488 J. W. Gibbs — Equilibrium of Heterogeneous Substances. 



if the fluid in contact with the solid is not renewed, the system will 

 generally find a state of equilibrium in which the outermost portion 

 of the solid will be in a state of isotropic stress. If at first the solid 

 should dissolve, this would supersaturate the fluid, perhaps until a state 

 is reached satisfying the condition of equilibrium with the stressed 

 solid, and then, if not before, a deposition of solid matter in a state of 

 isotropic stress would be likely to commence and go on until the fluid 

 is reduced to a state of equilibrium with this new solid matter. 



The action of gravity will not aflfect the nature of the condition of 

 equilibrium for any single point at which the fluid meets the solid, 

 but it will cause the values oi p" and /^," in (661) to vary according 

 to the laws expressed by (612) and (617). If we suppose that the 

 outer part of the solid is in a state of isotropic stress, which is the 

 most important case, since it is the only one in which the equilibrium 

 is in every sense stable, we have seen that the condition (661) is at 

 least sensibly equivalent to this : — that the potential for the sub- 

 stance of the solid Avhicli would belong to the solid mass at the 

 temperature t and the pressure ^/+ {<^ i-\- "^s) (^ must be equal to ///'. 

 Or, if we denote by (^^') the pressure belonging to solid with the 

 temperature t and the potential equal to /<i", the condition may be 

 expressed in the form 



{2)')=p"+{c,^c^)0. (662) 



Now if we write ;/" for the total density of the fluid, we have by (612) 



dp"=-gy"dz. 

 By (98) d{p')^y,'<ni,\ 



and by (617) c?//," =■ — (/ dz ; 



whence d {p'j =. — (/ Yi dz. 



Accordingly we have 



d{p')^dp" = g{y"-y^')dz, 

 and 



{p')-p" = g{r"-y,')z, 



z being measured from the horizontal plane for which {p')=^2^"- 

 Substituting this value in (662), we obtain 



c,+c^ = ''^^'"j^'''h , (663) 



generalized so as to hold true of the formation of new solid matter of any kind on 

 the surface as follows : — that new solid matter of any Ivind will not be formed upon 

 the surface (with more than insensible thickness), if the second member of ((361) cal- 

 culated for such new matter is greater than the potential in the fluid for such matter. 



