28 WILSON ART. c 



Lecture XVI IL The solid-liquid and solid- vapor lines; the 

 "triple-point" and the triply tangent plane. The relation 



dp Q 



dt {vv — VL)t 



for the invariant system consisting of liquid and vapor. 



Lecture XIX. Integrate de = td-q — pdv from liquid to vapor 

 phase, t and p being constant. 



€r — iL = t{T}v — -til) — p(vr — Vl) 



or 



^Y = tv — triv + PVV = €;. — tr}L + PVL = fi. 



The function f has the same value. The interpretation of f as 

 the intercept of the tangent plane on the e-axis. The equation 



,. ,. . dp rjv - riL Q 

 dtv = d^L gives — = = -• 



dt Vv — Vl [Vv — Vijt 



The discontinuity of dp/dt at the freezing point. Discussion of 

 the physical meaning of the Maxwell relations. 



Lecture XX.* In the py-diagram the isothermals in the vapor 

 state start from large values of v approximately like the hyper- 

 bolas pv = at; SiS V decreases their form is modified somewhat 

 because when the vapor becomes dense the relation pv = at 

 is somewhat inexact If the vapor starts to condense for values 

 p = p',v = v' the isothermal becomes a straight line p = p' 

 and so remains until condensation is completed aX p = p' = p" 

 and V = v" < v'. From this point as v decreases the iso- 

 thermal rises rapidly because a Hquid is compressed only with 

 rapidly increasing pressure. The locus of the points {p\ v') and 



* To this point the lecturer had been following his two Papers I and 

 II (Vol. I, pp. 1-54) with numerous omissions, with very few modifica- 

 tions, and with considerable elaboration of the physical principles and 

 facts underlying the subject. From here on he goes into a very consider- 

 able development, which though perfectly natural and now found in 

 other books, is not found in his writings. It seems that these applica- 

 tions of his own may have so great an interest as to justify following 

 them in considerable detail in the order of his thought. 



