1877.] 



Thickness of Soap Films. 



345 



The first of these numbers is considerably larger than the others, as it 

 is almost entirely deduced from the high values obtained during the early 

 experiments on the first cylinder. These experiments are, however, 

 deprived of the significance they might otherwise have seemed to possess 

 by the fact that the only other observations taken with the blue of the 

 second order in contact with the black gave for the resistance of the 

 latter the normal value 1*760, while, on the other hand, high values were 

 on one or two exceptional occasions obtained when the part of the film 

 next the black was sufficiently thick to show the orange of the second 

 order. 



It is not easy to decide whether the different values obtained at various 

 times correspond to real differences in the thicknesses of the black por- 

 tions of the films or are due to errors of experiment. 



The resistances measured were, as has been seen, very high ; but ex- 

 periments made for the purpose proved that the galvanometer was always 

 sensitive to at least 1 per cent, of the total resistance measured. The 

 most probable cause of error is the fact that the lower edge of the black 

 does not always lie in a horizontal plane. Thus on one occasion one end 

 of the boundary between the black and the coloured part of the film was 

 observed to sink no less than 0*5 millim. in a few seconds. In one or two 

 cases where this fact was noted, the number given for the length of the 

 black is a mean of readings taken in different parts ; but it was difficult 

 to determine whether the edge furthest from the observer was or was 

 not below that nearest to him. This source of error would, of course, be 

 of greater importance as the breadth of the black portion of the film 

 diminished ; but the magnitude of these deviations from horizontality 

 appeared to become greater as that breadth increased. 



Without, howevei, making any allowances for these causes of error, the 

 experiments certainly show, for the particular liquid and apparatus used, — 



i. That the variations in thickness of the black portion of the films 



were but a small fraction of that thickness. 



ii. That the thickness is independent of the breadth of the black ring. 



iii. That it is also independent of the thickness of that portion of the 



film which appears to the naked eye to be in immediate contact with 

 it. 



The last question on which the authors propose to touch is that of the 

 absolute thickness of the black portion of the films ; and though their ex- 

 periments only enable them to calculate that thickness on the assumption 

 that Ohm's law holds good, the result may be interesting. 



The mean of all their experiments gives for the resistance of a ring of 

 the black film 1 millim. broad, 1,750,000 ohms ; whence, since the diameter 

 of the cylinder is 33-51 millims., it is easy to calculate that, if Ohm's law 

 holds, the thickness of the film must be 12 millionths of a millimetre, or 

 about one third of the thickness corresponding to the beginning of the 

 black for the liquid submitted to experiment. 



