ON THE THICKNESS AND SURFACE TENSION OF LIQUID FILMS. 057 
It is, however, impossible to account for the smallest of the differences of surface 
tension shown in Table V. in this way. 
If a gramme of water were drawn out into a film of 100 scp cm. the cooling effect 
would be 1/4803 degree C. # But the thickness of the thinnest soap films has been 
proved by us to he about 10 -6 cm. Hence, in thinning to this degree of tenuity, the 
film would be cooled only a little more than 2° C. But since, if t is the temperature 
Centigrade, 
</T__T_ 
dt 550’ 
the increase of surface tension due to the cooling would be only about 0'4 per cent. 
Now a colourless film, which has been recently flooded, is certainly 250 times 
thicker than a black one, so that if the heat were distributed uniformly throughout the 
whole mass of the film the increase of surface tension would be only 0'0016 per cent. 
The enormous discrepancy between this number and that actually given by our 
experiments (9 per cent, in Experiment III.) cannot he explained away by the small 
corrections which would no doubt have to be made if data were used which apply 
accurately to the soap solution instead of those derived from water. One of these 
corrections would indeed strengthen the argument, for, as the surface tension of the 
solution is less than that of water, the cooling effect of the stretching would be 
decreased. 
Calculations based on Van der Mensbrugghe’s experiments indicate differences of 
surface tension as great as those on which our argument depends. We have, however, 
proved that the various possible sources of error discussed above, and which have not 
been previously investigated, do not seriously affect the result. We may add that, 
although we have only cited a few experiments, we have performed many. Thus 
when we balanced a sphere against a sphere the sensitiveness was so great that the 
films broke before the limit to the movement was approached. The change of form 
was so great that the limiting sensitiveness could not he considered to apply even 
approximately. 
It is not, however, easy to decide what is the particular cause, if it can be referred 
to one cause only, to which the change in the surface tension of one of the films 
is due. 
Experiment VI. 
We tried the effect of increasing largely the quantity of carbonic acid and of 
oxygen in the air within and without the films, and to this end passed gentle 
currents of these gases through the film box, and formed the films by means of them 
instead of air. 
As was to be expected, the liquid became turbid under the action of the carbonic 
* Baynes’ ‘ Thermodynamics,’ p. 156. 
4 P 
MDCCCLXXXVI. 
