256 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



required for the formation of such a globule of a certain size (viz., 

 that which would be in equilibrium with the surrounding mass), will 

 always be positive. Nor can smaller globules be formed, for they can 

 neither be in equilibrium with the surrounding mass, being too small, 

 nor grow to the size of that to which W relates. If, however, by 

 any external agency such a globular mass (of the size necessary for 

 equilibrium) were formed, the equilibrium has already (page 243) 

 been shown to be unstable, and with the least excess in size, the 

 interior mass would tend to increase without limit except that 

 depending on the magnitude of the exterior mass. We may therefore 

 regard the quantity W as affording a kind of measure of the stability 

 of the phase to which p" relates. In equation (557) the value of W 

 is given in terms of cr and p' p". If the three fundamental equa- 

 tions which give cr, p', and p" in terms of the temperature and the 

 potentials were known, we might regard the stability ( W) as known 

 in terms of the same variables. It will be observed that when^/=jp" 

 the value of W is infinite. If p' p" increases without greater 

 changes of the phases than are necessary for such increase, W will 

 vary at first very nearly inversely as the square of p' p". If p' p" 

 continues to increase, it may perhaps occur that W reaches the value 

 zero ; but until this occurs the phase is certainly stable with respect 

 to the kind of change considered. Another kind of change is con- 

 ceivable, which initially is small in degree but may be great in its 

 extent in space. Stability in this respect or stability in respect to 

 continuous changes of phase has already been discussed (see page 

 105), and its limits determined. These limits depend entirely upon 

 the fundamental equation of the homogeneous mass of which the 

 stability is in question. But with respect to the kind of changes 

 here considered, which are initially small in extent but great in 

 degree, it does not appear how we can fix the limits of stability with 

 the same precision. But it is safe to say that if there is such a limit 

 it must be at or beyond the limit at which <r vanishes. This latter 

 limit is determined entirely by the fundamental equation of the 

 surface of discontinuity between the phase of which the stability is 

 in question and that of which the possible formation is in question. 

 We have already seen that when a- vanishes, the radius of the 

 dividing surface and the work W vanish with it. If the fault in 

 the homogeneity of the mass vanishes at the same time (it evidently 

 cannot vanish sooner), the phase becomes unstable at this limit. 

 But if the fault in the homogeneity of the physical mass does not 

 vanish with r, or and W, and no sufficient reason appears why 

 this should not be considered as the general case, although the 

 amount of work necessary to upset the equilibrium of the phase 

 is infinitesimal, this is not enough to make the phase unstable. 



