J. Vi^. Glhhs — EquiUhrhou of Heterogeneous Substances. 357 



form iipou its surface (if the distoi'ting stresses and consequent 

 supersaturation of the fluid should be carried too far), before 

 they Avould 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 realiza- 

 tion, especially when the sohitions are such as can be easily super- 

 saturated.* 



It may be interesting to compare the variations of ^;, 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 

 reference and in its variable state. (This involves no loss of 

 generality, since we may make the unit of length as small as we 

 choose.) Let the fluid meet the solid on one or both of the surfaces 

 for which Z' is constant. We may su^^pose these surfaces to remain 

 perpendiculartotheaxisofZ in the variable state of the solid, and the 

 edges in which y' and z' are both constant to remain parallel to the 

 axis of JC. It will be observed that these suppositions only fix the 

 position of the strained body relatively to the co-ordinate axes, and 

 do not in any way limit its state of strain. 



It follows from the suppositious which we have made that 



dz dz d%i 



-^ = const. Z.0, —:= const. =0, ^ = const. =: ; (398) 



and 



A'„=:0, Fz, = 0, Zy,,=.—p~^-^-. (399) 



dx dy ^ ' 



7 w I ^-^ 7 ^^•'' I ^- 7 ^^^ . T^ 7 *^y (^^ (fy -, dz 



Hence, by (355), 

 dey—tdi/v,-\-X^,( 

 Again, by (388), 



* The 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 Tran^. R. S. 

 Edin., vol. xvi, p. 575; and Proc. Roy. Soc, vol. xi, p. 47.^>, or PJiil. Mag., S. 4, vol. 

 xxiv, p. 395. 



