and the Formation of Liquid Films. 109 



that the thickness is approaching molecular dimensions, but 

 the actual cause of which has remained completely obscure. 

 I have only been able to come across two suggested expla- 

 nations o£ the discontinuity. Remold and Rucker* suggest 

 that it is due to the forces between the molecules becoming- 

 repulsive within certain limited regions, Avhereby the surface 

 tension of the film alternately decreases and increases as the 

 thickness is diminished. On the other hand, Bakkerf 

 connects it with the region of instability in the isothermal 

 which represents the passage of liquid into vapour. An 

 objection to both of these explanations is that they neglect to 

 give a part to be played by the soap, although it has an 

 obvious and essential role in the experimental production of 

 the spectacle, It seems to me that an explanation on the 

 following lines is more satisfactory. 



Let us suppose (simply to make the argument more definite) 

 that the tension of a thin soap-film of thickness t and surface 

 excess a is actually represented by the f orm f(t){ 1 — k<r} . It is 

 true that from a mathematical point o£ view an infiuite number 

 of corresponding values of t and a may exist which will make 

 this function have the same value as in a thick film. We 

 have seen that if in any place the tension is accidentally less 

 than this value, thinning occurs by the extreme surface layer, 

 and with it the excess of oleate which it contains, being 

 dragged away from the place by the surrounding tensions ; 

 but when we come to molecular magnitudes the alterations of 

 the thickness and the excess produced in this way cannot be 

 perfectly continuous, but must occur in finite, if very small, 

 steps. Thus we may imagine that the thickness cannot alter 

 by less than that of a layer 1 molecule thick, and similarly the 

 surface excess by the amount of oleate contained in such a 

 layer. But unless the increase in the tension produced by 

 the second of these alterations is exactly of the right amount 

 to neutralize the decrease produced by the first, the portion 

 of the film thus thinned cannot remain in equilibrium with 

 the thicker parts. Hence either the thinning will not take 

 place, or the next layer will be removed simultaneously 

 with the first, when the same considerations will again be 

 applicable. It may not be until after a considerable number 

 of layers of molecules are considered removed, that a point is 

 reached at which the sums of the decreases of the thickness 

 and of the surface excess which correspond to the removal of 

 each layer exactly neutralize each other in their effects on the 



* Phil. Trans, vol. clxxvii. p. 627 (1886). 

 t Ann. der Physik, Bd. xx. p. 35 (190(3). 



