SURFACES OF DISCONTINUITY 627 



known functions. Let E represent the energy of the system if 

 the space were entirely filled with the second phase; then 

 E -\- [e], by the definition of [e] in the text, is the energy of the 

 system with the non-homogeneous nucleus formed inside. But 

 of course [e] is not the e^ (nor are [77], [mi], . . . the same as rj^, 

 mi«, . . . ) by means of which a is defined. As usual, we postu- 

 late a definite position for the dividing surface, a sphere of 

 radius r. For the purpose of defining e^ this is supposed to be 

 filled with the homogeneous phase of the first kind right up 

 to the dividing surface, the second phase occupying the space 

 beyond ; the energy then would be 



E+v' (e/ - 6/0, 



4 

 where v' = i^rr^, and so 



o 



es = E + [e]- {E + v'(ey' - e/')} 

 = [e] - v'iey' - e/O, 

 with similar definitions for rj^, mi^, ... as in the text. 



47. The PossihiliUj of the Growth of a Homogeneous Mass of One 



Phase from a Heterogeneous Globule Formed in the Midst 



of a Homogeneous Mass of Another Phase 



Imagine the heterogeneous globule to be formed in the midst 

 of the originally homogeneous mass of the second phase, the 

 formation being achieved by a reversible process and the globule 

 being in equihbrium. The additional entropy and masses, 

 Iv], [wi], [mi], ... in the space where the globule is situated 

 are supposed to be drawn from the rest of the system, which 

 may be conceived to be so large that these withdrawals do not 

 appreciably affect the temperature and potentials in the exterior 

 parts. The change of energy in the exterior will be a decrease 

 of amount 



t[v] + MiNi] + M2N2] + . . . 



The increase of energy in the space occupied by the globule is [c]. 

 Hence the increment of energy in the whole system, above 



