532 RICE ART. L 



radius of A'B'. This volume is equal to 



3 f, {sRHt -x) + 3R(r - xy + (r - xy + sr^x - srx^ + x^} 



= sf + ^ (f2 - 2^x) , 



neglecting the remaining terms which involve squares and 

 products of ^/R and x/R. Hence the difference of the volume 

 elements is 



^ (f ^ - 2fa:) , 

 and so the value for 8e^ calculated as suggested above is equal to 



= — (r - 2x). 



This is the same as 2C8c, i.e., 2C/R. Hence we find that 



C = ks(f - 2x). 



From this equation it is clear that C can have positive or 

 negative values according as x is less or greater than f/2. C is 

 zero if X = f/2, i.e., if the dividing surface is midway in the film. 

 Also if C is the value of C when x = x\ and C" its value when 

 X = x", these being in fact the values of C for two positions of 

 the dividing surface separated by X, where \ ^ x' — x", we have 



2(C" - C) = 2(Ts{x' - x") = 2as\. 



In this way we confirm the results obtained by Gibbs on 

 page 227. These results show that we can choose in any general 

 case a position for s which gets rid of the awkward terms 

 Cibc\ + CibCi in [493]; our sole object in presenting an alternative 

 method of derivation has been to show the physical basis for 

 introducing these terms at all. It may also help the reader to a 



