J. W. Gihhs — EquiUbrlnin of Heterogeneous Substances. 487 



of ('([nation ((j()l), when the stresses of the solid are sensibly iso- 

 tropic, is sensibly equal to the potential of the same body at the 

 same temperature but with the pressure p" -\- {(^^ -{• Co) ff, and the 

 condition of equilibrium with respect to dissolving for a solid of 

 isotropic stresses may be expressed with sutlicient accuracy by saying 

 that the potential for the substance of the solid in the fluid must 

 have this value. In like manner, when the solid is not in a state of 

 isotropic stress, the difference of the two pressures in question will 

 not sensibly affect the values of fy' ai^d ?;v', and the value of the 

 second member of the equation may be calculated as \i p"-\- (c, + Co) o' 

 represented the true pressure in the solid in the direction of the nor- 

 mal to the surface. Therefore, if we had taken for granted that the 

 (piantity G represents the tension of a surface between a solid and a 

 fluid, as it does when both masses are fluid, this assumption would 

 not have led us into any practical error in determining the value of 

 the potential ///' which is necessary for equilibrium. On the other 

 hand, if in the case of any amorphous body the value of o" differs 

 notably from the true surface-tension, the latter quantity substituted 

 for o' in (661) will make the second member of the equation equal to 

 the true value of ///, when tlie stresses are isotropic, but this will not 

 be equal to the value of yu /' in case of equilibrium, unless Cj -\- c^ = 0. 

 When the stresses in the solid are not isotropic, equation (661) 

 may be regarded as expressing the condition of equilibrium with 

 respect to the dissolving of the solid, and is to be distinguished from 

 the condition of equilibrium with respect to an increase of solid 

 matter, since the new matter would doubtless be deposited in a state 

 of isotropic stress. (The case woidd of course be different with 

 crystalline bodies, which are not considered here.) The value of 

 //j" necessary for equilibrium with respect to the formation of new 

 matter is a little less than that necessary for equilibrium with respect 

 to the dissolving of the solid. In regard to the actual behavior of 

 the solid and fluid, all that the theory enables us to predict with 

 certainty is tliat the solid will not dissolve if the value of the poten- 

 tial ///' is greater than that given by the equation for the solid with 

 its distorting stresses, and that new matter will not be formed if the 

 value of /<i" is less than the same equation would give for the case of 

 the solid w4th isotropic stresses.* It seems probable, however, that 



* 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 

 134-137, 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 



Trans. Conn. Acad., Vol. III. 63 - April, 1878. 



