144 BUTLER 



ART. D 



If it could be supposed that the relation between the energy, 

 entropy, volume and mass of the infinitely small new part were 

 the same as that of a large homogeneous body of similar com- 

 position, the quantities De, Drj, Dv, Drrii, etc., would be pro- 

 portional to the energy e, entropy 17, volume v, masses mi, etc., 

 of the large body, and (195) could be written in the form 



e - Tri -\- Pv - MiMx ... - Mnmn ^ 0. (197) [53] 



In general however such an assumption is not permissible. 

 For, apart from difficulties arising from the definition of the 

 boundary surface enclosing the new part, we neglect in deter- 

 mining the energy, entropy, etc., of a large homogeneous body 

 the contributions which arise from the action of capillary forces 

 at its surfaces, and it is obviously impossible to neglect these in 

 the case of very small bodies. Nevertheless it is probable that 

 when (197) is satisfied, (195) is also satisfied. This appears 

 from a consideration of the meaning of (197) in which e is the 

 energy of a body having entropy 17, volume v, masses mi, . . . nin, 

 which is formed in a medium having the temperature T, pressure 

 P and potentials Mi, . . . ilf „. Since the total entropy and vol- 

 ume are supposed to remain constant in the formation of this 

 body, 



— Trj + Pv — MiVfii ... - ilf „m„ 



is the change in the energy of the medium. The quantity rep- 

 resented in (197) is thus the energy change of the whole system 

 in the formation of the new body, and since there is no change of 

 entropy in the process this must be equal to the work which 

 would be expended in the formation of the body from the 

 medium by a reversible process. Now work must usually be 

 expended to reduce a body to a finer state of subdivision, so 

 that if (197) is positive or zero for a finite body there does not 

 appear to be any reason to suppose that it will become negative 

 even when the particles are infinitely small. So that if (197) 

 is satisfied it appears that (195) will also be satisfied. 



This argument would however break down if the energy of a 

 mass of a body within a medium ever decreased as the size of 

 the particles decreased (i.e., in cases of negative surface tension). 



