DIELECTRIC PROPERTIES OF INSULATING MATERIALS 527 



dispersion has no maximum when plotted against the frequency and 

 its behavior is, therefore, in contrast with the tangent of the loss angle 

 of the total polarization current, i.e., the sum of the optical polarization 

 current and the absorptive polarization current. 



From the above discussion it will also be evident that the physical 

 basis for the maximum in tan 5 is different from that of the maximum 

 in e". As we have just shown, the maximum in e"le (= tan 6) de- 

 pends upon the inclusion of optical polarizations in t' . On the other 

 hand, there would be a maximum in e" even if the part of the dielectric 

 constant which is due to optical polarizations (e^,) were neglected or 

 considered to be zero. This will be evident by differentiation of 

 equation (17). 



The maximum in e" is an intrinsic property of the absorptive polari- 

 zation. The general nature of the mechanism by which it occurs is as 

 follows: e" is proportional to y'loi] as the frequency increases y'jc^ at 

 first increases, but when y' reaches the constant value y^, further in- 

 crease in frequency causes y'/co to decrease. 



The quantity r which we have discussed here is a property of the 

 dielectric as a whole as we indicated in the preceding paper. This 

 quantity is connected with the relaxation-time t' of the individual 

 polarizable units by the relation 



when the material is of cubic or isotropic structure. This relation- 

 ship is a consequence of the fact that the actual force acting upon a 

 particle within a dielectric depends not only upon the applied field 

 of external origin but also upon a force exerted by the polarization 

 induced in the dielectric. 



The Relationship between Dielectric Constant and 

 Dielectric Loss 



If e'max is the value of the dielectric constant at the frequency where 

 the loss factor e" is at a maximum when plotted against frequency, 

 we have 



/ _ I ^0 ~ ^00 _ €o -|- 6^0 ,-,. 



e max — ^« ~r 1 I , 9 ^2 ~ 9 ' \^^) 



i ~r U' max" •^ 



// (fO ~ foojWmaxT' ^0 ~ ^<x, 



By addition and subtraction of (26) and (27) we obtain the following 



