496 J. W. Gibbs — Equilihrium of Heterogeneous Substances. 



sary that at every point of the line 



^{aST)^0 (671) 



for any j^ossible displacement of the line. Those displacements are to 

 be regarded as possible which are not prevented by the solidity of 

 the masses, when the interior of every solid mass is regarded as 

 incapable of motion. At the surfaces between solid and fluid masses, 

 the processes of solidification and dissolution will be possible in some 

 cases, and impossible in others. 



The simplest case is when two masses are fluid and the third is 

 solid and insoluble. Let us denote the solid by S, the fluids by 

 A and B, and the angles filled by these fluids by a and (3 respec- 

 tively. If the surface of the solid is continuous at the line where it 

 meets the two fluids, the condition of equilibrium reduces to 



Cab cos ol= 0-Bs- (^AS- (^'72) 



If the line where these masses meet is at an edge of the solid, the 

 condition of equilibrium is that 



Cab cos « ^ O-Rs — O'as, \ (573) 



and Cab cos /i ^ Cas — o-rs ; ' 



which reduces to the preceding when a-\-(3=:7t. Since the dis- 

 placement of the line can take place by a purely mechanical process, 

 this condition is capable of a more satisfactory experimental verifica- 

 tion than those conditions which relate to processes of solidification 

 and dissolution. Yet the frictional 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 distri- 

 buted, 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 inore 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 condi- 

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

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

 used on page 490. The condition of equilibrium relating to the line 



