In his Theory of Heat, Clerk-Maxwell gives a very elegant and simple geometrical proof of the four thennodynamical relations, and points out that his construction shows that the truth of any one is a necessary consequence of the truth of any other. The usual analytical proof of these relations can be made as simple as Maxwell's geometrical proof, and the fact that any one is a necessary consequence of any other becomes evident when it is considered that they are all deduced by a common process from identical transformations of one equation. The following method of proof seems to me to bring out more directly their necessary interdependence.