J. W. Gibhs — Eqiiilihriimi of Heterogeneoiis Substances. 489 



precisely as if both masses were fluid, and (J denoted the tension of 

 their common surface, and (/>') the true pressure in the mass specified. 

 [Compare (01 9). J 



The obstacles to an exact experimental realization of these rela- 

 tions are very great, principally from the want of absolute uniformity 

 in the internal structure of amorphous solids, and on account of the 

 l^assive resistances to the jjrocesses which are necessary to bring- 

 about a state satisfying the conditions of theoretical equilibrium, 

 but it may be easy to verify the general tendency toward diminution 

 of surface, which is implied in the foregoing equations.* 



Let us apply the same method to the case in which the solid is 

 a crystal. The surface between the solid and fluid will now consist 

 of plane portions, the directions of which may be regarded as invari- 



* It seems probable that a tendency of this kind plays an important part in some 

 of the phenomena which have been observed witli respect to the freezing together 

 of pieces of ice. (See especially Professor Faraday's " Note on Regelation" in the 

 Proceedings of the Royal Society, vol. x, p. 440 ; or in the Philosophical Magazine, 4th ser., 

 vol. xxi, p. 146.) Although this is a body of crystalline structure, and the action 

 which takes place is doubtless influenced to a certain extent by the directions of 

 the axes of crystallization, yet, since the phenomena have not been observed to 

 depend upon the orientation of the pieces of ice, we may conclude that the efEect, so 

 far as its general character is concerned, is such as might take place with an isotropic 

 body. In other words, for the purposes of a general explanation of the phenomena 

 we may neglect the diiierences in the values of c7iw (the suffixes are used to indicate 

 that the symbol relates to the surface between ice and water) for different orientations 

 of the axes of crystallization, and also neglect the influence of the surface of discon- 

 tinuity with respect to crystalline structure, which must be formed by the freezing 

 together of the two masses of ice when the axes of crystallization in the two masses 

 are not similarly directed. In reality, this surface — or the necessity of the formation 

 of such a surface if the pieces of ice freeze together — must exert an influence adverse 

 to their union, measured by a quantity an, which is determined for this surface by 

 the same princii^les as when one of two contiguous masses is fluid, and varies with 

 the orientations of the two systems of crystallographic axes relatively to each other 

 and to the surface. But under the circumstances of the experiment, since we may 

 neglect the possibility of the two systems of axes having precisely the same directions, 

 tills influence is probably of a tolerably constant character, and is evidently not suffi- 

 cient to alter the general nature of the result. In order wholly to prevent the 

 tendency of pieces of ice to freeze together, when meeting in water with curved sur- 

 faces and without pressure, it would be necessary that ffn— 2(Tiw, except so far as the 

 case is modified by passive resistances to change, and by the inequality in the values 

 of (Tn and (Tiw for different directions of the axes of crystallization. 



It will be observed that this view of the phenomena is in harmony with the 

 opinion of Professor Faraday, With respect to the union of pieces of ice as an 

 indirect consequence of pressure, see page 198 of volume xi of the Proceedings of the 

 Royal Society ; or the Philosophical Magazine, 4th ser., vol. xxiii, p. 407. 



