318 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



the solid in the two masses the same condition which would subsist 

 if both masses were fluid. 



Moreover, the compressibility of all solids is so small that, although 

 or may not represent the true tension of the surface, nor p" + (c^c^cr 

 the true pressure in the solid when its stresses are isotropic, the quan- 

 tities e v ' and jy v ' if calculated for the pressure ^ // +(c 1 +c 2 )o- with 

 the actual temperature will have sensibly the same values as if calcu- 

 lated for the true pressure of the solid. Hence, the second member 

 of equation (661), when the stresses of the solid are sensibly isotropic, 

 is sensibly equal to the potential of the same body at the same tem- 

 perature but with the pressure fi'+^+c^a; and the condition of 

 equilibrium with respect to dissolving for a solid of isotropic stresses 

 may be expressed with sufficient 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 e v ' and jj v ', and the value of the second member of the 

 equation may be calculated as if p" + (c^c^cr represented the true 

 pressure in the solid in the direction of the normal to the surface. 

 Therefore, if we had taken for granted that the quantity or 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 or differs notably from the true surface- 

 tension, the latter quantity substituted for <j in (661) will make the 

 second member of the equation equal to the true value of /*/, when 

 the stresses are isotropic, but this will not be equal to the value of /x/' 

 in case of equilibrium, unless ^-f c 2 = 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 would of course be different with 

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

 /*/' 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 that the solid will not dissolve if the value of the poten- 

 tial [if 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 PI is less than the same equation would give for the case of 



