SURFACES OF DISCONTINUITY 643 



the whole state of equilibrium if it exists. The six edges of the 

 tetrahedron are perpendicular to the corresponding surfaces 

 and represent by their lengths the six surface tensions. The 

 four sides of the tetrahedron, viz., the triangles ^y8, ya8, a^b, 

 a/37 are perpendicular to OX, OY, OZ, OU, respectively, and if 

 the tetrahedron ajSyd were drawn with the point inside it, 

 the four points a, /?, 7, 8 would be respectively situated in the 

 masses A, B,C, D. It is hoped that in this way the reader may 

 grasp the meaning of the earlier sentences of the paragraph, 

 where the "closed solid figure" is the tetrahedron in our illus- 

 tration for four masses. (There is a small misprint in the 

 second sentence of the paragraph. Beginning after the second 

 comma of the sentence it should read "the edges to the sur- 

 faces of discontinuity, and the sides to the lines in which 

 these surfaces meet." Notice that "edge" refers to a line of the 

 representative tetrahedron, and "side" to a triangular face of 

 this tetrahedron; "line" and "surface" are retained for the 

 physical lines and surfaces of discontinuity in the system.) 

 After this is grasped, consider a greater number of masses whose 

 dividing surfaces intersect in pairs in lines all of which meet in 

 one point 0. Any group of four masses which have six dividing 

 surfaces between them, say, A, B, C, D can be represented as 

 above by a tetrahedron a^y8. Suppose there is another mass 

 A ', which has three dividing surfaces with the masses B, C, D, 

 but has no dividing surface with A, having only the point 

 in common with A. The condition for equilibrium of these 

 surfaces is bound up with a tetrahedron q:'/375 where a' is on the 

 opposite side of Py8 to a. All the edges of this double tetra- 

 hedron will have the right directions and lengths to corre- 

 spond to the surfaces and their tensions. If now a new sur- 

 face were to develop at between A and A' and to be in 

 equilibrium, the normal to this new surface would be parallel to 

 aa' and the tension of the surface A A' would be represented by 

 aa', so that for stability with respect to such a formation the 

 tension of the surface between two masses of A and A' would 

 have to be greater than that represented by aa'. 



