GIBBS' PAPERS I AND II 



47 



The point P = 1, T = 1 corresponding to F = 1 is the critical 

 point. As 



(-) 



\dT/v 



8/3 



V - 1/3' 



= 4. 



The values of V, T, P and (dP/dT)v are entered in the table 

 which clearly shows the cusp at (1, 1, 1) and from which the 

 envelope may be plotted easily. 



Lecture XXIX. We return to the consideration of coexistent 

 phases, basing the development upon the condition ^2 = Ti or 



€2 - Cl - t(V2 - Vl) + V(V2 - Vi) = 0. 



For 62 — €i we use (10) ; for 772 — Vi we use 



dp _ 7/2 — rji _ Q 1 



dt 1^2—1^1 t Vi — Vi 



previously derived. Thus the condition may be given the form 



a 



--^ + 1 = 0. 



pviVi p dt 



But the three roots of van der Waals' equation for p = const, 

 satisfy 



/Rt \ 



v^ — I \- j v 



a ah 



^ + - V =0, 



P 



V 



