SURFACES OF DISCONTINUITY 645 



certain conditions; so also will (Tbd,(^cd, (Tbc, and aco, ctad, oca. 

 For instance, if oab > cid + obd no formation of D would take 

 place naturally; the problem of stability as regards formation 

 of Z> is settled at once. Thus for a problem to exist at all we 

 must postulate 



CfiC ^ o'bd "T O'er), 



<^CA = <^CD + ^AD, 

 CTaB = O-AD ~\~ CFbD- 



If now it happened to be true that cab = o-ad -\- o-bd we might 

 have the formation of Z) as a film between A and B, as in 

 Figure 6. This would resemble the similar cases dealt with on 

 pages 259-264 of Gibbs; the film would form if po were 

 greater than a certain critical pressure 



(TadPa + (TbdPb 

 (Tad -j- (Tbd 



If (Tab < (Tad -h (Tbd we would not have formation of D in this 

 way even in a lentiform mass, the argument being once more 

 that of pages 259-264. But taking the tension conditions to be 



(Tbc ^ (Tbd "r (Tcd, 



(T CA <^ (Tcd "I (Tad, 



(Tab <^ (Tad ~r (Tbd, 



we may consider the possibility of the mass D forming as a fil- 

 ament of triangular section stretching along the direction of the 

 original line of discontinuity. If the three pressures Pa, Pb, Pc 

 were equal, the sections of the surfaces B-C, C-A, A-B by the 

 plane of the paper would be straight lines, as in Figure 14 of 

 Gibbs, da, db, dc being the continuations of these lines. If the 

 pressure po happened also to be equal to Pa (or Pb or p c) the 

 sections of the surfaces A-D, B-D, C-D by the paper, i.e, the 

 lines be, ca, ab would also be straight; but if po 9^ Pa the surfaces 

 A-D, B~D, C-D will be cylindrical with their generating lines per- 

 pendicular to the plane of the paper (Fig. 7) . Thus the lines be, 



