xvi JOSIAH WILLARD GIBBS. 



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

 pressure and temperature may be immediately deduced by differen- 

 tiation ; but the converse is not true, and thus a knowledge of the 

 former relation gives more complete information 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 

 stability or instability, the conditions for coexistent states and for the 

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

 of this method for the solution of thermodynamic problems. The 

 exceptional importance and beauty of this work 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-entropy diagram) proved 

 to be of capital importance in the development 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, representing the different 

 portions, by a process like that of finding 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 principle that such a 

 substance will be in equilibrium if, when its energy is kept constant, 

 its entropy cannot increase ; at the head of the third paper the author 

 puts the famous statement of Clausius : " Die Energie der Welt ist 

 constant. Die Entropie der Welt strebt einem Maximum zu." He 



