336 J. W. Gihbs on Ghraphical Methods in the 



and the direction of the circuits makes the areas positive in both 

 cases. Now if we should change this diagram into any diagram of 

 constant scale, the areas of the circuits, as representing proportionally 

 the work done in each case, must necessarily have opposite signs, 

 i. e., the direction of the circuits must be opposite. We will siippose 

 that the woi-k done is positive in the diagram of constant scale, when 

 the direction of the circuit is that of the hands of a watch. Then, in 



that diagram, the circuit ABCD would have 

 ^ tliat direction, and the circuit EFGH the 



contrary direction, as in figure 11. Now if 

 we imagine an indefinite number of circuits 

 on each side of LL in the volume-entropy 

 diagram, it will be evident that to transform 

 such a diagram into one of constant scale, 

 so as to change the direction of all the cir- 

 cuits on one side of LL, and of none on the 

 other, the diagram must be folded over 

 along that line ; so that the points on one 

 side of LL in a diagram of constant scale do 

 not represent any states of the body, while 



on the other side of this line, each point, for 



^ a certain distance at least, represents two 

 different states of the body, which in the volume-entropy diagram are 

 represented by points on opposite sides of the line LL. We have thus 

 in a part of the field two diagrams superjiosed, which must be care- 

 fully distinguished. If this be done, as by the help of different colors, 

 or of continuous and dotted lines, or otherwise, and it is remembered 

 that there is no continuity between these superposed diagrams, exce])t 

 along the bounding line LL, all the general theorems which have been 

 developed in this article can be readily ai)plied to the diagram. But 

 to the eye or to the imagination, the figure will necessarily be much 

 more confusing than a volume-entropy diagram. 



If -^ r= for the line LL, there will be another inconvenience in 

 d?] 



the use of any diagram of constant scale, viz : in the vicinity of the 



line LL, ^, i. e., 1 -^ i/„ „ will have a very small value, so that areas 

 dy ' ' 



will be very greatly reduced in the diagram of constant scale, as com- 

 pared with the corresponding areas in the volume-entropy diagram. 

 Therefore, in the former diagram, either the isometrics, or the isen- 

 tropics, or both, will be crowded together in the vicinity of the line 

 LL, so that this part of the diagram will be necessarily indistinct. 



