662 
PROFESSORS REINOLD AND RUCKER ON LIQUID FILMS. 
region at about 14'5 X 10 -6 millims., and to prove that films generally thin to below 
but not to very much below it, so that the thickness of black soap films rarely differs 
from 11'6x 10 -6 millims., by more than one or two millionths of a millimetre. It has 
never been observed to fall below 7'2 X 10 -6 millims., and thus, without attaching any 
theoretical importance to the term, this thickness seems to be practically the limiting 
thickness of such liquid films as we have studied. 
We conclude by summarizing the results arrived at in this and our former papers 
with respect to black soap films : 
(1.) Persistent soap films, which thin sufficiently to exhibit the black of the first 
order of Newton’s rings, invariably display an apparent discontinuity in their thick¬ 
ness at the boundary of the black and coloured portions. 
(2.) The whole of the black region at the time of or very soon after its formation is 
of a uniform thickness. 
(3.) This thickness remains unaltered in any film, whether the coloured parts of the 
film are thinning or thickening, increasing or diminishing in extent. 
(4). It is different for different films, but no connexion has been traced between its 
magnitude and the time which elapsed between the first formation of the film, and 
the first appearance of the black, or between either and the time of observation. 
(5.) The mean values of this thickness are the same to within a fraction of a 
millionth of a millimetre, whether the films be plane or cylindrical, in contact with 
metal or with glass, formed of soap solution alone or with the addition of more than 
two-thirds of its volume of glycerine. 
(6.) Two completely independent methods of measuring the thickness of the black 
portions of the films give concordant results. 
(7.) The mean value of the thickness, calculated by giving equal weight to the 
results of the electrical and optical experiments, is 1I'6X10 -6 millims., the extreme 
values being 7 '2 X 10~ 6 and 14‘5 X 10 -6 millims. 
The smaller of these quantities is therefore a limiting thickness to which a soap film 
in air saturated with the vapour of the liquid from which it is formed rarely attains, 
and below which none of the films observed by us have thinned. 
I, 
