DIELECTRIC PROPERTIES OF INSULATING MATERIALS 529 



such that t::>> tc^ eooCoR, the apparent conductivity yciQ has the 

 value 



^0 ~ Coo ,,.< 



To = -^ = Too- (31) 



47rT 



The special value of ydt,) which we have designated as 70 in (31) will 

 be called the initial conductivity. 



Equation (31) states that the infinite-frequency conductivity (700), 

 obtained by a-c measurements, is equal to the initial d-c conductivity (70) 

 which would be obtained by extrapolating current-time curves toward the 

 instant of applying the voltage. This relationship, which has not been 

 demonstrated previously to our knowledge, is of interest in connection 

 with the interpretation of conductivity measurements. 



The model described in Appendix I and indicated schematically in 

 Fig. 3 illustrates the physical nature of the initial conductivity in a 

 simple manner. When a constant voltage Vi is applied to a dielectric 

 having the properties of this model an effective impressed field Fi is 

 established in the dielectric. This displaces the bound ion assumed 

 to be responsible for the polarization in this model. The magnitude 

 of the displacement 5 of this bound ion depends upon the length of time 

 that 7^1 is applied. If it is applied for a time which is much longer 

 than the relaxation-time, 5 approaches a constant value Si correspond- 

 ing to complete polarization of the dielectric. On the other hand, 

 during that stage of the charging process when the charging time tc is 

 negligible in comparison with the relaxation time t and at the same 

 time large as compared with the time constant e^C^R, the displacement 

 5 is negligible in comparison with Si. The resultant force tending to 

 displace the ion is then approximately equal to the impressed force; 

 eFi - fsi ^ eFi. 



Near the beginning of the charging process there is a brief interval 

 of time (e^Coi? <<C/c <^ t), when the motion of the bound ion of our 

 model in the applied field is essentially the same as that of a free ion. 

 During this interval the prevailing conductivity is the initial conduc- 

 tivity defined by equation (31). Although the bound ion of the model 

 is actually subjected to a force tending to restore it to its initial posi- 

 tion, this restoring force has not had time during the initial stage of the 

 charging process to build up to a magnitude appreciable in comparison 

 with the applied force. The initial conductivity corresponds to a 

 condition in the dielectric where bound ions act for a brief time as if 

 they were free as far as conduction processes are concerned. The 

 infinite-frequency conductivity corresponds also to this condition. 

 The variation of apparent conductivity with the time of charging is 



