TJiermodynamics of Fhiids. 317 



their properties from the well-known properties of the diagram in 

 which the volume and pressure are represented by rectangular co- 

 ordinates. For the relations indicated by the net-work of isometrics, 

 isopiestics etc., are evidently not alte,red by deformation of the sur- 

 face upon which they are drawn, and if we conceive of mass as belong- 

 ing to the surface, the mass included within given lines will also not 

 be eftected by the process of deformation. If, then, the surface upon 

 which the ordinary diagram is drawn has the uniform superficial den- 

 sity 1, so that the work and heat of a circuit, which are represented 

 in this diagram by the included area, shall also be represented by 

 the mass included, this latter relation will hold for any diagram 

 formed from this by deformation of the surface on which it is drawn. 

 The choice of the method of representation is of course to be deter- 

 mined by considerations of simplicity and convenience, especially in 

 regard to the drawing of the lines of equal volume, pressure, tempera- 

 ture, energy and entro|>y, and the estimation of work and heat. There 

 is an obvious advantage in the use of diagrams of constant scale, in 

 which the work and heat are represented simply by areas. Such dia- 

 grams may of course be produced by an infinity of diflerent methods, 

 as there is no limit to the ways of deforming a plane figure without 

 altering the magnitude of its elements. Among these methods, two 

 are especially important, — the ordinary method in which the volume 

 and pressure are represented by rectilinear co-ordinates, and that in 

 which the entropy and temperature are so represented. A diagram 

 formed by the former method may be called, for the sake of distinc- 

 tion, a volume-pressure diagram, — one formed by the latter, an entropy- 

 temperature diagram. That the latter as well as the former satisfies 

 the condition that ;^=1 throughout the whole diagram, may be seen 

 by reference to page 313. 



THE ENTROPY-TEMPERATURE DIAGRAM COMPARED WITH THAT IN ORDINARY USE. 



Considerations independent of the nature of the body in question. 



As the general equations (1), (2), (3) are not altered by interchang- 

 ing V, —p and — W with t], t and //respectively, it is evident that, 

 so far as these equations are concerned, there is nothing to choose 

 between a volume-pressure and an entropy-temperature diagram. In 

 the former, the work is represented by an area bounded by the path 

 which represents the change of state of the body, two ordinates and 

 the axis of abscissas. The same is true of the heat received in the 

 latter diagram. Again, in the former diagram the heat received is 

 represented by an area bounded by the path and certain lines, the 



