328 



J. W. Gihhs on Graphical Methods in the 



The properties of the diagrams obtained by the otlier methods men- 

 tioned on page 326 do not differ essentially from those just described. 

 For example, in any such diagram, if through any point we draw an 

 isentropic, an isothermal and an isopiestic, which cut any isometric 

 not passing through the same point, the ratio of the segments of the 

 isometric will have the value which has been found for BC : CD. 



In treating the case of vapors also, it may be convenient to use 

 diagrams in which x = log v and y =. log /», or in which x z= j/ and 

 y z=z log t; but the diagrams formed by these methods will evidently 

 be radically different from one another. It is to be observed that each 

 of these methods is what may be called a tnethod of definite scale for 

 work and heat ; that is, the value of y in any part of the diagram is 

 independent of the properties of the fluid considered. In the first 



In this respect these methods 



1 • , 1 1 



metliod y=i — ;— , m the second y=z—. 

 ^ ^ e^ 



have an advantage over many others. For example, if we should 

 make x z= log v, y ^=. //, the value of ;/ in any pai't of the diagram 

 would depend iipon the ])roperties of the fluid, and would probably 

 not vary in any case, except that of a perfect gas, according to any 

 simple law. 



The conveniences of the entropy-temperature method will be found 

 to belong in nearly the same degree to the method in which the co- 

 ordinates are equal to the entropy and the logarithm of the tempera- 

 ture. No serious difliculty attaches to the estimation of heat and 

 work in a diagram formed on the latter method on account of the 

 variation of the scale on which they are represented, as this variation 

 follows so simple a law. It may often be of use to remember that 



Fig. 7. 



such a diagram may be reduced to an entropy- 

 temperature diagram by a vertical compression 

 or extension, such that the distances of the iso- 

 thermals shall be made proj)ortional to their 

 diflerences of temperature. Thus if we wish 

 to estimate the work or heat of the circuit 

 >C ABCD (fig. 7), we may draw a number of equi- 

 distant ordinates (isentropics) as if to estimate 

 the included area, and for each of the ordinates 

 take the differences of temperature of the points 

 where it cuts the circuit; these differences of temperature will be 

 equal to the lengths of the segments made by the corresponding 

 circuit in the entropy-temperature diagram upon a corresponding- 

 system of equidistant ordinates, and may be used to calculate the 



