I 

 502 RICE ART. K 



necting the state of reference with the standard state (which will 

 vary in value from point to point of the state of reference). 



IS. Commentaiy on Pages 215-219. Solids Which Absorb 

 Fluids. Elucidation of Some Mathematical Operations. In the 

 final four pages of the section, viz., pp. 215-219, the general argu- 

 ment offers no difficulty and only a few comments need be made 

 on the mathematical operations. Regarding the equations 

 [463] and [464], we refer the reader to equations (38) of our 

 exposition. If we are considering a state of hydrostatic stress, 

 we know that 



Xx = Yy = Zz = -V 

 and 



Yz ^^ ^Y ^^ ^x = A z = A K = Yx ^ 0- 

 Hence by (38) 



Xx' = -Anp, Xy' = -A12P, 



Xz' = —Aisp, Yy' = —A22P, etc. 



which constitute [463] of Gibbs. 

 Also 



Xx'^aii -(- Xr'5ai2 ...-]- Z z'^azi 

 = —p{Aiiban + An^an . . . + Azzbazz). 



As we have already seen on several occasions, the bracketed 

 expression on the right hand side is bH, and of course H is the 

 ratio of enlargement of volume, i.e., the volume of an element 

 divided by its volume in the state of reference ov vv. Thus we 

 obtain [464]. 



The equations subsequent to [471] are obtained by the 

 familiar device by means of which we obtain the yp and ^ func- 

 tions from the e function. Thus since , 



dev = tdr]v -\- S2(Xx'6aii) + ^HadTa, 



