106 Dr. 8. It. Milner on Surface Concentration, 



very difficult measurements. The mean value is several 

 times larger than that obtained from the experiments on 

 bubbling. This might have been anticipated, since, as was 

 there pointed out, only a small fraction of the final excess 

 can have been formed in those experiments. 



The table shows further that in the black film of 27 '7 /jl/ul 

 thickness, a reduction to less than half its value in thick films 

 lias occurred in the excess. This is, I think, a point of con- 

 siderable importance in the explanation of the formation of 

 the black film, and is considered more fully on p. 107. 



Thinning oj Film*.— According to the theory of the for- 

 mation of a pellicle, the surface of a vertical soap-film is in 

 a state of statical equilibrium, and the thinning is due to the 

 gradual draining down of the layer between the two surfaces 

 impeded by the ordinary fluid viscosity of the liquid. In view 

 of the continual re-formation of the surface excess when the 

 surfjice is renewed, another cause will he seen to be operative 

 in ihe thinning. Consider a horizontal film suddenly turned 

 into a vertical position. In order for the film to be in equi- 

 librium, the tensions at different levels must he different 

 by the weight of the intervening film. This not being initially 

 the case, the surface, and with it a portion of the excess which 

 it contains, will be pulled down by the tension from higher 

 to lower levels. The surface tensions of the higher levels 

 will be thus increased until equilibrium results. This increase 

 in the tension is, however, only temporary, since the excess 

 removed from any portion of the surface is continually being- 

 replaced by diffusion of the oleate into the surface from the 

 interior. But this will be similarly removed, and thus a con- 

 .x mal circulation over the surface will be produced, the rate 

 of which, other things being equal, will depend on the rate at 

 which the surface excess is capable of being formed. Both 

 circulation and draining will assist in thinning the film, 

 and it is difficult to say a priori which of the two will be 

 the more potent cause. We may, however, infer that, since 

 the rate of formation of the surface excess is decreased by a 

 decrease in the concentration of the solution, the same will be 

 the case for the rate of thinning by circulation over the surface; 

 so that the extent to which this cause is operative may be 

 gauged by the extent to which the rate of thinning of films 

 depends on the concentration. I made some experiments on this 

 point by measuring the time required by films, formed in the 

 same way from sodium oleate solutions of different strengths, 

 to undergo a given degree of thinning. The films were formed 

 on a rectangular frame of glass fibre, 2 cms. wide by 4 cms. 

 high, having the handle attached at the bottom, and the whole 



