X-ray fluorescence methods offer the chemist a much speedier analysis of multicomponent mixtures than conventional procedures. Components can be analyzed by measuring the intensity of emission lines sent out after rays strike the mixture, However, variations in the measurement of intensity do occur and are discussed in this paper. Counting error, or the inability to duplicate the exact number of radiation counts from sample to sample, is investigated and its distribution and variance are derived. Using a hierarchical model variances of batch, sample, and within sample effects are examined. These variances are compared with each other and with counting variance. / M. S.