DIELECTRIC PROPERTIES OF INSULATING MATERIALS 513 



not great. It is to be expected that many complex materials would 

 not have a conductivity which varies with frequency in accurate 

 agreement with (18), because the assumptions from which (18) was 

 derived are perhaps the simplest which could be made regarding the 

 structure of a dielectric. 



Discussion of y^ in Terms of a Model 



A convenient way of demonstrating the physical meaning of 700 and 

 at the same time of showing the general character of the physical 

 mechanism which is responsible for 7' becoming larger as the frequency 

 increases is to consider the operation of the model * used in the pre- 

 ceding paper to develop the formulae for dispersion. This model 

 depends upon the dielectric containing bound ions about which the 

 only things specified were the following: 



(1) That the displacement of a bound ion from its equilibrium 

 position in the dielectric by the applied electric field is opposed by a 

 restoring force proportional to the displacement; if the displacement 

 is designated as 5 the restoring force is/5. 



(2) That these ions experience in their motion a frictional force 

 proportional to their velocity in the direction of the applied field; this 

 frictional force is given by rs, where s is the velocity and r is a constant. 



(3) That the moving ions have a charge e and a negligible mass. 

 These are the essential features of the model and they can be repre- 

 sented concretely by imagining an ion held in a certain small region, 

 electrically neutral as a whole, in for example a glassy dielectric, by 

 forces characteristic of the structure of the solid. We may suppose 

 that this ion makes small excursions within this region around the 

 point (0 in Fig. 3) toward which it is attracted by a force proportional 

 to the displacement, and that its interaction with the molecules which 

 surround it in the dielectric is such that it experiences in effect a 

 frictional force proportional to its velocity in the applied field. The 

 ion of this model is, therefore, subjected to the same sort of frictional 

 resistance as are ions in solution in a liquid. 



From the relationship between polarization and displacement which 

 was discussed in the preceding paper, it is evident that the polarization 

 may be considered to be proportional to the displacement of the bound 

 ion of this model. (If P is the polarization per unit volume due to a 

 large number (w) of bound ions, each of charge e, the polarization is 

 evidently proportional to the average displacement s per ion, where 

 s = Pjne, but for the present purpose it will be sufficient to consider 

 the displacement 5 of a single bound ion.) We may, therefore, discuss 



^ For further details, see page 652 of the preceding paper, B. S. T. J., 17 (1938). 



