EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 327 



condition is capable of a more satisfactory experimental verification 

 than those conditions which relate to processes of solidification and 

 dissolution. Yet the fractional resistance to a displacement of the line 

 is enormously greater than in the case of three fluids, since the 

 relative displacements of contiguous portions of matter are enormously 

 greater. Moreover, foreign substances adhering to the solid are not 

 easily displaced, and cannot be distributed by extensions and con- 

 tractions of the surface of discontinuity, as in the case of fluid masses. 

 Hence, the distribution of such substances is arbitrary to a greater 

 extent than in the case of fluid masses (in which a single foreign 

 substance in any surface of discontinuity is uniformly distributed, 

 and a greater number are at least so distributed as to make the 

 tension of the surface uniform), and the presence of these substances 

 will modify the conditions of equilibrium in a more irregular manner. 

 If one or more of three surfaces of discontinuity which meet in a 

 line divides an amorphous solid from a fluid in which it is soluble, 

 such a surface is to be regarded as movable, and the particular con- 

 ditions involved in (671) will be accordingly modified. If the soluble 

 solid is a crystal, the case will properly be treated by the method 

 used on pages 320, 321. The condition of equilibrium relating to the 

 line will not in this case be entirely separable from those relating to 

 the adjacent surfaces, since a displacement of the line will involve a 

 displacement of the whole side of the crystal which is terminated at 

 this line. But the expression for the total increment of energy in the 

 system due to any internal changes not involving any variation in 

 the total entropy or volume will consist of two parts, of which one 

 relates to the properties of the masses of the system, and the other 

 may be expressed in the form 



the summation relating to all the surfaces of discontinuity. This 

 indicates the same tendency towards changes diminishing the value 

 of Z(o-s), which appears in other cases.* 



* The freezing together of wool and ice may be mentioned here. The fact that a fiber 

 of wool which remains in contact with a block of ice under water will become attached 

 to it seems to be strictly analogous to the fact that if a solid body be brought into such 

 a position that it just touches the free surface of water, the water will generally rise up 

 about the point of contact so as to touch the solid over a surface of some extent. The 

 condition of the latter phenomenon is 



where the suffixes 8 , A , and w refer to the solid, to air, and to water, respectively. In 

 like manner, the condition for the freezing of the ice to the wool, if we neglect the 

 seolotropic properties of the ice, is 



where the suffixes e > w> and i relate to wool, to water, and to ice, respectively. See 

 Proc. Roy. Soc., vol. x, p. 447; or Phil. Mag., 4th ser., vol. xxi, p. 151. 



