ON THE THICKNESS AND SURFACE TENSION OF LIQUID FILMS. 
681 
which is always missing if the film is in equilibrium (i.e., not thinning very rapidly) 
and under the action of its own molecular forces only. 
In discussing such a theory, it is of primary importance to determine whether a 
critical value of the surface tension is physically possible. 
It is usual to assume that if the thickness of the film is less than that of two surface 
layers the tension must be less than that of the liquid in mass. 
Thus Plateau'" argues that in such a film the two layers “doivent necessairement 
exercer des actions rnoins fortes, et consequemment la somme de celles-ci, c’est-a-dire 
la pression sur fair interieur, doit etre plus petite que ne l’indique la formule.” 
Such arguments are based upon the assumption that the force in play between 
neighbouring molecules is attractive at all distances. The force exerted on a molecule 
by its neighbours must no doubt be, on the whole, attractive, and if the film is thin 
enough the surface tension must diminish. It is, however, usual, in dealing with other 
problems in molecular mechanics, to assume the existence of repulsive forces acting at 
all events between certain limits as to distance. We need only refer to the well- 
known instance of some forms of the dynamical theory of gases, and to the fact that 
the most recent theory of the nature of matter lately put forward by Professor 
Osborne Reynolds! leads to the conclusion that the force between two molecules 
which approach each other is alternately attractive and repulsive. 
If such an alternation really takes place the surface tension of a thinning film will 
alternately increase and diminish. This is clearly pointed out by Maxwell in his 
article on “ Capillary Action” (‘ Encycl. Brit.’), in which he says :—“ The force between 
the particle and the liquid is certainly on the whole attractive, but if between any two 
small values of c [the distance of a particle from the surface] it should be repulsive then 
for films whose thickness lies between these values the tension will increase as the 
thickness diminishes, but for all other cases the tension will diminish as the thickness 
diminishes.” 
It appears, therefore, that a critical value of the surface tension is not inconsistent 
with received views as to the nature of the forces in play between the particles of a 
liquid, and if it existed it would produce phenomena similar to those observed at the 
edge of a black film. In all cases we have supposed that the surface tension finally 
diminishes when the film is very thin, and is constant when it is very thick. If it 
has a critical value between these two states, the two simplest suppositions which we 
can make are (1) that it has a maximum and a minimum value, (2) that it has a 
maximum value only. 
(1.) The first of these, which is the more complex supposition, affords in some 
respects the better explanation of the behaviour of the black part of the film. Let 
us suppose that the change in the surface tension as the film becomes thinner is 
represented by the annexed curve (fig. 1). 
* ‘ Statique des Liquides,’ vol. 1, p. 205. 
t ‘ Phil. Mag.,’ vol. 20, 1885, p. 479. 
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MDCCCLXXXVI. 
