DIELECTRIC PROPERTIES OF INSULATING MATERIALS 537 



The superposition principle states that any of these discharge 

 curves may be derived from the discharge curve for complete polariza- 

 tion by subtracting from its ordinates the values which the charging 

 current would have if it had continued during the discharge. From 

 the method of deriving equation (21) it is clear that the superposition 

 principle is a necessary consequence of an assumed exponential growth 

 and relaxation of the residual polarizations, as required by the theory 

 of simple anomalous dispersion. If these in fact do not vary exponen- 

 tially with the time, whatever function they do follow appears in 

 general to obey an empirical superposition rule. Reference to (20o) 

 will indicate that if there are m polarizations of different relaxation- 

 times which are quite far apart, each polarization will simply contribute 

 two terms to the expression for Id', that is, 



m 

 3=1 



+ 7fi£ie-'''/*oo(^oK _ yj^g-Uc+td)if^CoR^ (22) 



Thus, the existence of the superposition principle for residual currents 

 as an empirical law suggests that the individual polarizations actually 

 vary exponentially with the time, though direct measurement of the 

 total discharge current seldom gives a single exponential curve. This 

 is, however, not the only possible interpretation. 



