632 
PROFESSORS A, W. REINOLD AND A. W. RUCKER 
assumptions, decided whether or no evidence of a difference of surface tension 
exceeding a given amount is forthcoming, we are then at liberty to reconsider the 
probable constitution of the film in view of the facts which experiment has elicited. 
In studying the properties of the black portion of a soap film, it is also important 
to remember that it has a well-defined boundary which indicates an apparent discon¬ 
tinuity in the thickness. It may be urged that if the thickness is less than that of 
two surface layers there must also be an apparent discontinuity in the surface tension 
at the edge of the black. If this were so, a free globular bubble, consisting of two 
parts, a coloured portion and a black “ polar cap,” could not be spherical, but must 
consist of two spherical segments which meet at a finite angle. This condition is not 
consistent with equilibrium, and therefore the black and coloured portions of the film 
must have the same tension. 
We think this argument deserves consideration, but we have not thought that it is 
so conclusive as to obviate the necessity of experiment to determine the facts. In 
the first place we are not aware that any evidence is on record that a perfectly free 
spherical bubble can have a black “ cap.” If the bubble is attached to a tube or other 
solid support the argument no longer applies, as that part which is in contact with 
the solid is not constrained to meet the axis of revolution, and may therefore be an 
unduloid or nodoid which can meet the spherical segment without any discontinuity. 
In order, therefore, that the argument might have the necessary basis of ascertained 
fact it would be requisite that bubbles should be formed without any solid supports, 
and should under these conditions be observed to reach a state in which they were 
partly black and partly coloured. Spherical bubbles when supported do not ordinarily 
exhibit more than a very small circular patch of black, and it would probably be very 
difficult to produce free spherical bubbles which should thin with sufficient rapidity 
for the purpose in view. 
Even supposing that such a result had been obtained, anything like accurate 
measurement to ascertain the spherical form of the bubble would under the required 
conditions be difficult or impossible. Unless these measurements were made the 
experiment would be open to the objection that the bubble might not be truly 
spherical, and that the same conditions which cause the sudden change in thickness at 
the edge of the black might also explain a very rapid change in curvature. 
It did not therefore seem wise to rely with implicit confidence on a priori reasoning' 
as to a region in the film which is the seat of phenomena which are confessedly imper¬ 
fectly understood. If experiment is necessary, observations on free spherical bubbles 
did not seem likely to be easy or conclusive. We therefore determined to adopt a 
modification of Ludtge’s method, and to balance against each other two films ot 
different degrees of tenuity. 
It was essential that our method of experiment should be such as would enable us 
readily to produce black films. We have found that this end is most easily obtained 
with cylinders. In most of our experiments, therefore, one of the films has been 
