600 RICE ART. L 



Thus we have the first part of the integral fp'bDv' in (23). 

 The second part will be the integral fp'bNDs throughout the 

 region between the two positions of the dividing surface, for p' 

 is the pressure which existed where the element bND8 was before 

 it moved into the region originally occupied by the double 

 accent phase. Hence in (23) f'p'bDv' is equal to the sum of a 

 surface integral, and a volume integral, viz., 



In the second integral of (23) we must, in the same way, first 

 integrate 



dv" dp" dp" \ ^ „ 



throughout the original region occupied by the double accent 

 phase and then subtract from this the surface integral fp"bNDs. 

 Thus we find that 



fp'bDv' + fp"bDv" 

 = j{p'- p") bNDs - /(!' bx + I' by + f bz) Dv' 



/( 



dp" dp" dp" \ ^ „ 



for which [609] is a condensed form. 



With reference to the term fabDsy we see in just the same way 

 that it is equal to the change produced by the variation in the 

 integral faDs, minus the value of the integral fbaDs, where 

 h(T is given by [608]. The term bfaDs consists of two 

 parts. To see this, imagine normals drawn to the surface s 

 at points on the boundaries between the various elements Ds. 

 The normals projecting, as it were, from the boundary of a given 

 Ds will form a tube which will cut out on the varied position of s 

 a corresponding element of area whose size isDs[l + (ci + c^) bN]* 

 All the original elements of s will thus mark out a defined 



* See the note on curvature p. 12 of this volume. 



