516 BELL SYSTEM TECHNICAL JOURNAL 



Rs both being shunted by a second air condenser C«. In this equiva- 

 lent circuit, Cs and Rs refer to the polarizations responsible for anoma- 

 lous dispersion, and C«. to the optical polarizations. The frequency- 

 dependence of the equivalent parallel capacitance and conductance 

 of this network is 



Cp = Coo I i 4- o}^T^ 



and 



(Co — Cx)orT 

 1 + oi'T^ ' 



(22) 



where Co = Cs + C^, and T = CsR,. In the above expressions 

 (Co — Co,) and T are analogous respectively to eo — e^ and t in equa- 

 tions (17) and (19). 



The physical basis for the infinite frequency conductivity in this 

 model depends upon the fact that at high frequencies the impedance 

 of Cs is so low that nearly the whole drop in voltage is over the re- 

 sistance Rs. This simple network is capable of representing the 

 frequency-dependence of materials exhibiting anomalous dispersion 

 due to a polarization having a single relaxation-time. In fact, when 

 the frequency is sufficiently high that it is in the range where the con- 

 ductivity is independent of frequency, the required network becomes 

 even more simple, for it then reduces to Cx shunted by Rs, where the 

 magnitude of C«, corresponds to e^ and that of Rs to I/tx- 



Polarization Conductivity 



The operation of the models which have been discussed above pro- 

 vides a basis for interpreting the physical nature of 7x. The essential 

 characteristics brought out by these models are listed below. They 

 show the justification for considering y^ to be a conductivity in the 

 same sense as the ordinary d-c conductivity. 



(1) To obtain y' in an actual measurement on a dielectric, we sub- 

 tract the d-c conductivity 7/ from the total a-c conductivity. There 

 is then no contribution from free ion conduction in y' and consequently 

 none in 700, its limiting value at high frequencies. Polar molecules or 

 other polarizable aggregates in the dielectric must then be the origin 

 of 7x. 



(2) In the second place 700 is independent of frequency, a property 

 which puts it on the same footing as the d-c or free-ion conductivity 

 in at least one respect. 



(3) Earlier in this paper it was mentioned that the heat developed 

 in a conductor for a given voltage is proportional to the total current, 



