506 RICE 



ART. L 



sequent pages he formulates in his customary careful and 

 rigorous manner the fundamental differential equation for this 

 region and gradually leads the reader to the abstract idea of a 

 'dividing surface" as a convenient geometrical fiction with which 

 to represent the 'physical non-homogeneous region which has in 

 reality extension in three dimensions, one however being very 

 small. This region he frequently refers to as a "surface of dis- 

 continuity" but is careful to point out that the term does not 

 imply that "the discontinuity is absolute," or that it "dis- 

 tinguishes any surface with mathematical precision." The 

 term "dividing surface" does, however, refer to a surface in the 

 strict geometrical sense and the reader is warned to keep this 

 distinction well in mind. There is a certain latitude, as he will 

 presently learn, in the precise position to be assigned to the 

 dividing surface and in later developments of Gibbs' work this 

 latitude has been the cause of some doubt concerning the 

 validity of certain deductions. 



In this way a certain part of the whole energy of the system is 

 associated with this dividing surface. Now this part is not 

 actually the energy situated in the non-homogeneous region or 

 "surface of discontinuity," but is the excess of this energy over 

 and above another quantity of energy whose amount depends on 

 the precise location of the dividing surface. The matter is 

 carefully dealt with by Gibbs (I, 223, 224), in equations [485] 

 to [492]. Thus there is a certain latitude in the quantity of 

 energy which is to be associated with the dividing surface, and 

 this lack of precision in the value of this energy must not be lost 

 sight of. A similar lack of precision accompanies the amounts 

 of entropy and of the various components which are to be 

 associated with the dividing surface, and whose actual values 

 will in any given system depend to some extent on where we 

 conceive the dividing surface to be situated. Gibbs denotes a 

 physically small element of the dividing surface by s, and the 

 quantities of energy, entropy, etc. associated with this element 

 by e'^, rf, nii^, w/, etc. 



As is the case for any of the homogeneous phases, the variables 

 which determine the state of such an element of the surface of 

 discontinuity include the quantities s, t]^, nh^, rui^, etc., just 



