108 Dr. S. R. Milner on Surface Concefitration, 



of the same thickness will depend on both the thickness and 

 the magnitude o£ the surface excess. While a diminution of 

 the thickness will tend to decrease the tension, a diminution 

 of the excess will tend to increase it ; and clown to a certain 

 limiting thickness there will always be a possible value of the 

 excess which will enable the tension to keep uniform. 



Now from the results on p. 105 for the value of the surface 

 excess calculated from the conductivity of films, we must con- 

 clude that it is considerably less in black films than in thick 

 ones. Another argument for the same thing may be adduced 

 in the fact that when the black spot is formed its edge is (in 

 my experience) always surrounded by a great many of the 

 little white flakes, the formation of which as a precipitate 

 formed from a supersaturated solution has already been 

 adverted to. On this view they form a visible piece of 

 evidence of oleate removed from the black spot. We must 

 consequently conclude that the tension so. far as it depends 

 on the thickness has been diminished, and that in black films 

 a thickness less than the range of molecular action has been 

 reached. It would be interesting to know, even if only 

 roughly, what the tension of a pure water-film of the same 

 thickness would be. If we assume, as is suggested by the 

 approximate agreement of the time-curves for the surface 

 tension with diffusion curves, that the diminution of the 

 surface tension of oleate solutions below that of pure water 

 is proportional to the actual amount of the surface excess, an 

 estimate of the value may be made from the results of Remold 

 and Rticker's conductivity experiments. On this assumption, 

 if t is the surface tension of a water-film, that of a soap-film 

 will be t(1 — &cr), where a is the magnitude of the surface 

 excess; and since both in thick films and thin ones the tension 

 must have the same value, 27*5 dynes per cm., we must have, 

 for a thick film, where t is 71 dynes per cm., and g is 2'4, 



27-5 = 74(1-/; x 2-4), 



and for a black film of 27*7 fifi thickness, where cr = l*09, 



27-5 = t(1-£x1'09). 



This makes t = 38'5, only about half as great as the normal 

 value. Although no great stress can be laid on the actual 

 number, it is evident from the calculation that a thickness of 

 27*7 /JL/Jb is well within the limits of the range of molecular 

 action. 



There remain outstanding the sudden formation, and the 

 discontinuous thickness at the edge, of the black spot, — phe- 

 nomena which have long been recognized as an indication 



