SURFACES OF DISCONTINUITY 665 



or 8/3 times the corresponding Poiseuille value for equal 

 values of D. It is this fact which enables Gibbs to convert 

 Poiseuille's experimental result for tubes into the result [657], 

 somewhat greater than [656], but of the same order of magnitude 

 and sufficiently approximate for the purpose in hand. 



Towards the end of the succeeding paragraph there occurs 

 one of those almost casual statements, so common in Gibbs' 

 writings, which have the appearance of extreme simplicity but 

 are not so easy to justify as one might imagine. Somewhat 

 earlier we have shown how the evaporation of Si, would diminish 

 the tension of the film. (This volume, p. 661, referring to 

 Gibbs, I, 303.) This implies that if we have two elements such 

 that the ratio of the quantity of S2 to the quantity of Si in the 

 first is greater than the corresponding ratio in the second, then 

 the tension in the first element would be smaller than in the 

 second. Suppose the second element to be in equilibrium at 

 the level which it occupies, and that the first element should 

 happen to be situated at the same level. Clearly a small strip 

 of the film lying between this first element and the part of the 

 film immediately above this level would not be in equilibrium. 

 The pull upwards on this strip, which would be balanced by the 

 pull downwards on it if the second element were below it, is 

 greater than the pull downwards on it due to the first element ; 

 thus the first element would tend to rise and of course to ex- 

 perience a stretching and have its tension increased. 



In the final paragraph of page 309 the observation referred 

 to is now generally known by the name, the "Gibbs ring," and 

 we shall comment on it presently when giving a few details 

 concerning experimental work on films. 



Passing on to the middle paragraph of page 310, the writer 

 supposes that the reasoning by which the stated conclusion 

 "may easily be shown" is as follows. We have already seen 

 that a vertical film is not an example of true equilibrium, and 

 although the variation of a with the height z necessitates varia- 

 tion of some at least of the potentials with z, since equation 

 [508] must be satisfied, the law of variation is not necessarily 

 the genuine equilibrium law [617]. For, if that were valid for 

 all the potentials, p would have to vary with z according to the 



