ON THE THICKNESS AND SURFACE TENSION OF LIQUID FILMS. 
667 
inappreciably from a cylinder if the difference of surface tension was only 1 per cent. 
The pressure, however, would have altered by 0'5 per cent., and if the film were now 
put into communication with another which was coloured throughout an appreciable 
change in the principal diameters would take place. This is evident from the fact 
that, if the change in the pressure exerted by the first film had been due to its surface 
tension having altered throughout by O'5 per cent., the difference in the principal 
diameters would have been 0'451/2=0'225 mm. It follows, therefore, that if two 
films are in communication, and if the surface tension of a part of one differs slightly 
from that of the remainder, the asymmetry of this film is small compared with the 
change produced in the principal diameters of the two films. We may, therefore, as a 
first approximation to the truth, regard the sensitiveness of an experiment in which 
part only of the film is black as proportional to dp/dp . 
The numbers given in the last column of Table VII. may be plotted in a curve, the 
abscissae being the fractions of the whole length of the cylinder covered by the black, 
and the ordinates the values of dp/dp'. 
If in any experiment the length of the black part of the film increased from (say) 
0'2 to 0'8 of the whole length of the cylinder, the effective length would be 0'6 ; and 
the alteration of pressure is shown by the curve to be from 0'1 to 0'9, i.e., 0'8 of the 
whole alteration which would be produced if a coloured film became completely black. 
If the thicker film displays some black, the effective length of the black in the 
thinner film is the difference of the lengths in the two films. It will be observed that 
O 
different changes in the pressure may be produced by the same change in the effective 
length. Thus dp/dp' is 0'66 or 0'8 according as the length of the black increases 
from 0 to 0'6, or from 0'2 to 0'8 of the whole length of the cylinder. 
We now proceed to describe the experiments. It is necessary to do this in con¬ 
siderable detail, as no two were alike, and the results do not admit of being stated 
shortly so as to include all facts which might have affected the results. 
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