662 RICE 



ART. L 



for the thick and thin films. This is held by Gibbs to justify 

 his statement near the top of page 305 that, just as the film 

 reaches the limit where the nature of the interior begins to 

 alter, the elasticity cannot vanish and the film is not then 

 unstable with respect to extension and contraction, a statement 

 which has proved to be a remarkably acute prevision of the true 

 state of affairs despite the qualifications of the following 

 paragraph; for quite recent investigation has shown that the 

 thinnest possible film, that showing black by interference, is 

 remarkably stable under proper conditions, and the old idea 

 that thinning necessarily leads to rupture has been disproved. 



57. The Equilibrium of a Film 



Returning to the thick film, Gibbs shows on page 306 how the 

 mechanical conditions for its equilibrium can be approximately 

 satisfied by regarding it simply as a membrane of evanescent 

 thickness, its plane being placed between the two dividing 

 surfaces of the film according to the rule which connects the 

 line of action of the resultant of two parallel forces with the 

 lines of action of the forces. But the following paragraph 

 shows that such a method of dealing with these conditions of 

 equilibrium is really inadequate, and that the film is not really 

 in equilibrium when it apparently is at rest and the conditions 

 called for by this restricted point of view presumably satisfied. 

 The argument reverts to the equations developed on pages 

 276-282, and resembles in some particulars the line of reasoning 

 on page 284. Thus according to [612] since the pressure in the 

 film satisfies 



"^ = — gill + 72 + . . .) 



it should decrease rapidly with height in a vertical film, yet by 

 [613] if we suppose p' to be the pressure at an interior point 

 and p" the pressure in one of the contiguous gaseous masses 

 the value of p' anywhere in the film must be between the 

 pressures of the gaseous masses for a film in any orientation, 

 since 



p' - Pa' = o-a(ci + C2) + ^(Sr) cos Ba, 

 Ph" - p' = (Tb{ci 4- C2) + £7(2r) cos dh, 



