498 J. W. Gibbs — £!quilibriuni of Heterogeneous Substances. 



nature and state of these masses together with the quantities of the 

 foreign substances which may be present in the iihn. (See page 483.) 

 Problems relating to processes of solidification and dissolution seem 

 hardly capable of a satisfactory solution, except on this supposition, 

 which appears in general allowable with respect to the surfaces pro- 

 duced by these processes. But in considering the equilibrium of 

 fluids at the surface of an unchangeable solid, such a limitation is 

 neither necessary nor convenient. The following method of treating 

 the subject will be found more simple and at the same time more 

 general. 



Let us suppose the superficial density of energy to be determined 

 by the excess of energy in the vicinity of the surface over that which 

 would belong to the solid, if (with the same temperature and state 

 of strain) it were bounded by a vacuum in place of the fluid, and to 

 the fluid, if it extended with a uniform volume-density of energy just 

 up to the surface of the solid, or, if in any case this does not suffi- 

 ciently define a surface, to a surface determined in some definite way 

 by the exterior particles of the solid. Let us use the symbol (fg) to 

 denote the superficial energy thus defined. Let us suppose a superficial 

 density of entropj^ to be determined in a manner entirely analogous, 

 and be denoted by (;/§). In like manner also, for all the components 

 of the fluid, and for all foreign fluid substances which may be present 

 at the surface, let the superficial densities be determined, and denoted 

 by (/"a), (^ a)? •-'^c. These superficial densities of the fluid components 

 relate solely to the matter which is fluid or movable. All matter 

 which is immovably attached to the solid mass is to be regarded as a 

 part of the same. Moreover, let ? be defined by the equation 



i={f.^)-t{iH)~ ^,_{r.,)- f.i^{T\)- iitc. (676) 



These quantities will satisfy the following general relations — 



c?(fs) = t (^Vs) +M2 ^{^2) + /^3 ^(^3) + 6tc., (677) 



cU=z-{f]^)dt-{r.^)dfA^—{r^)d].i^-^lc. (678) 



In strictness, these relations are subject to the same limitation as 

 (674) and (675). But this limitation may generally be neglected. 

 In fact, the values of ?, (fg), etc. must in general be much less 

 affected by variations in the state of strain of the surface of the solid 

 than those of O", fs(i)? etc. 



The quantity 5 evidently represents the tendency to contraction in 

 that portion of the surface of the fluid which is in contact with the 

 solid. It may be called the sitperficifd tension of the fluid in co)itact 

 with the solid. Its value may be either positive or negative. 



