DIELECTRIC PROPERTIES OF INSULATING MATERIALS 519 

 for the model we have employed to illustrate this discussion, 



The factors in this expression may be seen to have the following general 

 significance: the quantity e is the charge on each bound ion; n is the 

 number of bound ions per unit volume; and ej^irr is a measure of the 

 mobility per ion. This mobility does not refer to the motion of an 

 ion which is free to move through the dielectric from one electrode to 

 the other but to the mobility of a bound ion in small, local translational 

 motions or the rotational mobility of a polar molecule. The remaining 



(I 9 \ 2 

 -^^— r — I is not of direct significance in the present connection.^ 



We see then that y^ is also analogous to ordinary electrolytic conduc- 

 tion in that its physical mechanism may be represented as depending 

 upon a mobility, a concentration and a factor such as dipole moment 

 or charge per bound ion. The latter factor has a function in this 

 mechanism which is similar to that of the valence or charge per ion in 

 electrolytic conduction. 



These considerations indicate that although 700 is a property of 

 polarizable units such as polar molecules it has the usual attributes of 

 a conductivity due to free ions or free electrons. A dielectric which 

 exhibits simple anomalous dispersion conforming to equations (17) 

 and (19) then has two conductivities. One of these is the conductivity 

 due to free ions; this will be called the free ion conductivity and desig- 

 nated throughout this paper by 7/. The other is a conductivity which 

 is a characteristic of the polarizable complexes responsible for anoma- 



5 When 600 = 1, equation (23) reduces to 



-^—zi — I would be absent if the material possessed 



no optical polarizations. Evidently 70, depends upon the optical refractive index 

 Vfx, as well as upon the characteristics of the absorptive polarization. In mixtures 

 it may be possible to vary these two factors independently. Since optical polarization 

 currents make no direct contribution to the energy dissipation in the dielectric, even 

 up to the highest radio frequencies, it is interesting to observe that they make an 

 indirect contribution according to equation (23). Their indirect action takes place 

 by virtue of their effect on the actual internal field which acts upon each polarizable 

 aggregate in the dielectric. The effect of the interaction of the optical polarization 

 with the absorptive polarizations is to increase the apparent mobility of the polar- 

 izable complexes responsible for anomalous dispersion. 



