662 BELL SYSTEM TECHNICAL JOURNAL 



where 



C' = Cod + Z i A> (41a) 



1 + U^T^ 



.// (to — Coo) 



OJT 



e = 



1 + 

 if T is considered to be given by 



(416) 



60+2 , 

 Coo + 2 



when the complex dielectric constant is given by (39), that is when 

 the Clausius-Mosotti relation applies, and by 



I 



when the material is a gas, or when Wy man's relation between polariz- 

 ability and dielectric constant applies. 



The real part e' of the complex dielectric constant is usually referred 

 to simply as the dielectric constant, while the imaginary part e" is 

 frequently called the loss factor?^ There are alternative ways of 

 expressing the same property of the material; for example, the tangent 

 of the loss angle, e"/e', is frequently used instead of e". 



Comparison of Dispersion Formulce 



Comparison of (39) or (41), (41a), (416) with equation (69), page 97, 

 of Debye's "Polar Molecules" shows that the equation for the complex 

 dielectric constant derived here is identical with that of the Debye 

 theory (in the present notation r' corresponds to r in Debye's bookj. 

 This means that any characteristics which can be derived from equa- 

 tions (41), (41a), (416) without specifying the values of the constants 

 Coo, Co and t are common to at least two types of polarization, that is, 

 to the polarization due to the effect of an applied field on the orientation 

 of polar molecules according to the Debye theory, and to the polariza- 

 tion described by equation (18) or equation (21). 



The difference between the formulae for dispersion derived here and 

 those of the Debye theory are best seen by comparing the expressions 

 which they yield for the molar polarization. On the Debye Theory: 



M e - 1 ^ 4xiV r mW 1 



pe + 2~ 3 1''°^ 3kT\l -\-ia:T' 



1* After a suggestion made by E. T. Hoch, B. S. T. J., November (1922), and by 

 H. H. Race, Jour. A. I. E. E., 51, 354 (1932). 



