DIELECTRIC PROPERTIES OF INSULATING MATERIALS 663 

 The present derivation gives: 



M € - \ _ 47riV 

 P 6 + 2 3~ 



ki ne^ I 1 



L ' fL \l -i- iwr' 



The constant ao has the same significance as kijL, only the notation 

 being different; both represent the optical frequency, or "instantane- 

 ous," polarizability ; /x is the permanent electric moment of the molecule, 

 k Boltzmann's constant and T the absolute temperature. The quan- 

 tity ne^/fL which corresponds to fx^/3kT'm the Debye formula contains 

 three constants n, e, and/ whose physical significance is indicated only 

 in a general way (see Appendix), r' (or in Debye's notation r) 

 is equal to ^Trrja^/kT in the Debye theory while in the formula derived 

 here t' = r/f where r is a frictional coefficient whose physical origin 

 is not specified. Thus though the formula for molar polarization 

 derived here is not directly useful as a means of investigating the 

 molecular (or other) origin of dielectric polarizations, it facilitates 

 distinguishing those aspects of the Debye formula which are peculiar 

 to a polarization depending upon changes in the orientation of polar 

 molecules which are free to assume any (or at least more than one) 

 orientation from the more general aspects shared by other types of 

 polarization, such as the one specified by (18) and (21). Thus, the 

 functions iJ.'^jSkT and 4:irr]a^lkT are peculiar to the Debye theory, while 

 the function (1 + iwT)~'^ also appears in the dispersion formula derived 

 here, as well as in other formulae to be discussed below. 



We have seen that the viscous-elastic type of polarization specified by 

 (18) and (21) produces a complex dielectric constant given by (39), or by 

 the equivalent equations (41), (41a), (41&), where 



_ r'jeo -\- 2) 

 ^ (600 + 2) ' 



and that the same formulae express the complex dielectric constant 

 on the Debye theory of polar molecules when the constants r' and 

 60 — Coo (or ko — kca), are given the values derived for them on the 

 Debye theory. Other theories have been proposed to explain the 

 variation of dielectric constant and dielectric loss with frequency, but 

 for the most part these have been derived for composite dielectrics, 

 consisting of two or more layers of different materials, or of small 

 spheres of one material dispersed or embedded in another material. 

 These theories also yield formulae (41), (41a) and (416) for the complex 

 dielectric constant, the expressions for r' and eo — eoo being, of course. 



