Richmond Paper - The Use of the Tri-Axial Diagram in the Calculation of Slags

The advantages of the tri-axial diagram in representing the composition of slags and silicates are well appreciated by many metallurgists. Prof. H. M. Howe* has pointed out the application of a fourth variable, in connection with the diagram, and has called attention to the usefulness of the general systern of tri-axial representation. In the discussion of Prof. Howe's paper, Mr. Firmstone† indicated how certain distances could be measured directly by projection. Prof. R. H. Thurston,‡ as early as 1877, had made use of a typtic model and of triangular diagrams, with contour-lines, rekrresenting varying physical properties corresponding to varying chemical composition. Still earlier, Prof. J. Willard Gibbs§ had used the diagram in similar work; and other scientists were thought by him to have preceded him in its use. During the period of nearly a quarter-century, following these early publications, there has been an ever-increasing use of graphic methods in numerous branches of scientific work, stimulated, in part, by the possibility of representation by three co-ordinates upon plane-surfaces. Yet the number of possible co-ordinates for graphic representation has always been, and always must be, insufficient to express many facts which are shown mathematically; while, without graphic representation, the involved nature of mathematical expression often fails to facilitate and promote research. The coming into use, therefore, of the fourth co-ordinate, permitting representation by four variables, marks but the beginning of some lines of research which could not well advance without this aid.