320 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



precisely as if both masses were fluid, and a- denoted the tension 

 of their common surface, and (p f ) the true pressure in the mass 

 specified. (Compare (619).) 



The obstacles to an exact experimental realization of these relations 

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

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

 passive resistances to the processes 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 invariable. If the crystal grows on one side a distance SN, 

 without other change, the increment of energy in the vicinity of 

 the surface will be 



(e v ' - e v '> 8N+ If(e m ' I' cosec o>' - e s(1) I' cot co')SN, 



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

 of the phenomena which have been observed with 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 effect, 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 differences in the values of <7 IW (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 discontinuity with respect to crystalline structure, which must be 

 formed by the freezing together of the two masses of ice when the axes of crystal- 

 lization 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 <r n , which is 

 determined for this surface by the same principles 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, this influence is probably of a tolerably constant 

 character, and is evidently not sufficient 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 surfaces and without pressure, it would be necessary 

 that <r n ^2or iw , except so far as the case is modified by passive resistances to change, 

 and by the inequality in the values of <TH and <r iw 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. 



