650 RICE ART. L 



enough it would mean that the equiUbrium of the Hne of dis- 

 continuity at d, without any formation of the phase D, would be 

 at least practically unstable ; for if a small filament of the phase 

 D should be formed a little greater than Vd in size per unit length 

 the formation of more of the phase would tend to occur. 

 On the other hand, if po happened to be less than the expression 

 written above, Wv would be negative, and the equilibrium of 

 this filament of the phase D would be stable; any small dis- 

 turbance increasing it would not tend to cause further growth 

 but the filament would tend to return to its equilibrium size. 

 Were Vd small enough this would be tantamount to saying that 

 the equilibrium of the original Une of discontinuity was stable. 

 On pages 294-296 Gibbs goes into more detail concerning this 

 for each of the three special cases where the tensions can be 

 represented as in his Figure 15, or are too small to be so repre- 

 sented, or are too large. 



53. The Details of the Argument Omitted from the Summary 



in {52) 



Let us now return and fill in the omitted details. We know 

 from earlier parts of Gibbs' treatise that when the values of tem- 

 perature and potentials remain constant, so that all the tensions 

 and pressures are determined, the equilibrium of any configura- 

 tion is determined by the test that for any deformation of the 

 configuration to an adjacent configuration, equilibrium or not, 

 the variation 



S(t5s - 2p5v = 0, 



and if the equilibrium is stable the variation 



2o-As - SpAv > 0, 



which means that for given values of the tensions and pressures 

 the quantity 



'Zas — Spy 



is a minimum for a stable configuration of the surfaces and 

 volumes. (For convenience we denote the points where the 



