514 RICE ART. L 



In terms of 4>{r) it is easy to express the mutual potential 

 energy of one molecule with respect to all the molecules within 

 its sphere of action; but, of course, the result will vary according 

 to the situation of the selected molecule. Suppose in the first 

 instance that it is well within the general body of the liquid, so 

 that a sphere around this molecule as center with a radius 

 equal to the radius of molecular action, denoted by /i, is com- 

 pletely filled with liquid. It is easy to see that the potential 

 energy in question is represented by 



47rn / r^(f>(r)dr f (1) 



where n is the number of molecules per unit volume and I is the 

 minimum distance between molecules, a distance which must 

 approximate closely to the critical distance referred to above. 

 Doubtless the integral form of this result should not be taken too 

 seriously for purposes of actual calculation in view of our pres- 

 ent-day knowledge of the properties of molecules, especially 

 the fact that the radius of molecular action is not many times 

 larger than a molecular diameter. But it will serve as a repre- 

 sentative expression suitable for the purpose we have in mind, 

 viz., the elucidation of the true nature of the "surface tension" of 

 a simple liquid. Actually the numerical value of the expression 

 (1) (we must bear in mind that it is an essentially negative 

 quantity according to our conventions) is the amount by which 

 the energy referred to is less than that for a molecule separated 

 by relatively great distances from all others. It must also be 

 noted that while this expression represents the potential energy 

 of one molecule, this energy is nevertheless shared, as it were, 

 with other molecules, so that when we wish to represent in a 

 similar manner the potential energy of the group of molecules 

 in unit volume we do not multiply the above expression by n 

 but by n/2; otherwise we should be counting the energy of 

 every pair of molecules twice. Thus the potential energy of 

 the molecules in unit volume is 



27r?i2 / r^(f>(r)dr. (2) 



