48o TEE POPULAR SCIENCE MONTHLY 



entropy diagram, which represents the efficiency of a Carnot cycle as 

 a simple rectangular figure and is, he points out, " nothing more nor 

 less than a geometrical representation of the second law of thermo- 

 dynamics." The area of the Watts diagram represents the work done 

 by the engine; the area of the Gibbs diagram represents the heat it 

 has received and, either upon separate blackboards or upon " quadrant 

 diagrams," the two taken together have proved invaluable in teaching 

 thermodynamics to engineers. As the indicator diagram tells the engi- 

 neer what he wants to know about the work done upon the piston, the 

 efficiency of the valves and passages and the total horse power of the 

 engine, the entropy diagram gives him the heat taken in or given out 

 and shows directly the losses of efficiency from such heat wastes as 

 wire-drawing of steam, incomplete expansion, etc. Professor John 

 Perry says that the thermod3Tiamics of heat engines is revealed by the 

 entropy diagram " as it can be revealed in no other way," and he 

 describes how " a man almost illiterate, innocent of algebra, can use 

 his t, ^ diagram of water steam or air or ammonium anhydride, obtain- 

 ing in a few minutes answers to problems which the mathematical 

 engineers of years ago spent days in solving."^^ In England the tem- 

 perature-entropy diagram has been found very useful in " engine test- 

 ing laboratories," and its ultimate adoption is due to the persistent 

 crusade of Mr. Macfarlane Gray, late chief engineer of the Eoyal Navy, 

 who introduced it independently in 1880 as the " theta-phi " (0, cj)) 

 diagram. American engineers should not forget that this diagram was 

 first described in scientific literature by Professor Willard Gibbs,^^ who 

 clearly pointed out its advantages, in visualizing the second law, for 

 teaching purposes and its use and significance when attached to heat- 

 engines. In his second memoir^^ Gibbs extends his graphical methods 

 to three-dimensional space, the first example of which was the volume- 

 pressure-temperature diagram employed by James Thomson^® in 1871. 

 The first solid diagram described by Gibbs had for its coordinates, 

 volume, entropy and energy and is now generally known as the " ther- 

 modynamic surface." It is a solid model or relief-map, affording a 

 bird's-eye view of the chemico-physical changes of a system at constant 

 temperature and pressure as it passes through the coexistent states of 

 solid, liquid, vapor or gas. Maxwell, who had himself written learn- 



^^ Nature, London, 1902-3, LXVII., G04. 



=' Gibbs, Tr. Connect. Acad., April, 1873, II., 317-25. The equivalent of an 

 entropy diagram was laid down and described by the Belgian physicist M. Bel- 

 paire in 1872 (Bull. Acad. roy. d. sc, Brux., 1872, 2. s., XXXIV., 520-6), but his 

 treatment of the matter is so sketchy and slight in comparison with the 

 exhaustive and illuminative handling of Gibbs that it seems negligible. The 

 mere plotting of the diagram itself is nothing, for it was for years implicit in 

 Rankine's algebraic use of the "thermodynamic function" (0) as a coordinate 

 (1854), and to this day the British unit of entropy is called a "Rank." 



» Tr. Connect. Acad., 1873, II., 382-404. 



"J. Thomson, Proc. Roy. Sac. Lond., 1871, XX., 1. 



