THICKNESS AND ELECTRICAL RESISTANCE OF THIN LIQUID FILMS. 
527 
of diiferent conductivity from the liquid in mass, bounded by pellicles of 
different conductivity from itself, and that when it becomes thin (about 
300 /x./r.), new forces (presumably surface forces) modify the conductivity in 
a way which can be approximately represented by supposing that the con¬ 
ductivity of the interior alone alters. 
We do not, however, at present wish to draw from these observations any but two 
conclusions :— 
(1) The theory of the formation of a pellicle of different conductivity from the 
rest of the film will not by itself explain all the facts. 
( 2 ) Something in the nature of a discontinuity appears to occur at a thickness of 
about 100 /x./x., which is but little greater than that which we have already 
fixed as the upper limit of the range of unstable thicknesses to which we 
attribute the discontinuity at the edge of the black part of a film. 
On the whole, then, we think it most likely that the changes observed at the 
smaller thickness are in part at all events due to the direct action of the surface 
forces, but that their action is complicated by some cause which at greater thicknesses 
forms a pellicle and also affects the interior of the film. 
There is indeed a great deal of evidence for the fact that if the surface of a solution 
of soap in water has been long exposed a pellicle is formed upon it. The surface 
tension of such a solution is about one-third of that of pure water, but Lord Rayleigh 
has shown that there is no measurable difference if the surface of the solution has 
only been formed for a very small portion of a second. It is obvious, therefore, that 
the surface of a solution of soap in water is modified when exposed to the air. 
We, on the other hand, have proved (‘Phil. Traus.,’ 177, Part 2 , 1886, p. 659) that 
every disturbance of the surface of a soap film increases its surface tension, and that 
the normal value proper to wLat may be called an aged surface is not regained for 
several minutes. 
In this respect the variations of surface tension and of electrical conductivity 
behave similarly. Both are affected when the film is disturbed by the passage of an 
electrical current. 
On referring to Table XIV. we observe that two of the values of the ratio of the 
electrical to the true thickness (r), viz., those which correspond to the thicknesses 
388 and 314 /x./x. respectively, are inconsistent with the others. 
If the table is rearranged in the order in which the experiments were performed, 
these facts gain significance. The exact sequence of events was as follows 
Current from 20 cells sent down the film before the measurement was made : 
( 1 ) T (truethlckuess) = 641 /x./x., r= 1 ' 66 . 
