326 



J. W. Gihhs 0)1 Graphical Methods in the 



of the logarithms of the vohimes, the distances of the isopiestics being 

 proportional to the differences of the logarithms of the pressures, and 

 so with the isothermals and the isodynamics, — the distances of the 

 isentropics, however, being proportional to the differences of entropy 

 simply. 



The scale of work and heat in such a diagram will vary inversely 

 as the temperature. For if we imagine systems of isentropics and iso- 

 thermals drawn throughout the diagram for equal small differences of 

 entropy and temperature, the isentropics will be equidistant, but the 

 distances of the isothermals will vary inversely as the temperature, 

 and the small quadrilaterals into which the diagram is divided will 

 vary in the same ratio: .'. y ct) l-^t. (See page 313.) 



So far, however, the form of the diagram has not been completely 

 defined. This may be done in various ways : e. g,, if x and y be the 

 rectangular co-ordinates, we may make 



( X =z log V. i X z= /), { X = loo; V. . 



■! ° ' or ^ " or -^ *=' ' etc. 



iy = \ogp; ly = \ogt; i y = >r, 



Or we may set the condition that the logarithms of volume, of pres- 

 sure and of temperature, shall be represented in the diagram on the 



same scale. (The logarithms of energy 

 are necessarily represented on the same 

 scale as those of tempei'ature.) This will 

 require that the isometrics, isopiestics and 

 isothermals cut one another at angles of 

 60°. 



The general character of all these dia- 

 grams, which may be derived from one 

 another by projection by parallel lines, 

 may be illustrated by the case in which 

 X = log V, and y =z log p. 



Through any point A (fig. 6) of such a 

 diagram let there be di-awn the isometric 

 vv', the isopiestic pp", the isothermal tt' 

 and the isentropic ;///'. The lines pp' and 

 vv' are of course parallel to the axes. Also by equation (h) 



and by (g) 



. ld'/\ ld\o<ip\ 



Fig. 6. 



d loff V 



c-\-a 

 c 



