26 GRAPHICAL METHODS IN THE 



being that of the hands of a watch, the work and heat of the circuit 

 will be positive. But if we draw any circuit EFGH in the same 

 direction on the other side of the line LL, the work and heat will 

 be negative. For 



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 suppose 

 that the work 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 

 that direction, and the circuit EFGH the con- 

 trary direction, as in figure 11. Now if we 

 imagine an indefinite number of circuits on 

 each side of LL in the volume-entropy dia- 

 gram, it will be evident that to transform 

 such a diagram into one of constant scale, so 

 as to change the direction of all the circuits 

 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 



v 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 

 superposed, which must be carefully 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, except along the bounding line LL, all the 

 general theorems which have been developed in this article can be 

 readily applied to the diagram. But to the eye or to the imagination, 

 the figure will necessarily be much more confusing than a volume- 

 entropy diagram. 



dt) 

 If -7 =0 for the line LL, there will be another inconvenience in 



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

 line LL, -g-, i.e., l + y v>1l will have a very small value, so that areas 

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



