510 BELL SYSTEM TECHNICAL JOURNAL 



This demonstrates the statements made earlier that 7' is proportional 

 to the heat developed per second and e" to that developed per cycle in 

 the dielectric. In the above equations W is in ergs per second or per 

 cycle when Eq, 7', and e" are in e.s.u. 



It can be seen from equation (8) that the total current flowing in the 

 dielectric has a dissipative and a non-dissipative part: e' is proportional 

 to the non-dissipative part, and e" to the dissipative part. The loss- 

 angle, €" je' , may be interpreted as the ratio of the dissipative to the 

 non-dissipative current and the power factor as the ratio of the dissi- 

 pative current to the total current. 



The Frequency-Dependence of Conductivity 



When the dielectric with which we are dealing possesses the property 

 of anomalous dispersion, the expression for the loss factor e" as a 

 function of frequency is 



1 -f co2r2 



(17) 



as was shown in the preceding paper. Substituting this expression 

 for t" in (14) we obtain: 



, _ e^ ^ J_ (ep - eoo)coV , . 



'^ 47r 47r ■ 1 + co^r^ ^^^ 



1 (eo-eJcoV ^^g^^ 



47r X 0.9 X 10^2 1 -f- coV^ 



where 7' is expressed in e.s.u. in (18) and in ohm"^-cm~^ in (18a), and 

 Co is the static dielectric constant, e^ the infinite-frequency dielectric 

 constant and t is the relaxation-time. 



Differentiation of (18) with respect to frequency shows that 7' has 

 no maximum when plotted against frequency; the conductivity of any 

 dielectric to which {18) applies should always increase with frequency, 

 where it changes at all. On the other hand, dififerentiation of (17) with 

 respect to w shows that the dielectric loss-factor has a maximum which 

 occurs when wr = 1. The dielectric constant e' is given by 



e' = 6. + ^^^^, (19) 



1 + w r 



and it will be seen that it shares with the conductivity the property of 

 having no maximum when plotted against frequency. In Fig. 1 

 schematic curves are drawn which show the diff^erences in the frequency 

 dependence of 7', e" and e' for a material having an absorptive polariza- 



