ON THE LIMITING THICKNESS OP LIQUID FILMS. 
6G1 
in the specific resistance. Finally, the absolute constancy of the hygrometer and 
thermometer seem to preclude the possibility of any considerable change of constitu¬ 
tion even in a black film. On the whole then we think that the thickness of the 
black portions is really different in different films. These differences are in general 
relatively small. According to Newton, the thickness of the “beginning of the 
black” would be 36X10 -6 and 37 X 10 -6 millims. for the liquide glycerique and 
the soap solution respectively. Apart, therefore, from our previous knowledge of 
molecular magnitudes, any thickness less than these would be equally probable; but 
the following table of the results obtained proves that both methods concur in showing 
that the average thickness is about 11'GXlO -6 millims., while the electrical experi¬ 
ments show that the “ probable error,” or divergence of the thickness of any given 
film from the mean value, is l'2x 10 -6 millims. 
Table Y. 
Liquide glycerique. 
Soap solution. 
Electrical method 
(1877). 
Optical method 
(1883). 
Electrical method. 
Optical method. 
12-2 
10-6 
12-32 
14-4 
11-9 
10-2 
13-32 
11-7 
12-0 
12-5 
13-36 
11-9 
11-6 
10-7 
13-13 
11-4 
12-0 
10-2 
14-46 
10-6 
110 
12-58 
11-8 
9-4 
7-82 
13-2 
7-19 
10-3 
10-74 
13-4 
12-07 
11-01 
12-29 
12-46 
Mean 1L9 
10-7 
11-74 
12-1 
Into the causes of the variations in the thickness of different black films we do not 
now propose to enquire. The above observations prove that they are comparatively 
small. The fact that the boundary between the black and coloured portions of a film 
is always well defined, and that there must therefore be a very sudden change of 
thickness in passing from the one to the other seems to point to a region of instability 
m the neighbourhood of the beginning of the black, such that films, the thicknesses of 
which are included within it, thin very rapidly to below its lower limit. Very short¬ 
lived films made of ordinary soap and water sometimes exhibit a grey tint, inter¬ 
mediate to the white and black of the first order, but persistent films, as far as our 
experience goes, never do. The foregoing observations seem to fix the limit of this 
MDCCCLXXXIII. 4 Q 
