has been shown in previous chapters that for "homogeneous specimens," characteristic x-ray line intensity is subject to random and systematic errors determined mainly by instrumental limitations and artifacts, plus matrix effects arising from some or all of the elements making up the analyzed specimens. It was also stated that specimen heterogeneity problems are best reduced by adequate specimen preparation rather than by attempting to express the x-ray intensity/concentration relationship in terms of particle size distribution and particle statistics. Whereas the previous chapter was concerned mainly with the causes and prediction of random and systematic errors in quantitative analysis, this chapter is concerned with methods of quantitative analysis, which to a large extent means the compensation for matrix interferences in homogeneous specimens. It is thus assumed that in all cases the specimen has been rendered homogeneous. It is also assumed that the magnitude of random and systematic errors arising from the instrument are known and are controllable within the range of accuracy required by the quantitative method in question. Finally, it is assumed that random errors due to counting

statistics will not represent the limiting factor in the ultimate accuracy of a given determination.