39^ PROCEEDINGS OF THE AMERICAN ACADEMY § lO 



"The peculiarity of this curve is that between the pres- 

 sures indicated by the horizontal lines, ^J^and DH^ any 

 horizontal line, such as CEG, cuts the curve in three differ- 

 ent points. One of these, indicated by C, evidently cor- 

 responds to the liquid state. Another, indicated by G, 

 corresponds to the gaseous state." 



Maxwell continues to the effect that E may be left out 

 of consideration, being a point of unstable equilibrium. 



Curves are also given of the general form A' B' C D' E' 

 F'G'H'K' and yl'^^"^V"^^ representing isothermals 

 at and above the critical temperature. All these curves 

 are concave upward as far as a certain point, such as E^ 

 then convex as far asy, and finally concave again. The 

 slope of all is at first downwards, and finally downwards. 

 Below a certain isothermal, the concave curvature is suf- 

 ficient to cause an upward slope between D and F; 

 above it, it is insufficient; and this particular isothermal is 

 characterized by having a slope which reaches zero as its 

 limit and then tends downward again. Now unless the 

 curvature changed its sign at the point where the curve 

 becomes horizontal, the slope on one or the other side of 

 this curve would be upward ; hence we may determine 

 this curve by supposing the slope and curvature to be 

 equal simultaneously to zero. It is evident, moreover, 

 that this is a complete definition of the curve, since no 

 other can at any point fulfil the same conditions. 



It is hardly necessary to add that this isothermal belongs 

 to what is called the "critical temperature." Below it, 

 since at E the slope is upward, there can always be found 

 for a given pressure two volumes, C and G^ at which the 

 substance is in stable equilibrium. Above it, since the 

 slope is always downwards, only one state is possible. 

 That is, the temperature of this isothermal is the limit up 

 to which a liquid is possible in contact with its vapor. 



The method of treating isothermals and determining 

 the critical temperature by the theory is extremely sim- 



