DIELECTRIC PROPERTIES OF INSULATING MATERIALS 651 



been made by Van Vleck by the methods of statistical mechanics. He 

 obtains an expression which agrees to a second approximation with 

 that obtained by Onsager. Thus it seems that for highly polar liquids 

 the relations between polarization and dielectric constant developed 

 by Onsager, Wyman and Van Vleck may be more satisfactory than 

 the Clausius-Mosotti relationship, though for many other materials 

 the Clausius-Mosotti relationship is apparently valid or approximately 

 valid. 



In deriving expressions for the dependence of dielectric constant on 

 frequency later in this article the formulae obtained will naturally 

 depend upon which of the equations, (5), (6) or (9), is taken as the 

 relationship between polarizability and dielectric constant. The 

 alternative expressions will be listed. 



Derivation of a Dispersion Formula 



The above-described relations between polarization and dielectric 

 constant provide the means of obtaining expressions for the variation 

 of dielectric constant with frequency when we have determined the 

 dependence of polarizability on frequency. As our object is to exhibit 

 the general features of anomalous dispersion shared by several par- 

 ticular types of polarization, it will be sufficient to derive dispersion 

 formula? containing constants the values of which are not specified, 

 but which have a sufficiently obvious physical significance. The 

 derivation given will parallel that of Lorentz in deriving a formula for 

 optical dispersion, ^^ and in fact is simply a special case of it in which 

 certain terms are considered to be negligible by comparison with others. 



An analogous procedure was used in one of the earliest attempts to 

 explain anomalous dispersion in the electrical frequency range, the 

 theory proposed by Drude '^ in 1898. This theory was based upon the 

 hypothesis that anomalous dispersion in the electrical frequency range 

 depends upon a mechanism similar to that to which optical dispersion 

 was attributed, the difference being that the particles which produce 

 anomalous dispersion in the electrical frequency range are so large that 

 some of the terms in the optical dispersion formula can be neglected. 

 The formulae which Drude derived for electrical anomalous dispersion 

 yield the same form of variation of dielectric constant with frequency 

 as do the generally accepted theories of the present time, such as the 

 Debye theory; the differences lie in the expressions given for the con- 



" H. A. Lorentz, "The Theory of Electrons," Chapter IV. See also Korff and 

 Breit, Reviews of Modern Physics, 4, 471 (1932), where a review of the classical theory 

 of optical dispersion is given. 



" P. Drude, Arm. d. Physik, 64, 131 (1898), " Zur Theorie der anomalien elek- 

 trischen Dispersion." 



