101 Dr. S. R. Miiner on Surface Concentration, 



sodium-oleate solutions to an extent which increases with the 

 time: this may well be the solid phase which causes the irre- 

 versibility. (2) If the surface of a soap-bubble, which has 

 thinned so as to exhibit the reds and greens, is carefully 

 watched as the bubble is allowed to decrease in size, it will 

 be found to suddenly become covered with a large number of 

 minute white flakes. These flakes are not formed in a film 

 of constant size, except at places towards which the surface is 

 being pulled by local want of balance of the tensions. On 

 the above view, we should expect the precipitate to be 

 formed in such cases, where, but for its occurrence, super- 

 saturation * of the oleate in the surface would be produced. 

 (3) In the experiments on the surface tension, in dilute 

 solutions, on sucking the liquid down in the capillary it 

 is brought back sharply to its previous position ; but after 

 pressing it up, it comes back onlv very slowly in accordance 

 with the time-curve of fig. 2. This shows that while the 

 tension increases when the surface is increased, it does not 

 decrease, but even tends to increase, when the surface is 

 diminished. Thus, whatever the cause of the want of re- 

 versibility may be, there can be little doubt as to the fact of 

 its existence. 



In the rest of this paper the above conceptions are applied 

 to some results on the conductivity of soap-films obtained by 

 Messrs. Remold and Rlicker, and to the explanation of the 

 manner of thinning of films, and of the formation of the black 

 spot. 



Conductivity of Films. — Remold and Riickert measured 

 the true, and what they called the ' ; electrical" thickness 

 (i. e., the thickness calculated from the conductance on the 

 assumption that the conductivity is the same as that of 

 the liquid in mass) of a series of films formed from a solution 

 containing 1 part, of sodium oleate to GO parts of water. They 

 found that the electrical thickness was always greater than 

 the true thickness measured optically; and from their results 

 we may determine approximately the magnitude of the surface 

 excess at different thicknesses of the film. 



On the assumption that the conducting-power per molecule 

 of the surface excess is the same as that of the rest of the 

 solution, the conductance of a film of thickness t and con- 

 centration c and possessing an extra number a of gram- 

 molecules per sq. cm. of each surface, will be proportional to 



* The minimum value of the surface tension and the variability of its 

 ultimate value in the same solution described on p. 100 may be easily 

 accounted for as due to a slight supersaturation of the surface. 



t Phil. Trans, clxxxiv. p. 505 (1893). 



