EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 197 



adapt our language to what we may regard as the most general case, 

 viz., that in which the fluids contain the substance of the solid but 

 are not wholly composed of that substance), the fluids in equilibrium 

 with the solid are all supersaturated with respect to the substance 

 of the solid, except when the solid is in a state of hydrostatic stress ; 

 so that if there were present in any one of these fluids any small frag- 

 ment of the same kind of solid subject to the hydrostatic pressure of 

 the fluid, such a fragment would tend to increase. Even when no 

 such fragment is present, although there must be perfect equilibrium 

 so far as concerns the tendency of the solid to dissolve or to increase 

 by the accretion of similarly strained matter, yet the presence of the 

 solid which is subject to the distorting stresses, will doubtless facilitate 

 the commencement of the formation of a solid of hydrostatic stress 

 upon its surface, to the same extent, perhaps, in the case of an 

 amorphous body, as if it were itself subject only to hydrostatic 

 stress. This may sometimes, or perhaps generally, make it a necessary 

 condition of equilibrium in cases of contact between a fluid and an 

 amorphous solid which can be formed out of it, that the solid at the 

 surface where it meets the fluid shall be sensibly in a state of hydro- 

 static stress. 



But in the case of a solid of continuous crystalline structure, sub- 

 jected to distorting stresses and in contact with solutions satisfying 

 the conditions deduced above, although crystals of hydrostatic stress 

 would doubtless commence to form upon its surface (if the distorting 

 stresses and consequent supersaturation of the fluid should be carried 

 too far), before they would commence to be formed within the fluid 

 or on the surface of most other bodies, yet within certain limits the 

 relations expressed by equations (393)-(395) must admit of realization, 

 especially when the solutions are such as can be easily supersaturated.* 



It may be interesting to compare the variations of p, the pressure 

 in the fluid which determines in part the stresses and the state of 

 strain of the solid, with other variations of the stresses or strains in 

 the solid, with respect to the relation expressed by equation (388). 

 To examine this point with complete generality, we may proceed in 

 the following manner. 



Let us consider so much of the solid as has in the state of reference 

 the form of a cube, the edges of which are equal to unity, and 

 parallel to the co-ordinate axes. We may suppose this body to be 

 homogeneous in nature and in state of strain both in its state of 



*Tbe effect of distorting stresses in a solid on the phenomena of crystallization and 

 liquefaction, as well as the effect of change of hydrostatic pressure common to the 

 solid and liquid, was first described by Professor James Thomson. See Trans. R. S. 

 Edin., vol. xvi, p. 575; and Proc. Roy. Soc., vol. xi, p. 473, or Phil. Mag., ser. 4, vol. 

 xxiv, p. 395. 



