ON THE THICKNESS AND SURFACE TENSION OF LIQUID FILMS. 
631 
the various methods which had been employed. Theoretically, these methods can be 
made infinitely sensitive, and practically, slight variations in the adjustment of the 
apparatus alter very considerably the value of the experiment as a means of detecting 
small changes in the tension. Van der Mensbrugghe had indeed proved that 
Ludtge’s experiment is infinitely sensitive when the two films are hemispheres. As 
we have already stated, he had not, as far as we are aware, calculated the value of the 
difference of surface tension in play in any particular observation. We have in the 
following pages discussed the theory of the methods of experiment, instituted a 
comparison between them, and, in the case of the arrangement which we ourselves 
adopted, have investigated the various sources of error to which it is subject. For 
such a purpose calculation alone would not suffice. The practical limit to the 
sensitiveness is fixed by the impossibility of eliminating small perturbations, and 
could therefore only be found by trial. 
While, therefore, on the one hand, it seemed that experiment alone could decide 
what could be done by experiment, on the other hand, it was theoretically probable 
that, if the thickness of a black film was less than twice that of the surface layer, its 
viscosity might be great. The surface layer of a liquid must consist of elementary 
layers, the properties of which are different. The mean viscosity of the surface layer 
being, in the case of soap solution, greater than that of the liquid, the viscosity of 
some of the elementary layers must be, to an unknown extent, greater than this 
mean. Thus it is probable that, when the thickness of a film becomes less than twice 
the radius of molecular action, its viscosity increases. It would not be safe to extend 
to a black film conclusions drawn from experiments which prove that the liquid of 
which a moderately thick film is composed moves readily under the influence of a 
small difference of surface tension. 
If, therefore, the general opinion that it was possible that a change in the tension of 
thin films might be detected by experiment was erroneous, it was not possible to con¬ 
fute it by a priori reasoning. It had the support of high authority. Professor 
Clerk Maxwell, in his article on “Capillary Action,” says, “measurements of the 
tensions of a film, when drawn out to different degrees of thickness, may possibly lead 
to an estimate of the range of the molecular forces, or at least of the depth within a 
liquid mass at which its properties become sensibly uniform. We shall, therefore, 
indicate a method of investigating the tension of such films,” &c. 
On the whole, then, though all a priori considerations pointed to the conclusion 
that, if any difference of surface tension existed between the black and coloured parts 
of a film, it must be small, it appeared to us that the question as to whether it existed 
could only be settled beyond the possibility of dispute by experiment. We have, 
therefore, assumed in this paper that such a difference is possible. We have also 
supposed that the relation between the difference of surface tension and the other 
properties of the film is such that the only considerable movement to which it gives 
rise is a change of curvature. Having by experiments, conducted on these favourable 
