DIELECTRIC PROPERTIES OF INSULATING MATERIALS 649 



The quantity (47r/3)iVa is the molar polarization, Na being the polariz- 

 abiHty per mole.^ 



Equation (8), and also (7), expresses the Clausius-Mosotti relation 

 when a is considered to be a constant characteristic of the individual 

 molecule and independent of density. The function of e on the left- 

 hand side of (8) is independent of density whenever a is independent of 

 density. 



The following relation, analogous to that of Clausius and Mosotti 

 but expressed in terms of the refractive index n, was derived by Lorentz 

 and by Lorenz : 



M n^ - I 4t ^, 

 p «- + 2 3 



The left-hand member of this equation is called the molar refraction. 

 Equations (8) and (8a) are equivalent because of the general relation 

 between refractive index and dielectric constant {n^ = e), but owing 

 to the fact that refractive indices are measured at optical frequencies 

 the molar refraction contains only the electronic part of the total molar 

 polarization of the material. Subtracting the molar refraction from 

 the total molar polarization, is one of the methods of determining the 

 amount of polarization contributed by non-electronic polarizations. 



It has been found that the Clausius-Mosotti relation is not equally 

 satisfactory for all kinds of dielectric polarization. It gives good 

 results when applied to electronic and atomic polarizations. For 

 example, in an interesting paper on materials of high dielectric con- 

 stant, Frank "^ has recently shown that the Clausius-Mosotti-Lorentz- 

 Lorenz relationship aids materially in explaining the behavior of the 

 dielectric constants of crystalline materials of high dielectric constant 

 where the dielectric constant depends upon electronic polarizations. 

 Where the polarizability of a molecule is the sum of the polarizabilities 

 of the atoms of which it is composed it is to be expected that if the 

 relation (5), or (8) or (8a) is valid the sum of the atomic polarizations 

 would be equal to the molar polarization. Experimental agreement 



* The polarizabilities of non-polar molecules and atoms are usually of the order 

 of magnitude of 10""^'' c.c, and the molar polarizations of such substances, conse- 

 quently, are of the order of magnitude of a few c.c, since the molar polarization is 

 (47r/3) X 6.06 X 10^' times the polarizability of the individual molecule. The 

 polarizability of a conducting sphere is equal to the cube of its radius. And, as 

 atomic dimensions are of the order of magnitude of 10~* cm., it is evident that the 

 polarizabilities of atoms tend to be of a similar order of magnitude to the polarizabil- 

 ities which would be expected if they behaved as conducting spheres, though there 

 are large differences in the ratio of polarizability to volume for different atoms. The 

 molar polarizations of polar molecules are in general larger than those of similar non- 

 polar molecules and may be a few hundred c.c. (Cf. P. Debye, "Polar Molecules," 

 pp. 12-19.) 



^ F. C. Frank, Trans. Faraday Society, 23, (4), 513 (1937). 



