Sources for a history of the ternary diagram

Abstract

Anyone reading the literature on the history of graphs will soon realize that the use of graphie displays of any type was really quite unusual until the mid-ninetenth century and that those scientists who did make use of them are often familiar to us as creative thinkers in their own fields of endeavour. A ternary diagram (also known as a triangular diagram) is a particular type of graph which consists of an equilateral triangle in which a given plotted point represents the relative proportions (a, b, c) of three end-members (A, B and C), generally expressed as percentages and constrained by a + b + c = 100%. It has long been used to portray sample composition in terms of three constituents, or an observed colour in terms of three primary colours, because it is a convenient means of representing a three-component System in a planar projection, rather than as an isometric, or similar, view of a three-dimensional space. Recent papers suggest that its use is not as familiar to some statisticians as are other commonly used forms of graph. For example, although it was cited by Peddle in 1910 and more recently by Dickinson, it is not discussed in modern texts on statistical graphies nor in the key papers on the history of graphs. However, beginning with studies of colour-mixing in the eighteenth century, it has subsequently become widely used, particularly in geology, physical chemistry and metallurgy. In this paper, I attempt to document its gradual uptake as a standard method of data display and some of the scientific advances which its use has facilitated.