396 ./. W. Gihbs on a Represent<(tion by Surfaces 



wliere the line of that priucipiil curvature wliicli changes its sign 

 is tangent to the line whicli sepai'ates positive from negative curv- 

 atures. 



From the last paragraphs we may derive the folloAving physical 

 property of the critical state: — Although this is a limiting state 

 between those of stability and those of instability in respect to con- 

 tinuous changes, and although such limiting states are in general 

 unstable in respect to sucli changes, yet the critical state is stable in 

 regard to them. A similar proposition is true in regard to absolute 

 stability, i. e., if we disregard the distinction between continuous and 

 discontinuous changes, viz: that although the critical state is a limit- 

 ing state between those of stability and instability, and although the 

 equilibrium of such limiting states is in general neutral (when we sup- 

 pose the substance surrounded by a medium of constant pressure and 

 temperature), yet the critical point is stable. 



From what has been said of the curvature of tlie j>rimitive surface 

 at the critical point, it is evident, that if we take a ])oint in this sur- 

 face infinitely near to the critical point, and siich that the tangent 

 planes for these two points shall intersect in a line perpendicular to 

 the section of least curvature at the critical point, the angle made by 

 the two tangent planes will be an infinitesimal of the same order as 

 the cube of the distance of these points. Hence, at the critical point 



(!)<="• (|),=°' (li="' (li=''' 



(cPp\ l(Pp\ /(Pt\ ^ /dH\ 



{M="' {m="' (*^l="' {^-1="' 



and if we imagine the isothermal and isopiestic (line of constant pres- 

 sure) drawn for the critical point iipon the primitive sui'face, these 

 lines will have a contact of the third order. 



Now the elasticity of the substance at constant temperature and 

 its specific heat at constant ])ressure may be defined by the equations, 



= -"(^l ^='(§'1' 



therefore at the critical point 



The last four equations would also hold good if p were substituted 

 for t, and vice versa. 



