SURFACES OF DISCONTINUITY 641 



placement of the line of discontinuity to an adjacent position 

 which is cut by the plane of the paper in a point 0'. (Not as 

 represented in Figure 12, however, but with four displaced Imes 

 all branchmg from 0'.) If the resolved components of the 

 displacement, perpendicular to the line of discontinuity and 

 lying individually in the surfaces, are 6Ti, 8T2, 8T3, 8Ti, then 

 the system of surfaces is in equilibrium if 



<TidTi -\- (X28T2 + asdTz + aidTi = 



for all possible displacements 00'. That is condition [615]. 

 Since the components of the displacements are actually parallel 

 to the lines OA, OB, OC, OD it appears that this is just the same 

 as the well-known "virtual work" condition for the equilibrium 

 of four coplanar forces which could be conceived to exist in the 

 plane of the paper, with magnitudes ai, 0%, az, a and with direc- 

 tions along the four hues.* Or for that matter we could 

 consider the system of conceptual forces "swung round" 

 through a right angle so that their directions would be at right 

 angles to the four surfaces as Gibbs conceives them to be drawn; 

 such a change in orientation would not affect their equilibrium, 

 if it existed before the change. Gibbs' Figure 13 is the usual 

 polygon -of -forces diagram drawn on this principle. Now sup- 

 pose that two masses of the liquids A and C were brought into 

 contact with one another and were found to have a surface 

 tension larger than that represented by the length of ay in 

 Figure 13; the condition represented in Figure 11 would be per- 

 fectly stable, since free energy does not tend to increase. If, 

 however, this tension were less than that represented by 0:7, 

 the condition would be practically unstable; but to come to a 

 definite conclusion in that case one would have to go more 

 fully into changes in the several components and potentials in 

 the four homogeneous masses occasioned by the development 

 of the surface represented by O'O". Smiilar considerations in 

 relation to the diagonal /3§ would govern the possible growth 

 of a surface between the masses B and D. 



* The reader must guard against the inference that the surface 

 tensions are really tangential forces in the surfaces. We have already 

 referred on p. 510 of this article to the convenience, but the physical 

 unreality, of this conception. 



