388 J. W. Gibhs OH a Represent ( (Hon by Surfaces 



tangent plane i)i rolling upon the })riniitive surt'aee to turn al)Out its 

 instantaneous axis LV an infinitely small angle, so as to meet vVB in 



A', (^2) fiwd <^t will be equal to —^- and 1, respectively. Therefore, 

 ^ _ BL _ i]"—jl 



where v' and ;/' denote the volume and entropy for the point L, and 

 v/' and //" those for the point V. If we substitute for //" — //' its 



equivalent - {r denoting the heat of vaporization), we have the equa- 

 tion in its usual form, — 



dt t {v"— v')' 



Properties of the Surface relating to StabHity of Theriuodynafnic 



Equilibrium. 



We will now turn our attention to the geometrical properties of 

 the surface, which indicate whether the thermodynamic equilibrium 

 of the body is stable, unstable, or neutral. This will involve the con- 

 sideration, to a certain extent, of the nature of the processes which 

 take place when equilibrium does not sul)sist. We ^vill suppose the 

 body placed in a medium of constant pressure and temperature ; but 

 as, when the pressure <h- temperature of the body at its surface dif- 

 fers from that of the medium, the immediate contact of the two is 

 hardly consistent with the continuance of the initial pressure and 

 temperature of the medium, both of which we desire to suppose con- 

 stant, we will suppose the body separated fi-om the medium by an 

 envelop which will yield to the smallest differences of pressure 

 between the two, but which can only yield very gradually, and 

 which is also a very poor conductor of heat. It will be convenient 

 and allowable for the jmrposes of reasoning to limit its properties to 

 those mentioned, and to suppose that it does not occupy any space, 

 or absorb any heat except what it transmits, i. e., to make its volume 

 and its specific heat 0. By the intervention of such an envelop, we 

 may suppose the action of the body upon the medium to be so 

 retarded as not sensibly to disturb the uniformity of pressure and 

 temperature in the latter. 



When the body is not in a state of thermodynamic equilibrium, its 

 state is not one of those which are i-epresented l)y our surface. The 

 body, however, as a whole has a certain volume, entropy, and energy, 



