130 ./. IK (xibbs — EnullibrlaiH of Heteroaeneous Substances. 



mutual actiou of the new and the original parts, which can aftect the 

 result. It will be easy to give such a meaning to the expressions 

 7>f, Di}, DiJ, D„i^, Dni^, . . . Dm„ that this shall be evidently the 

 case. It will be observed that the quantities represented by these 

 expressions have not been pei-fectly defined. In the first place, we 

 have no right to assume the existence of any surface of absolute dis- 

 continuity to divide the new parts from the original, so that the 

 position given to the dividing surface is to a certain extent arbitrary. 

 Even if the surface separating the masses were determined, the 

 energy to be attributed to the masses separated would be partly 

 arl)itrary, since a part of the total energy depends upon the mutual 

 action of the two masses. We ought perhaps to consider the case 

 the same in regard to the entropy, although the entropy of a system 

 never depends upon the mutual relations of parts at sensible dis- 

 tances from one another. Now the condition (52) will be valid if 

 the quantities Df, 7>//, l>f, I)m^, Dm.-, . . . I))u„ are so defined that 

 none of the assmuptious which have been made, tacitly or otherwise, 

 relating to the formation of these new parts, shall be violated. These 

 assumptions are the following: — that the relation between the varia- 

 tions of the energy, entropy, volume, etc., of any of the original parts 

 is not aifected by the vicinity of the new parts; and that the energy, 

 entropy, volume, etc., of the system in its varied state are correctly 

 represented by the sums of the energies, entropies, volumes, etc., of 

 the various parts (original and new), so far at least as any of these 

 quantities are determined or aftected by the formation of the new 

 parts. We will suppose Z>f, Dij, iJv, Dm ^, Dni^ . . . Dm,, to be 

 so defined that these conditions shall not be violated. This may be 

 done in various ways. We may suppose that the jjosition of the 

 surfaces separating the new and the original parts has been fixed in 

 any suitable way. Tiiis Avill detej-mine the space and the matter 

 belonging to the parts separated. If this does not determine the 

 division of the entropy, we may suppose this determined in any suit- 

 able arbitrary way. Thus we may suppose the total energy in and 

 about any ne\v part to be so distributed that equation (12) as applied 

 to the original parts shall not be violated by the formation of the 

 new parts. Or, it may seem more simple to suppose that the 

 imaginary surface which divides any new part from the original is 

 so placed as to include all the matter which is affected by the 

 vicinity of the new formation, so that the part or parts which we 

 regard as original may be left homogeneous in the strictest sense, 

 including uniform dentilties of eneryij and entropy., up to the very 



