516 RICE ART. L 



p is the expression (2) and c is the expression 



Trn^ 



r^({>(r)dr*. (3) 



(Once more, since the definite integral in (3) is essentially 

 negative, a itself is essentially positive.) The expression (3) 

 represents the potential energy per unit area of surface. This 

 is not the whole energy of the surface since in that we must also 

 include the kinetic energy of the molecules in the surface layer. 

 We have here a mechanical interpretation of the well-known 

 division of the total surface energy into the surface "free 

 energy" a, and the "bound energy" - tda/dt. 



5. An Alternative Method of Treatment 



There is another method of approaching this question of 

 surface energy which leads to the same result. In the interior 

 of a liquid mass there is on a given molecule no force perma- 

 nently acting in a given direction. As the molecule changes its 

 relative position and suffers many more encounters with other 

 molecules than it would meet in a gas in the same tune, the 

 attractions and repulsions of its neighbors on it change in a 

 fortuitous fashion. At the surface of a Hquid, within the layer 

 of thickness h, there is an inward normal resultant force on a 

 molecule which increases in value as the molecule approaches 

 the surface. Also in a layer of the vapor outside the surface 

 of the liquid this field of force also exists, reaching the value 

 zero when the molecule is at a distance h from the surface. A 

 molecule in such a situation possesses potential energy, just 

 like a body raised above the ground against gravity. Just as a 

 body under gravity tends to move downwards, so molecules in 

 the surface tend to "fall inwards" towards the interior and so 

 reduce the extent of the surface, thus producing the illusion of a 

 surface contracting "under tension." But of course the truth 

 is that the effective force on a molecule in the surface layer is 



* In arriving at (3) certain assumptions are made about the behavior 

 of 0(r) and certain functions derived from it at the lower limit I of r. 

 This, however, concerns mathematical details and does not concern 

 physical interpretation. 



