632 RICE ART. L 



Now a third fluid mass C is conceived to exist, made up entirely 

 of components which belong to A or B; i.e. C, having no com- 

 ponents other than those in A and B, might conceivably form 

 at the surface dividing A and B, and we are once more supposed 

 to know the fundamental equations of this fluid C so that 

 Pc(t, m) is a known function whose numerical value can therefore 

 be calculated for given values of t, ni, /X2, • • • In addition, 

 (TABit, m), (^Ac{t, m)> <^Bcit, fJi) are also known functions. For the 

 problem to be not merely trivial it is essential that (XAsit, /x) 

 should not be greater than (7Ac{i, m) + o-Bc{t, n). To see this 

 conceive a very thin layer of C to be situated between A and 

 B. This is equivalent to a dividing surface between A and B 

 whose surface tension is o-^ c + ctb c- Referring to the previous 

 subsection on conditions of stability (Gibbs, I, 240), we see 

 that if aAB > ctac + o'sc this is a more stable state than 

 if A and B exist with the ordinary surface of discontinuity 

 between them having the surface tension (Tab, which is presum- 

 ably greater than (Tac + (^b c- Thus for such a condition the 

 problem is settled offhand— the layer of C would certainly 

 form on the slightest disturbance. The problem is really 

 worth considering if (Tab ^ <tac -\- (^bc, or if ctab < c^c + csc- 

 Although in the latter case a plane film of C would obviously be 

 unstable for a reason similar to that just given, a lentiform film 

 might develop and so a quite definite problem is posited in this 

 case also. In a paper on emulsification (J. Phys. Chem., 31, 

 1682, (1927)) Bancroft criticizes the statement that vab cannot 

 be larger than cac + <^b c, but seems to be under a misapprehen- 

 sion as to the situation. Gibbs on page 258 does not assert 

 that as a general rule for three such fluids cab cannot be greater 

 than (Tac -\- (tbc'i he merely, for the purposes of the problem he is 

 discussing, rules out of account fluids for which such an in- 

 equality would be true, presumably (as the writer has pointed 

 out definitely) on the grounds that the problem does not 

 exist; it is solved in the very statement of such a condition. 

 Now if the temperature and potentials have such values that 

 Pc < VA{t, ij) (and of course < psit, m)), the phase cannot 

 form under any circumstances ; for if it formed as a plane sheet 

 between A and B (or as an anticlastic sheet for which Ci + C2 



