6 PROF. OSBORNE REYNOLDS ON THE 



ter 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, if 

 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 Avould require infinite tension. 



That the cohesion is infinitely great is not probable, to 

 say the least. Hence it is improbable that the surface- 

 tension 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 ordi- 

 nary circumstances ; but it has never been measured for 

 bubbles of very small diameter, and there appears to be 

 every probability 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 

 rupture solid mercury, or as great tension to rupture 

 water as to rupture ice. 



The Effect of Vapour. 



Nothing has yet been said about the efifect of the 

 pressure of vapour within the bubbles in balancing the 

 surface-tension. It may, however, be shown that this can 

 be of no moment. Even supposing that the tension of the 

 vapour within the opening of the liquid were equal to the 



