A theory was developed for evaluating a complex, prompt gamma ray spectrum to serve as the basis for an instrument to monitor continuously the sulfur content of tonnage streams of coal. Equations for the energies and intensities of prompt gamma rays emitted from 13 most significant elements in coal are combined into a single equation that defines the basic electronic design of the meter. The sulfur content of up to 10 tons per hour of coal was determined in pilot plant tests with a prototype meter. The precision of 0.04 percent sulfur substantiates the validity of the theory. In subsequent industrial plant tests the precision was determined to be a comparable 0.05 percent sulfur.