154 Mr Kleeman, On the Properties of a liquid ° 
surface tension. Let the film now be evaporated and the vapour 
expanded or compressed at constant temperature till its density — 
is the same as that of the vapour at the end of the previous | 
process, and let w, denote the external work done. Now ac-_ 
cording to thermodynamics the external work done at constant — 
temperature during a reversible process between given limits is _ 
independent of the nature of the path of the process. Hence 
W,=w,—w,, and therefore w, is greater than W. 
It follows therefore that if a film of liquid is gradually 
stretched out a thickness would ultimately be reached at which 
the pressure of the saturated vapour begins to increase with 
decrease of thickness of film. It can be easily shown that this 
thickness is equal to twice the radius of the sphere of action of 
a molecule. For if a film has a thickness equal to or less than 
this quantity it requires the expenditure of less energy to move 
a molecule to infinity than in the case of a much thicker film. 
Consequently a larger proportion of molecules will possess suffi- 
cient velocity to be able to overcome the molecular attraction 
and escape from the liquid surface in the former case than in the 
latter, producing a corresponding difference in the pressures of 
the saturated vapours. Also the attraction of one half of the 
film on the other half per cm.? of surface would in such a case 
be less than the attraction of a large mass of liquid on a cm 
of its surface transition layer. This should have the effect of 
making the transition layer for the film less abrupt than for a 
much thicker film. Further, the density of the liquid mid-way 
between the surfaces of such a film should be less than that in - 
the centre of a large mass of liquid. 
An inferior limit of the radius of the sphere of action of a 
molecule can be obtained. When the surface of a liquid is 
increased at constant temperature an amount of heat is absorbed 
dn 
dT 
of liquid be stretched out till it consists of a film contaming one 
layer of molecules only the amount of heat absorbed should be 
practically equal to the internal heat of evaporation Lp, of the 
e.c. of liquid, or 
equal to 7'=,, per unit increase of surface. Therefore if a cc. 
an CDS 
[er sr = Te. 
It is evident therefore that the surface tension should undergo 
a change during the process before the area of the film is equal 
to A, where 
Nes 
Tf A denote the thickness of the film we have AA = 1. 
