DIELECTRIC PROPERTIES OF INSULATING MATERIALS 655 



anomalous dispersion, equation (10) reduces to 



r,s-^f,s = eF (17) 



and equation (11) becomes 



r2p +hP = n,e'F. (18) 



Decombe's theory, which has been mentioned earlier, was based upon 

 an equation equivalent in most respects to (18), while Drude's expres- 

 sions for dispersion were obtained by a method equivalent to neglecting 

 wco^ in (12). 



Each term in equations (17) and (18) has an evident dynamical 

 significance. Consequently, a physical picture of the essential nature 

 of the anomalous dispersion process is given by equations (17) and 

 (18) even though the values of constants r2,/2, «2 and e are not specified 

 in terms of independently measurable properties of the dielectric. 

 Thus the term f2S represents a restoring force tending to return the 

 particles displaced by the impressed field to their initial positions, the 

 constant /2 acting as a stiffness coefficient; the term r2S acts as a fric- 

 tional force, r being a measure of the friction experienced by, for exam- 

 ple, a moving ion or a rotating polar molecule; and, finally, eF is the 

 driving force tending to displace a particle of charge e. Evidently 

 conditions which are sufficient to produce anomalous dispersion exist 

 whenever the motion of charged particles in an applied field is suffi- 

 ciently specified by considering the effects of a restoring force pro- 

 portional to the displacement of the typical particle and of a frictional 

 force proportional to the velocity of the particle in the direction of 

 applied field, as in equation (17). Or, putting it in more general terms, 

 we may say that anomalous dispersion occurs whenever the relation 

 between the polarization per unit volume and the force due to the 

 internal electric field is given by an equation which can be reduced to 

 (18). However, the possibility that anomalous dispersion may also 

 occur under conditions which cannot be described by equation (18) 

 is not excluded by the considerations given here. 



A third type of polarization which can be obtained by selecting 

 suitable sets of values for the constants of equation (12) is that in 

 which none of the terms in the denominator of (12) can be neglected in 

 the electrical range of frequencies. Let ks be the polarizability for 

 this type of polarization which can then be represented by affixing the 

 subscript 3 to the constants m, r, f and n of equation (12). This type 

 of dispersion includes both the normal and the anomalous types but, 

 as has already been indicated, in the radio and power ranges of fre- 



