282 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



by the work of a number of observers. 30 Now according to a familiar 

 equation of thermodynamics 



dH=TdN+v dp 



for any transformation, and in particular for one along the saturation 

 line. Dividing by dt and passing along that line to the critical temper- 

 ature as a limit, gives 



' r * n Vdi) = Tc *** \ii) + v < (i) sa , cri , 



= — go- -f- constant. 



Figure 7 a. 



Figure 7 6. 



The steam dome on the temperature-entropy plane. The full lines are 

 drawn to scale ; the dotted lines show two possible shapes near the critical 

 point, of which the first is almost certainly right. 



That is, H must not only pass a maximum below the critical tempera- 

 ture, but must approach that temperature with so sharp a turn down- 

 ward as'to reach it with a vertical tangent. The H curve is throughout 

 a curve not only of constantly changing slope but also of constantly 

 increasing curvature as is shown in the upper part of Figure 8, and it is 

 only in very limited regions that the first three terms of a Taylor's 

 development can be expected to represent it with sufficient exactness. 

 It might be possible to invent a function having the general properties 

 indicated by Figure 8, if one knew the value of H at the critical 



30 See for example papers by Cailletet and Mathias, C. R., 1886, 102, 1202, 

 and 1887, 104, 1563; by Amagat, C. R., 1892, 114, 1093; and by Young, 

 Phil. Mag., 1900, 50, 291. See also the diagrams for normal pentane on pages 

 166 and 167 of Young's book on Stoichiometry, Longman's (1908). 



