Families of Thermodynamic Equations. II. The Case of Eight Characteristic Functions

The geometrical methods of Koenig and of Prins for resolving into families a certain class of thermodynamic equations involving four characteristic functions, are extended to the next higher case, of eight characteristic functions. The extension consists of operations upon a regular octahedron analogous to those upon a square (``the thermodynamic square'') in the former case. In the present case, the number of distinct equations in a family may be 48, 24, 12, 8, 6, 3, 1. Some examples of physical interest are described.