GIBBS' PAPERS I AND II 35 



AP PB 



'^ = ab'^^ab'^^ 



_ AP PB 



Shut up in the volume v and isolated, changes will go on in the 

 mixture which while unable to change e or y will increase 77. 

 Thus the unit of the substance will come to equilibrium at a 

 point on the thermodynamic surface e = tp, v = Vp, ri "^ tjp. 

 As the proof holds for any point P no point between A and B 

 can lie in the surface unless they all do. It follows that if a 

 tangent plane is drawn to the surface at any point which repre- 

 sents an entirely stable state of the body no point of the surface 

 can lie on that side of the plane for which entropy is greater. 

 Physically, in any change that would increase rj but involves the 

 formation of a state widely different (such as a new phase) there 

 is a certain reluctance* to take the step and this phenomenon 



* Lewis and Randall in their Thermodynamics, and the Free Energy 

 of Chemical Substances, McGraw-Hill (1923), say, on p. 17: "In the 

 work of Gibbs and some other writers upon thermodynamics, some proc- 

 esses are supposed to be of infinite slowness, but this view of the exist- 

 ence of a so-called "passive resistance" is apparently not supported by 

 experimental evidence . . . . " The term "passive resistance" is appar- 

 ently not used by Gibbs in Papers I and II; but that he would have re- 

 garded the reluctance to change exhibited in the phenomena of super- 

 cooling, superheating and supersaturating as due to such resistances is 

 rendered likely by his definitions and illustrations when he first intro- 

 duces the term, namely, in Paper III (Gibbs, I, p. 58) where he writes: 

 "In order to apply to any system the criteria of equilibrium which have 

 been given, a knowledge is requisite of its passive forces or resistances 

 to change, in so far, at least, as they are capable of preventing change. 

 (Those passive forces which only retard change, like viscosity, need 

 not be considered.) ... As examples, we may instance the passive 

 force of friction which prevents sliding when two surfaces of solids are 

 pressed together, . . . , that resistance to change which sometimes pre- 

 vents either of two forms of the same substance (simple or compound), 

 which are capable of existing, from passing into the other. ..." It cer- 

 tainly does not appear from this phraseology that Gibbs was supposing the 

 processes which he associated with the term passive resistance to be of 

 infinite slowness; indeed his underlining of the word preventing and his 



