DIELECTRIC PROPERTIES OF INSULATING MATERIALS 659 

 Wyman applies the procedure followed above yields 



On multiplying equations (29), (30) and (31) by Mjp three alterna- 

 tive formulae for the molar polarization of a dielectric having polariza- 

 tions of the type specified by equation (21) are obtained; the constants 

 in these formulae include only special values (eo and €oo) of the dielectric 

 constant and the relaxation-time, all of which can be obtained from 

 dispersion curves. 



The quantity ka — ^oo is a constant of the material, which, as equa- 

 tion (26) shows, represents the largest value which the absorptive part 

 of the total polarizability, i.e., the ka term in (19), can have for a given 

 material ; it may be described as the zero-frequency or static value of 

 the absorptive part of the polarizability. Evidence as to the nature 

 of a polarization can be obtained by investigating experimentally the 

 dependence of (^o — ^oo)/p on temperature; for example, if the polariza- 

 tion is due to the changes of orientation of polar molecules according 

 to the Debye theory this quantity should increase linearly with the 

 reciprocal of the absolute temperature. It is useful, therefore, to 

 express (^o — ^co)/p in terms of observable values of the dielectric 

 constant so that it may be plotted against temperature. In this con- 

 nection there is, however, the same complication which has appeared 

 in other places in this discussion regarding the relation between dielec- 

 tric constant and polarizability. The three relations which have been 

 discussed here yield for (^o — k^)lp the following expressions: 



eo — 1 eco — 1 



(^0 — ka,)lp == 



3 



47rp 



eo + 2 eco + 2 



_3_/eo_ 



(Clausius-Mosotti) (32a) 

 4^ I 3 / (for gases) {d>2b) 



The Complex Dielectric Constant 

 As the dielectric constant (e) is the quantity directly measured in 

 experimental investigations it is desirable to determine how it should 

 vary with frequency for the type of dielectric polarization described in 

 equation (21) or (29). Solving equation (5) for e we obtain 



1 +8^^ 

 e = —. {33>^ 



