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of the surface-tension divided by the radius of the sphere. 
Hence the cohesive tension must he equal to twice the sur- 
face-tension of the liquid divided by the diameter of the 
smallest opening for which the surface-tension exists . — 
Q.E.D. 
It immediately follows from the foregoing proposition, 
that no matter how small the surface-tension may be, pro- 
vided it is finite, even when the opening is infinitely small, 
then the cohesion of the liquid must be infinitely great. 
For if the liquid were continuous in its origin the opening 
must always be infinitely small ; and hence to cause such 
an opening would require infinite tension. 
That the cohesion is infinitely great is not probable, to 
say the least. Hence it is improbable that the surface-ten- 
sion remains finite when the opening becomes infinitely 
small. As has already been stated, it has been found that 
the surface-tension is constant, or nearly so, under ordinary 
circumstances ; but it has never been measured for bubbles 
of very small diameter, and there appears to be every pro- 
bability that when the size of the bubble comes to be of the 
same order of small quantity as the dimensions of a molecule 
the surface-tension must diminish rapidly with the size of 
the bubble. 
If this is the case, then we have a limit to the cohesion, 
although it is probably very great for most liquids. Some- 
thing like the cohesion of solid matter of the same kind. 
That is to say, it is probable that it would require nearly as 
great intensity of stress to rupture fluid as it would to rup- 
ture solid mercury ; or as great tension to rupture water as 
to rupture ice. 
The Effect of Vapour. 
Nothing has yet been said about the effect of the pressure 
of vapour within the bubbles in balancing the surface ten- 
sion. It may, however, be shown that this can be of no 
moment. Even supposing that the tension of the vapour 
