EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 289 



the sides to these surfaces, each side being perpendicular to the 

 corresponding surface, and equal to its tension. With respect to 

 the formation of new surfaces of discontinuity in the vicinity of the 

 point especially considered, the system is stable, if every diagonal 

 of the polygon is less, and practically unstable, if any diagonal is 

 greater, than the tension which would belong to the surface of dis- 

 continuity between the corresponding masses. In the limiting case, 

 when the diagonal is exactly equal to the tension of the corresponding 

 surface, the system may often be determined to be unstable by the 

 application of the principle enunciated to an adjacent point of the 

 line in which the surfaces of discontinuity meet. But when, in 

 the polygons constructed for all points of the line, no diagonal is in 

 any case greater than the tension of the corresponding surface, but 

 a certain diagonal is equal to the tension in the polygons constructed 

 for a finite portion of the line, farther investigations are necessary 

 to determine the stability of the system. For this purpose, the 

 method described on page 249 is evidently applicable. 



A similar proposition may be enunciated in many cases with 

 respect to a point about which the angular space is divided into 

 solid angles by surfaces of discontinuity. If these surfaces are in 

 equilibrium, we can always form a closed solid figure without re- 

 entrant angles of which the angular points shall correspond to the 

 several masses, the edges to the surfaces of discontinuity, and the 

 sides to the lines in which these edges meet, the edges being per- 

 pendicular to the corresponding surfaces, and equal to their tensions, 

 and the sides being perpendicular to the corresponding lines. Now 

 if the solid angles in the physical system are such as may be sub- 

 tended by the sides and bases of a triangular prism enclosing the 

 vertical point, or can be derived from such by deformation, the 

 iigure representing the tensions will have the form of two triangular 

 pyramids on opposite sides of the same base, and the system will 

 be stable or practically unstable with respect to the formation of 

 a surface between the masses which only meet in a point, according 

 as the tension of a surface between such masses is greater or less 

 than the diagonal joining the corresponding angular points of the 

 solid representing the tensions. This will easily appear on consider- 

 ation of the case in which a very small surface between the masses 

 would be in equilibrium. 



The Conditions of Stability for Fluids relating to ike Formation 

 of a New Phase at a Line in which Three Surfaces of Dis- 

 continuity meet. 

 With regard to the formation of new phases there are particular 



conditions of stability which relate to lines in which several surfaces 

 G.I. T 



