622 RICE ART. L 



de , I dH , „ 



For equilibrium de/dv' must be zero. For stable equilibrium 

 we must have the additional condition 



dH' 



The amplification of this condition on page 250 to the form [544] 

 is easy; in [544] we regard dp' /dv', dp" /dv\ da/dv' as given 

 by the equations above, and of course ds/dv', d^s/dv'^ can be 

 calculated from the geometrical form of the system and the 

 fixed perimeter of the film. Equation [547] is the result for the 

 special case when one potential only is variable. 



45. An Approach to this Problem from a Consideration of the 

 Purely Mechanical Stability of the Surface 



Thus we have learned the general theoretical method of 

 dealing with stability when sufficient knowledge is available 

 concerning the functional forms of the various energy functions. 

 It involves no trouble concerning the mechanical stability of 

 the surface of discontinuity, which in a manner of speaking 

 takes care of itself. However, it is interesting to approach 

 the problem from that angle as well, and this is what Gibbs 

 does in the pages immediately preceding those on which we 

 have just commented. Going back we take up this aspect at 

 the bottom of page 244 where a system just like the one we have 

 been considering is posited. (We are not assuming a circular 

 orifice.) Passing by the two short paragraphs at the top of 

 page 245 (which are unimportant for our present purpose) we 

 have the relation for equilibrium 



p' — p" = o-(ci + C2), 



where, as before, p' , p", <r are functions of y' the volume of 

 one phase. A slight variation of the surface of discontinuity 

 will cause a change in p' — p", a and Ci + Ci. If there is to 

 be stability the surface must tend to return to its original 



