458 RICE ART. K 



of the solid as it is when the deposition of matter takes 

 place, viz., in the state of strain. (Note lines 4 and 5, where 

 Gibbs expressly indicates this.) We could, however, conceive 

 the solid to be brought back to the unstrained state after the 

 deposition, the additional matter following the same change. In 

 consequence the solid would be larger in its unstrained state 

 than the original solid (before the increment) in the unstrained 

 state by an amount J'dN'Ds'; where 8N' now represents the 

 thickness of the additional layer in the unstrained state and Ds' 

 the size of the element of area which is Ds in the strained state. 

 Since ev > refers to the quotient of the energy of strain of a small 

 portion of the strained matter by its volume in the unstrained 

 state, the expression J'evdN'Ds' is justified. (It could, of 

 course, be just as well represented by J^evdNDs, but the former 

 expression is the more convenient for Gibbs' argument.) In 

 cases where the solid has in part dissolved, 8N and 8N' would 

 be negative in value. Thus we arrive at expression [357] for 

 the variation of the intrinsic energy of the solid. 



We are not however concerned with this energy alone, 

 nor with the entropy and mass of the solid alone. The system is 

 heterogeneous and involves fluid phases also, and so we are led 

 to the considerations dealt with in the remainder of page 187. 

 Again the form of [358] may puzzle readers not acquainted with 

 the methods of the calculus of variations, although the 

 content or meaning of it should not be very much in doubt. 

 The passage of matter and heat to (or from) the solid from (or 

 to) the liquid will change the entropy Dt] and the volume Dv 

 of a given elementary mass of the fluid by amounts 8Dr} and 

 8Dv; and in addition will alter the masses of the constituents 

 Dmi, Dm2, etc., composing it. The condition laid down towards 

 the end of page 187, which obviates the necessity of dealing 

 with the internal equilibrium of the fluid itself, involves as a 

 natural result the simplification that the integrations through- 

 out the narrow layers of fluid between rigid envelop and solid 

 are free from any troubles concerning original and present states, 

 and do not require the use of accents to avoid ambiguity. 

 Expression [359] embodies the fact that the potential energy of 

 an element of matter 7n, raised through a height 8z, acquires 

 potential energy of an amount ing8z. 



