EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 319 



the solid with isotropic stresses.* It seems probable, however, that 

 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 affect the nature of the condition of 

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

 it will cause the values of p" and fa" 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 substance of 

 the solid which would belong to the solid mass at the temperature t 

 and the pressure p"+(c 1 H-c 2 )0" mu st be equal to fa". Or, if we denote 

 by (p') the pressure belonging to solid with the temperature t and the 

 potential equal to fa", the condition may be expressed in the form 



(/)=/' +( Cl + C2 )o-. (662) 



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



By (98) 



and by (617) dfa" = gdz\ 



whence d(p') g y^dz. 

 Accordingly we have 



and 



z being measured from the horizontal plane for which (p')=p". 



Substituting this value in (662), we obtain 



*The possibility that the new solid matter might differ in composition from the 

 original solid is here left out of account. This point has been discussed on pages 

 79-82, but without reference to the state of strain of the solid or the influence of 

 the curvature of the surface of discontinuity. The statement made above may be 

 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 kind will not be formed upon 

 the surface (with more than insensible thickness), if the second member of (661) cal- 

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



