SURFACES OF DISCONTINUITY 657 



so that the analogous result to [632] is 



d(Ws — Wr) = i d{(rAD Sad+ • . . — (Tbc Sbc— ' . .) 



= ^dW. 



and it follows that 



Hence 



3) 



Wa= IWy 

 Ws- Wy == i Wy. 



In the subsequent steps one need only consider conditions of 

 temperature and potentials for which pD{t, m) is greater than the 

 other pressures. Clearly the figure would not be possible 

 otherwise. 



55. The Stahility of a New Homogeneous Mass Formed at the 

 Point of Concurrence of Four Lines of Discontinuity 



In the last subsection on stability we have to return to the 

 equilibrium considered in the last paragraph on page 289 and to 

 the commentary thereon. Exactly the same principles are 

 applicable as before, and there will be no difficulty experienced 

 in following the argument, once the figure has been visualized. 

 The modification in the thread diagram used in commenting on 

 page 289 can easily be indicated. Above the drawing board 

 used there we place a wire frame in the shape of a tetrahedron 

 abed, with the vertex d uppermost and the base ahc nearest the 

 drawing board. Tie aioX,h to Y, cto Z and d to U, which is 

 above the frame, by tight threads. We now conceive the 

 phase D to be in the space in the truncated tetrahedron abcXYZ 

 between the surface ahc and the exterior envelop of the whole 

 system, and so on. The phase E is supposed to form inside the 

 tetrahedron. We are not to suppose that the surfaces abc, 

 etc., i.e. E-D, etc., are necessarily plane, nor for that matter 

 the surfaces D-A, etc. There are ten of these surfaces now. 



