640 RICE ART. L 



a definite size a drop reaches a similar critical state as regards 

 its free energy. 



Considerations of space prevent us from anything more than 

 a passing reference to this very important theoretical problem ; 

 but the interested reader will find further discussions, which 

 bring in thermodynamical principles and the effects of surface 

 electric charges, in papers by R. C. Tolman (J. Am. Chem. 

 Soc, 35, 307, 317 (1913)) and N. von Raschevsky (Z. /. Physik, 

 46, 568 (1928); 48, 513 (1928); 51, 571 (1928)). In particular, 

 Raschevsky's papers emphasize the fact that in addition to the 

 purely surface phenomena a further important factor consists 

 in the rate at which differences of concentration arising from a 

 fast enough velocity of diffusion may give rise to inhomo- 

 geneities in the drop. 



XVI. The Formation of New Phases at Lines and Points of 



Discontinuity 



49. The Possible Growth of a Fifth Surface at a Line of Dis- 

 continuity Common to Four Surfaces of Discontinuity 

 Separating Four Homogeneous Masses 



Pages 287-300 deal with fresh possibilities in the way of new 

 formations in addition to the natural processes studied in pages 

 252-264. It might be possible under certain circumstances for 

 a new surface phase to develop in a system consisting of more 

 than three homogeneous masses. If there were three homo- 

 geneous masses a surface of discontinuity would already exist 

 between any pair, but if four masses were in existence and four 

 surfaces of discontinuity had one line in common, there would 

 be no surface between two pairs of the masses, and the problem 

 arises as to the possibility of the growth of a fifth surface be- 

 tween such a pair. This problem is treated in pages 287-289. 



The condition of equilibrium used is stated in equation [615]. 

 In Figure 11 on page 287 of Gibbs, the common line is supposed 

 to run perpendicular to the plane of the paper. We consider 

 ci, 0-2, o's, 0-4 to be the four tensions in the surfaces A-B, B-C, 

 C-D, D-A of which the lines in the figure are supposed to be 

 sections by the plane of the paper. Conceive any virtual dis- 



