Page:Scientific Papers of Josiah Willard Gibbs.djvu/363

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 contractions 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 conditions 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

$\textstyle \sum \displaystyle (\sigma S),$

the summation relating to all the surfaces of discontinuity. This indicates the same tendency towards changes diminishing the value of $\textstyle \sum \displaystyle (\sigma S)$, which appears in other cases.^[1]

1. 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

   $\sigma _{SA}+\sigma _{WA}>\sigma _{SW},$

   where the suffixes $_{S},_{A},$, 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 æolotropic properties of the ice, is

   $\sigma _{SW}+\sigma _{IW}>\sigma _{SI},$

   where the suffixes $_{S},_{A},$, 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.