66 2 
PROFESSORS A. W. REINOLD AND A. W. RUCKER 
merit, not from the theoretical position of equilibrium, but from that assumed by two 
films which were as similar as we could make them. 
Two cylindrical films were therefore flooded and put into communication. Their 
diameters were measured several times, and the difference, if constant, gave the zero 
reading. After an interval, which depended on the rate of thinning, the films were 
separated, and one was thickened by means of the current, generally until the colours 
of the third order reached the top. If no black appeared on the thicker film 
communication was re-established after 17 ra , and the diameters were measured about 
3 ra afterwards. If the black began to appear at the top of the thick film before 17 m 
after thickening, the stop-cock was opened sooner. By this means we generally 
succeeded in comparing two films, one of which was nearly all black, while the other 
displayed a little black and the colours of the first or second orders. If the position 
of equilibrium was the same as when both films were thick the experiment gave no 
evidence of any difference of surface tension between a black film and one many times 
thicker than itself. If it was not the same the apparent difference of surface tension 
was calculated from the sensitiveness. 
Both films were then allowed to thin, and, assuming that that which was already 
black remained in a constant state, we were able to observe whether any change of 
diameter took place as the coloured film became black. If it did it furnished us with 
another measurement of the difference of surface tension under investigation. It is 
evident that the mean of two such measures obtained from the same films would 
probably be free from error caused by any slight change in the position of equilibrium 
due to causes other than the increasing tenuity of the films. Accidental errors would 
of course disappear on the mean of a number of experiments. 
This method is, however, open to an objection which requires discussion. We were 
seeking for evidence of a difference of surface tension (if any such existed) between a 
black and a coloured film. Most of the films observed were, however, partly black 
and partly coloured. If any difference of tension existed between their different parts 
the films would not be cylinders or simple unduloids, but the black and coloured 
portions would be of different curvatures. Measurements based on the sensitiveness 
would not therefore be trustworthy if, upon the comparatively simple changes of form 
assumed in the calculation of that quantity, other and more complex variations were 
superposed. We have therefore investigated the form of a film consisting of two 
parts of different surface tensions, assuming that it does not differ much from a 
cylinder. 
If the surface tensions are T and T-{-c?T, the generating curve of the film may be 
regarded as consisting of two parts, PB and BQ, which produce unduloidal surfaces 
of different curvatures. 
The conditions which these curves must satisfy are as follows :— 
(1.) If X x and X 2 are the differences of the abscissm of B and P, and Q and R, 
