ON THE THICKNESS AND SURFACE TENSION OF LIQUID FILMS. 
G29 
tlieir surface tensions were identical, the curvature of each would be the same. Van 
der Mensbrugghe, however, considers that a zone of liquid in the upper bubble 
would in descending increase its surface, while in the lower bubble the surface of the 
descending’ mass would diminish. Hence the upper bubble would become cooled, 
while the temperature of the lower one would be raised, and this would be indicated 
by a difference of curvature, due to the fact that the surface tensions were not the 
same. Observation showed that such a difference of curvature existed. In one 
experiment the sagittte of the spherical segments differed by 1*15 mm., which 
diminished after 45 m to 0'1 mm. When the system had apparently reached a 
permanent state the plate was reversed, the upper and lower bubbles exchanged 
places, and the fact that the measurements were to within the error of experiment 
the same as before was taken as evidence that the phenomenon observed was not due 
to any inequality produced directly by the weight of the films. 
The investigations of these observers have not left the question of the relation 
between the surface tension and the thickness of a liquid film in a satisfactory state. 
We have already pointed out* that the experiment of Plateau, who observed a 
bubble formed of liquids glycerique which lasted for three days, and was enclosed in a 
vessel containing sticks of caustic potash to dry the air, offers no guarantee that the 
composition of the liquid remained unaltered. As we have found that under circum¬ 
stances much less favourable to change! a soap film lost in thirty-eight minutes 23 out 
of the 57*7 volumes of water contained in every 100 volumes of solution, it is practically 
certain that the constitution of Plateau’s bubble could not have been constant. 
Ludtge and Van der Mensbrugghe were on their guard against this difficulty, 
and, though they experimented with liquids glycerique without any of the elaborate 
precautions which we have since shown to be necessary if the percentage of water is 
to remain unaltered, they checked these observations with others made with solutions 
of Quillaja and of Marseilles soap. Neither, however, appears to have put his conclu¬ 
sions to a certain and satisfactory test. If it be true that the surface tension of a 
film varies with its thickness it would be a matter of the highest interest to deter¬ 
mine the law of change. No such attempt was made by Ludtge, who remarked 
only that the method did not admit of great accuracy, and that one of his experiments 
indicated a chanve of tension in the ratio of 2'8 to 2'84 in five minutes. Van der 
Mensbrugghe, on the other hand, though he has no doubt suggested a vera causa 
which may completely explain some of the phenomena he describes, made no attempt 
to determine whether the lowering of temperature to which he ascribes them could be 
produced by such increments of the surface as could reasonably be supposed to take 
place. For this purpose the change of tension must be measured, and though he gives 
the data for the calculation he does not make it. The reason for this probably was 
* ‘ Phil. Trans.,’ vol. 172 (Part 2, 1881), p. 448. 
t Log. cit., p. 486. 
