The hyperbolic relationship between quality and quantity formulated as c = K Qb, in which c is the mineral concentration, Q is the stream discharge, and K and b are regression coefficients, is taken and refined for use on rivers of the southwest or of other semi-arid regions. A modified Cauchy function is used to fit frequency curves for both quantity and quality. Gumbel's methods of extremal statistics are applied to the frequencies of extremes for quality and inorganic quality. A mathematical model for making a materials balance analysis of the chlorides in rivers of the southwest is presented.