DIELECTRIC PROPERTIES OF INSULATING MATERIALS 503 



which is not less important than the dielectric constant as a property 

 of an insulating material. Though general aspects of the conductivity 

 will be described for the sake of completeness, we wish mainly to show 

 that materials which possess the property of anomalous dispersion 

 may be considered to have two quite definite conductivities: one of 

 these is the ordinary d-c conductivity due to free ions or electrons; 

 the other is a special value of the a-c conductivity which will be dis- 

 cussed in this paper. We believe that the recognition of the existence 

 in many materials of two conductivities instead of one is of considerable 

 advantage, particularly in interpreting the behavior encountered in 

 direct-current conductivity measurements on insulating materials, a 

 subject upon which there has existed a considerable divergence of 

 opinion. 



The measurement of the direct-current conductivity of an insulating 

 material is usually complicated by the fact that the current which 

 flows when a constant potential is applied does not remain constant 

 but decreases with time. The meaning of this variation of the current 

 is open to more than one interpretation. Some investigators consider 

 that its final value, approached asymptotically, and perhaps not closely 

 approximated until a constant potential has been applied for an hour 

 or more, is the proper basis for the calculation of the true conductivity 

 of the material. Other investigators, notably Joffe, consider that the 

 current/time curve should be extrapolated toward the instant of 

 applying the voltage in order to obtain the proper value of the current 

 to use in calculating the true conductivity. On this account the terms 

 initial conductivity, final conductivity and true conductivity frequently 

 appear in papers on the conductivity of insulating materials. While 

 it has been usual to take either the initial or the final conductivity as 

 the true conductivity, rejecting the other, it is shown here that with 

 certain exceptions both conductivities are true conductivities in the 

 sense that they are independent properties of the material having a 

 different, though related, physical significance. 



The relationships which will be brought out here depend in an 

 essential way on the nature of the variation of a-c conductivity with 

 frequency for materials which possess the property of anomalous dis- 

 persion. The a-c conductivity of a dielectric exhibiting simple anoma- 

 lous dispersion increases as the frequency increases until the frequency 

 is high as compared with the reciprocal of the relaxation-time; it then 

 approaches asymptotically a constant limiting value. It is shown 

 here that this limiting value of the conductivity, which will be referred 

 to as the infinite-frequency conductivity, is a true conductivity of the 

 material, analogous to the ordinary d-c conductivity, and that it is 



