JOSIAH WILLARD GIBBS. xv 



illustrations, which he employed as symbols and aids to the imagin- 

 ation, rather than the mechanical models which have served so many 

 great investigators ; such models are seldom in complete correspondence 

 with the phenomena they represent, and Professor Gibbs's tendency 

 toward rigorous logic was such that the discrepancies apparently 

 destroyed for him the usefulness of the model. Accordingly he usually 

 had recourse to the geometrical representation of his equations, and 

 this method he used with great ease and power. With this inclination, 

 it is probable that he made much use, in his study of thermodynamics, 

 of the volume-pressure diagram, the only one which, up to that time, 

 had been used extensively. To those who are acquainted with the 

 completeness of his investigation of any subject which interested him, 

 it is not surprising that his first published paper should have been a 

 careful study of all the different diagrams which seemed to have any 

 chance of being useful. Of the new diagrams which he first described 

 in this paper, the simplest, in some respects, is that in which entropy 

 and temperature are taken as coordinates ; in this, as in the familiar 

 volume-pressure diagram, the work or heat of any cycle is proportional 

 to its area in any part of the plane ; for many purposes it is far more 

 perspicuous than the older diagram, and it has found most important 

 practical applications in the study of the steam engine. The diagram, 

 however, to which Professor Gibbs gave most attention was the 

 volume-entropy diagram, which presents many advantages when the 

 properties of bodies are to be studied, rather than the work they do or 

 the heat they give out. The chief reason for this superiority is that 

 volume and entropy are both proportional to the quantity of substance, 

 while pressure and temperature are not ; the representation of coexis- 

 tent states is thus especially clear, and for many purposes the gain in 

 this direction more than counter-balances the loss due to the variability 

 of the scale of work and heat. No diagram of constant scale can, for 

 example, adequately represent the triple state where solid, liquid and 

 vapor are all present; nor, without confusion, can it represent the 

 states of a substance which, like water, has a maximum density; in 

 these and in many other cases the volume-entropy diagram is superior 

 in distinctness and convenience. 



In the second paper the consideration of graphical methods in 

 thermodynamics was extended to diagrams in three dimensions. 

 James Thomson had already made this extension to the volume-pressure 

 diagram by erecting the temperature as the third coordinate, these 

 three immediately cognizable quantities giving a surface whose inter- 

 pretation is most simple from elementary considerations, but which, 

 for several reasons, is far less convenient and fertile of results than 

 one in which the coordinates are thermodynamic quantities less directly 

 known. In fact, if the general relation between the volume, entropy 



