Josiah Willard Gihbs. 189 



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 useful- 

 ness 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 thermo- 

 dynamics, of the vohime-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 wdiicli he first described in this 

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

 temperative 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 Pro- 

 fessor Gibbs gave most attention w^as the volume-entropy dia- 

 gram, 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 repre- 

 sentation of coexistent 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. ]^o diagram of constant scale can, for example, ade- 

 quately 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 dimen- 

 sions. 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 interpretation is most simple from ele- 

 mentary considerations, but which, for several reasons, is far 

 less convenient and fertile of results than one in ^vhich the 

 coordinates are thermodynamic quantities less directly known. 

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



