the Black Spot in Liquid Films. 507 



breaking into the second, is about twice the thickness of the 

 second. From this it might be inferred that the thickness of 

 the second black film is possibly once the radius of molecular 

 attraction, or some multiple, while the limiting thickness of 

 the first is twice as great. 



It is generally considered that the film whose thickness is 

 once the radius of molecular attraction has a smaller tension 

 than one twice as thick, and would thus be unstable. Max- 

 well*, however, has shown, on the assumption that the density 

 is uniform in a region within the distance equal to the radius 

 of molecular attraction from the surface of a liquid, and equal 

 to the density of the liquid in mass, that a film whose thick- 

 ness is once the radius of molecular attraction would have the 

 same surface-tension as one twice as thick. That is, a film 

 whose thickness is once the radius would be stable. 



Statement of Results, — A curve illustrating the effect of 

 temperature changes on the thickness of the sealed black film 

 is first given. 



Fig. 4 (p. 508).— This curve was taken May 6th, with a 1 : 70 

 oleate of soda solution that had been sealed 24 hours. 38 of 

 the original 54 films remained to the end of 40 hours. The 

 abscissae represent the age of the film in hours, and the 

 ordinates, on the left, the mean thickness in /Afj, \ on the right 

 the ordinates represent the temperature in degrees centigrade. 

 No attempt was made to influence changes in the temperature. 

 The whole apparatus was enclosed in a thick wooden box and 

 the room carefully guarded against air-currents. No observa- 

 tion was made for the second black film as this was taken 

 before its existence had been noticed. Apparently the in- 

 flexions of the thickness-curve follow, inversely, those of the 

 temperature-curve, indicating an increase in thickness with a 

 fall in temperature. Owing to the small deflexion and fewer 

 films, the readings became more uncertain towards the end ; 

 hence, there the thickness-curve is not drawn as indicated by 

 the points. When there are 54 films a deflexion of one 

 fringe corresponds to a mean thickness of 16 jx/ul. 



Hygrometric Condition. — This curve, taken with the fact 

 that exposure tends to thin the films, would indicate that the 

 thickness depends on the hygrometric condition of the atmo- 

 sphere about the films. An unsatisfactory attempt was made 

 to measure the relative humidity with a wet and dry bulb 

 hygrometer. Even with as great an exposure as was used 

 in any observation, the difference in the readings of the ther- 

 mometers was less than o, 2, which at 23° C. would indicate 

 a relative humidity greater than *995. 



* " Capillary Action," Encyc, Brit. 



