320 J. W. Gihbs on Graphical Methods in the 



It is often a matter of the first importance in the study of any ther- 

 modynamic engine, to compare it with a perfect engine. Such a com- 

 parison will obviously be much facilitated by the use of a method in 

 which the perfect engine is represented by such simple forms. 



The method in which the co-ordinates represent volume and pressure 

 has a certain advantage in tlie simple and elementary character of the 

 notions upon which it is based, and its analogy with Watt's indicator 

 has doubtless contributed to render it popular. On the other hand, 

 a method involving the notion of entropy^ the very existence of which 

 depends upon the second law of thermodynamics, will doubtless seem 

 to many far-fetched, and may repel beginners as obscure and difficult 

 of comprehension. This inconvenience is perhaps more than counter- 

 balanced by the advantages of a method which makes the second law 

 of thermodynamics so prominent, and gives it so clear and elementary 

 an expression. The fact, that the different states of a fluid can be 

 represented by the positions of a point in a plane, so that the ordi- 

 nates shall represent the tem[)eratures, and the heat received or given 

 out by the fluid shall be represented by the area bounded by the line 

 representing the states through which the body passes, the ordinates 

 drawn through the extreme points of this line, and the axis of abscis- 

 sas, — this fact, clumsy as its expression in words may be, is one which 

 presents a clear image to the eye, and which the mind can readily 

 grasp and retain. It is, however, nothing more nor less than a geo- 

 metrical expression of the second law of thermodynamics in its appli- 

 cation to fluids, in a form exceedingly convenient for use, and from 

 which the analytical expression of the same law can, if desired, be at 

 once obtained. If, then, it is more important for purposes of instruc- 

 tion and the like to familiarize the learner with the second law, than 

 to defer its statement as long as possible, the use of the entropy- 

 temperature diagram may serve a useful purpose in the popularizing 

 of this science. 



The foregoing considerations are in the main of a general character, 

 and independent of the nature of the substance to which the graphical 

 method is applied. On this, however, depend the forms of the iso- 

 metrics, isopiestics and isodynamics in the entropy-temperature dia- 

 gram, and of the isentro})ics, isothermals and isodynamics in the 

 vohime-pressure diagram. As the convenience of a method depends 

 largely upon the ease with which these lines can be drawn, and upon 

 the peculiarities of the fluid which has its properties represented in 

 the diagram, it is desirable to compai'e the methods under considera- 

 tion in some of their most important applications. We will commence 

 with the case of a perfect gas. 



