190 Josiak Willard Gihbs. 



and energy of any body is known, the relation between the 

 volume, pressnre and temperature may be immediately deduced 

 by differentiation ; but the converse is not true, and thus a 

 knowledge of the former relation gives more complete infor- 

 mation of the properties of a substance than a knowledge of 

 the latter. Accordingly Gibbs chooses as the three coordinates 

 the volume, entropy and energy and, in a masterly manner, 

 proceeds to develop the properties of the resulting surface, the 

 geometrical conditions for equilibrium, the criteria for its sta- 

 bility or instability, the conditions for coexistent states and for 

 the critical state ; and he points out, in several examples, the 

 great powder of this metliod for the solution of thermodynamic 

 problems. The exceptional imj^ortance and beauty of this 

 w^ork by a hitherto unknown writer was immediately recognized 

 by Maxwell, who, in the last years of his life, spent considerable 

 time in carefully constructing, with his own hands, a model of 

 this surface, a cast of which, very shortly before his death, he 

 sent to Professor Gibbs. 



One property of this three dimensional diagram (analogous 

 to that mentioned in the case of the plane volume-entro|)y 

 diagram) proved to be of caj^ital importance in the develop- 

 ment of Gibbs's future -work in thermodynamics ; the volume, 

 entropy and energy of a mixture of portions of a substance 

 in different states (whether in equilibrium or not), are the sums 

 of the volumes, entropies and energies of the separate parts, 

 and, in the diagram, the mixture is represented by a single 

 point which may be found from the separate points, represent- 

 ing the different portions, by a process like that of iinding 

 centers of gravity. In general this point is not in the surface 

 representing the stable states of the substance, but within the 

 solid bounded by this surface, and its distance from the surface, 

 taken parallel to the axis of energy, represents the available 

 energy of the mixture. This possibility of representing the 

 properties of mixtures of different states of the same substance 

 immediately suggested that mixtures of substances differing in 

 chemical composition, as well as in physical state, might be 

 treated in a similar manner ; in a note at the end of the second 

 paper the author clearly indicates the possibility of doing so, 

 and there can be little doubt that this was the path by which 

 he approached the task of investigating the conditions of 

 chemical equilibrium, a task which he was destined to achieve 

 in such a magnificent manner and with such advantage to 

 physical science. 



In the discussion of chemically homogeneous substances in 

 the first two papers, frequent use had been made of the prin- 

 ciple that such a substance will be in equilibrium if, when its 

 energy is kept constant, its entropy cannot increase ; at the 



