J. W. Gihhs — EipdUhrlum of Ileteroffeneous Substances. 485 



element of the surface may be neglected (with respect to its effect on 

 the value of a) in the case of isotropic solids, it is quite otherwise 

 with crystals. Also, while the surfaces of equilibrium between fluids 

 and soluble isotropic solids are without discontinuities of direction, 

 being in general curved, a crystal in a state of equili'/rium with a 

 fluid in which it can dissolve is bounded in general by a broken sur- 

 face consisting of sensibly plane portions. 



For isotropic solids, the conditions of equilibrium may be deduced 

 as follows. If we suppose that the solid is unchanged, except that an 

 infinitesimal portion is dissolved at the surface where it meets the 

 fluid, and that the fluid is considerable in quantity and remains 

 homogeneous, the increment of energy in the vicinity of the surface 

 Avill be represented by the expression 



/[6v'- fv" 4-(c^ + c^) 6s^,,] SNDs 

 where Ds denotes an element of the surface, dN^ the variation in its 

 position (measiired normally, and regarded as negative when the solid 

 is dissolved), Cj and C2 its principal curvatures (positive when 

 their centers lie on the same side as the solid), fgci) ^he surface- 

 density of energy, fy' a.nd fy" tbe volume-densities of energy in the 

 solid and fluid respectively, and the sign of integration relates to the 

 elements Ds. In like manner, the increments of entropy and of the 

 quantities of the several components in the vicinity of the surface 

 will be 



fbh'-V^'" + (c,4-'-o) %(!,] SNBs, 



etc. 

 The entropy and the matter of different kinds i-epresented by these 

 expressions we may suppose to be derived from the fluid mass. 

 These expressions, therefore, with a change of sign, will represent 

 the increments of entropy and of the quantities of the components 

 in the whole space occupied by the fluid except that which 

 is immediately contiguous to the solid. Since this space may be 

 regarded as constant, the increment of energy in this space may be 

 obtained [according to equation (12)] by multiplying the above 

 expression relating to entropy by —t, and those relating to the 

 components by — /.</', - /./g, etc.,* and taking the sum. If to this 



* The potential jj^ , " is marked by double accents in order to indicate that its value 

 is to be determined in the fluid mass, and to distinguish it from the potential/^,' 



