GIBBS' PAPERS I AND II 41 



1 a 8a 



2762' ^^ " 27 Rb' 



la 8a 



Vc = 3o, P' ~ 7^77' ^c ~ > (5) 



and 



6=^^ a = 3po^;c^ 7^ = ^^^ (6) 



3' " ' 3 f, 



c 



There is no great difficulty in determining pc, tc from observa- 

 tion. Sketch of possible methods. The determination of Vc is 

 more difficult because infinitesimal changes in v near Vc produce 

 changes of p, t from pc and tc which are infinitesimals of higher 

 order and hence slight changes in p and t from pc and tc produce 

 large variations in v from Vc, — as may be seen geometrically 

 from the shape of the isothermals in the vicinity of the critical 

 point. However, we may determine Vc by the known value 

 oiR. 



Lecture XXV. Discussion of the accuracy with which van 

 der Waals' equation represents the physical facts. The critical 

 locus may be obtained from the condition that Sv^v along the 

 isothermal from one of its intersections (p, v^ with the critical 

 locus to the other {p, v^ must be equal to p{v2 — Vi) by the areal 

 of property previously proved. Hence 



p{v2 -V,) - ~ -^ - + nt log -^— - = 0. (7) 



V2 vi V2 — 



Equation (1) holds for p, Vi, t and for p, V2, t. Eliminate p, t. 

 Then 



V2 + vi , yi - & , Vi , V2 



log -I + — = 0. 



Let 



^^2 — i^i 1^2 — 6 Vi — b V2 — b 



Vr-b _ V2-b 



^'~ b ' ^'- b 



Then with P = F1/F2 we have 



V2 21ogP _ L _ 1' 

 P - 1 P 



7i = PV2. 



