528 BELL SYSTEM TECHNICAL JOURNAL 



relationships: 



Co = C niax "I t max) (28) 



too t max C maX) \^^/ 



€0 — Coo = 2c"n,ax- (30) 



The comparison of the last equation with equation (20) brings out 

 an interesting contrast between the maximum dielectriQ loss per cycle 

 («"niax) and the maximum dielectric loss per second (tx)- The maxi- 

 mum dielectric loss per cycle is completely determined by the difference 

 between the static dielectric constant and the optical dielectric constant. On 

 the other hand, the dielectric loss per second depends as well upon the 

 relaxation-time. The relaxation-time usually varies rapidly with 

 temperature, whereas (eo — €«,) changes comparatively slowly with 

 temperature. The temperature-dependence of the maximum dielec- 

 tric loss per cycle is related to the polarizability of the material, whereas 

 the temperature variation of the maximum dielectric loss per second is 

 primarily a measure of the change of internal friction with temperature. 



In the foregoing we have discussed the conductivity, dielectric loss 

 and relaxation-time of dielectrics which have simple properties with 

 respect to the frequency-dependence of these quantities. However, 

 for many dielectrics, particularly solids, the experimental data are not 

 in agreement with the dispersion formulae for a single relaxation-time 

 which has been discussed here. The explanation usually adopted for 

 this discrepancy is that the polarizations induced in the dielectric 

 possess a distribution of relaxation-times. 



The D-C Counterparts of Anomalous Dispersion 



A dielectric so constructed that it exhibits anomalous dispersion 

 under an alternating voltage should show some equally characteristic 

 behavior when a direct voltage is substituted for the alternating one. 

 These characteristics may be described as the d-c counterparts of 

 anomalous dispersion. They include certain definite types of variation 

 of current with time under constant applied potential. 



In the appendix the d-c counterparts of anomalous dispersion are 

 derived by employing the model used throughout this paper. This 

 enables us to demonstrate an especially simple relationship between 

 the a-c and d-c conductivity. 



Equation (16) of the appendix gives the apparent conductivity as a 

 function of charging time. As it has been assumed that e^CoR <$C t, 

 the first term of equation (16) will quickly become negligible. Then 

 for charging times, measured from the instant of applying the voltage, 



