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One of the major goals of 18th century chemistry was to determine the components of substances. In this paper we describe STAHL, a system that models significant portions of 18th century reasoning about compositional models. The system includes a number of heuristics for generating componential models from reactions, as well as error recovery mechanisms for dealing with inconsistent results. STAHL processes chemical reactions incrementally, and is therefore capable of reconstructing extended historic episodes, such as the century-long development of the phlogiston theory. We evaluate STAHL's heuristics in the light of historical data, and conclude that the same reasoning mechanisms account for a variety of historical achievements, including Black's models of mild alkali and Lavoisier's oxygen theory. STAHL explains the generation of competing accounts of the same reactions, since the system's reasoning chain depends on knowledge it has accumulated at earlier stages.