650 BELL SYSTEM TECHNICAL JOURNAL 



with this requirement has been found in optics where the refractive 

 indices of molecules can be calculated approximately from the molar 

 refraction (eq. 8a) obtained by adding the atomic refractions. 



This additive property of electronic polarizations has been employed 

 by Frank ^ to interpret the tendency of crystalline materials hav- 

 ing high dielectric constants to be characterized by a high polariz- 

 ability/volume ratio for the atoms or ions of which they are composed. 

 This condition would tend to allow the largest number of highly 

 polarizable particles to be concentrated in a given space, giving, on 

 the additivity rule, a high molar polarization and a high dielectric 

 constant. 



On the other hand Wyman ^ has pointed out that the Clausius- 

 Mosotti relation is not satisfactory when applied to highly polar liquids, 

 such as water, and has found that for these substances it appears to 

 be more satisfactory to consider that the polarization is related to the 

 dielectric constant by the empirical relation 



^+^ ^""k. (9) 



8.5 3 



The calculation of the internal field by Lorentz, which provides the 

 theoretical basis for equation (8), was made before the theory of polar 

 molecules had been developed, but equation (8) has since been applied 

 tentatively to polar molecules."* The problem of obtaining an im- 

 proved relationship between polarizability and dielectric constant for 

 materials having molecules with permanent electric moments has been 

 studied in recent years by several investigators. ^^ The calculation of 

 the internal field usually involves the assumption that the efifect 

 of the molecules included in a small sphere surrounding the central 

 molecule on which the force is being calculated is negligible on the 

 average because of the random motions due to thermal agitation. On 

 the supposition that such an assumption is not justified in a polar 

 material because of the interactions of adjacent polar molecules, 

 Onsager ^^ has obtained a relation between polarizability and dielectric 

 constant which for high dielectric constants is nearly the same as 

 Wyman's empirical relation, equation (9). A comprehen.sive study of 

 the efifects of interaction between the dipoles of polar molecules has 



8 Lqp Clt 



^Cf. Wyman, Jour. Amcr. Chein. Soc, 56, 539 (1934); 58, 1482 (1936). 



i» Cf. Debye, loc. cit., p. 13. 



" Cf. Onsager, Jour. Anier. Chem. Soc, 58, 1486 (1936); Van Arkel and Snoek, 

 Trans. Faraday Soc, 30, 707 (1934); Wyman, Jour. Amer. Chem. Soc, 58, 1482 

 (1936); Van Vleck, Jour. Chem. Physics, 5, 320 (1937) and 5, 556 (1937). 



'^ Loc. cit. 



