SURFACES OF DISCONTINUITY 639 



page 241 of Gibbs, the reader will see that he comes to the con- 

 clusion that "the system consisting of two homogeneous masses 

 and the surface of discontinuity with the negative tension is 

 ... at least practically unstable, if the surface of discontinuity 

 is very large, so that it can afford the requisite material without 

 sensible alteration of the values of the potentials." In conse- 

 quence Gibbs excludes from the discussion of stability surfaces 

 with negative tensions. Nevertheless the proviso about the size 

 of the surface is important; for if it is not satisfied the con- 

 clusion may not be entirely valid, and so stability might be 

 insured in cases where the interfacial surface is very small. 

 Another instance where the conclusion might not be justified 

 would arise if one of the masses took the form of a stratum so 

 thin that it no longer had the properties of a similar body in a 

 less laminated shape. (See the remark at the bottom of Gibbs I, 

 page 240.) 



The reader's attention is drawn to these points because in 

 the treatment of the colloid state negative interfacial tensions 

 must come into consideration. A large drop within another 

 medium will only break up "spontaneously" into two or more 

 drops if the free energy of the latter system is less than that 

 of the single drop. As the sum of the surfaces of the separate 

 drops is certainly greater than the surface of the parent drop, 

 this is impossible with a positive interfacial tension; but a de- 

 creased free energy becomes a possible result if the tension is 

 negative. In a paper published in the Z. physik. Chem., 46, 

 197 (1903) Donnan showed that from the point of view of the 

 Laplace-Gauss theory of capillary forces (briefly outlined in the 

 introductory sections of this article) it was possible to introduce 

 negative interfacial tensions and draw the conclusion that "in 

 certain cases the theory leads us to predict the spontaneous 

 production of extremely fine-grained heterogeneous mixtures, 

 in which one phase is distributed throughout another in a state 

 of very fine division." Of course the difficulty of the problem 

 is not in simply applying the notion of a negative tension, but 

 in demonstrating that at a certain critical thickness the free 

 energy of a film which is thinning out reaches a minimum and 

 thereafter increases if further thinning is continued, or that at 



