Predicting bronze casting recipes in ancient China: ternary copper-lead–tin alloys and the “unit sum problem”

This paper explores the relationship between trends in the observed composition of ternary copper-lead–tin alloys and the recreation of “recipes” used for the casting of bronze objects, and in particular, to ask if the recipe can be reconstructed from the chemical data. The archaeological context is specifically the manufacture of bronzes in pre-Dynastic China, but the nature of the discussion is essentially mathematical. Although the chemical compositions of Chinese bronzes have been well-studied and the casting processes have been exhaustively researched in terms of mould technology, little attention has been given to understanding the recipes used by the bronze casters when producing the alloy to pour into the moulds. The mathematical issue is simple—clearly, in a ternary alloy, the weight percentage compositions of the three components are intimately connected, such that if one goes up, the other two must reduce. Within this constraint, can the correlation patterns seen when assemblages of such objects are plotted as simple binary diagrams be interpreted in terms of the recipe used to create that alloy, and, in particular, can such recipes be replicated by simple numerical models?