266 PHENOMENA, ATOMS, AND MOLECULES 



krypton, xenon, nitrogen, oxygen and ethylene which have molecules of the 

 non-polar type. For hydrogen and helium, however, the errors are about 

 50 per cent. Debye concludes that this good agreement indicates that "the 

 law of force (Equation i) and its interpretation correspond completely to 

 reality." Undoubtedly the agreement justifies the use of the inverse 9th 

 power law of attractive force between non-polar molecules and the relation 

 between the attractive forces and the refractive index, but it should not be 

 concluded that this is evidence of the correctness of the relation between t 

 and the assumed arrangement of electrons (electric moment of inertia). 



With a force which varies with the inverse 9th power, the force falls to 

 one-half value for an increase of only 8 per cent in the distance. Thus the 

 cohesive forces corresponding to the van der Waals and Sutherland con- 

 stants are determined mostly by the forces exerted by the molecules upon 

 one another during the times that their distance apart does not exceed the 

 distance of minimum approach by more than 10 per cent. 



When a molecule is as close as this to another the force acting at the 

 near side -of the first molecule would be about loooo times as great as the 

 further side of the molecule. We are then surely not justified in considering 

 that the deformation would be the same as if the molecule were in a uni- 

 form field having the intensity of that at the center of the molecule. The 

 fact that Debye does get good agreement must be due to two compensating 

 errors, ist the field at the near side of the molecule where it alone needs to 

 be considered is much stronger than that calculated by Debye, and 2nd this 

 field acts effectively on only a small part of the molecule and its effect is 

 thus reduced. 



Examining Debye's data we find that the values of t which he finds are 

 quite accurately proportional to the 4th power of the molecular diameter. 

 From this it can be shown that the root-mean square electric field at the 

 surface of the molecule which causes the mutual polarization of the mole- 

 cules when they are in contact is practically the same for all the substances 

 considered, and has the value of 9.8 X 10^ volts per cm. (for r = d) which 

 is the field that exists at a distance 1.2 1 X io~^ cm. from an electron. 



Thus we see that the intensities of the fields around different non-polar 

 molecules are practically identical when regarded as surface forces rather 

 than as forces which originate at the center of the molecules. 



SURFACE FORCES AS THE CAUSE OF MOLECULAR ORIENTATION 



The surface tension y of a liquid is the free energy per unit area or is 

 that part of the surface energy which can do work. The total energy per 

 unit area yo is given by 



Yo = Y — ^ ^ (4) 



