534 BELL SYSTEM TECHNICAL JOURNAL 



Let gc be the charge per unit area on either of the condenser plates 

 at any stage of the charging process, that is, at any time tc after the 

 instant at which the voltage was applied. On converting (12) into 

 e.s.u., we have for the charge at any time during the charging process: 



D,^e^_ e ^^^_^,,^^c.u _ (fiZLi^ £^,-,./.. (13) 



47r 47r 47r 47r 



Therefore the ballistic or d-c dielectric constant at any time of charg- 

 ing tc, is 



e(/.) = ^ = 60 - e«oe-'^'^-^"« - (eo - e^)e-'^''. (14) 



The d-c dielectric "constant" appears in this equation as a function 

 of the charging time. Its dependence on charging time is analogous 

 to the dependence of the a-c dielectric " constant " on frequency. The 

 static dielectric constant eo is obtained when charging has been con- 

 tinued until tc ^ r, that is, when te is infinite the dielectric constant 

 has its static value {tc = «= , €(/c) = eo) and when tc is zero the dielectric 

 constant is zero {tc = 0, e{tc) = 0). 



The charging current is obtained by differentiation of (13) and is 



The charging current per unit voltage gradient, or the apparent con- 

 ductivity 7t(^<), is 



7c(/o) = 1^ = -y^e-'c/^xCofi + ^,g-'c/r, (16) 



where ^r = (47rCoi?)~^ and 7oo = (eo — e«,)/4Tr. (It will be noticed 

 that if we define a quantity Gn = 1/R, it follows that (4xCo-R)~^ 

 = GjfdIA = jr since 47rCo = A/d. The quantity jr is the specific 

 conductance which a fictitious material must possess if it were put in a 

 condenser of geometric capacitance Co and required to conduct the 

 same current as Co when in series with an external resistance R.) 



At any stage of the charging process such that tc is large as compared 

 with e^CoR, but at the same time small as compared with r the ap- 

 parent conductivity given by (16) reduces to 



yc{tc) = Too. 



This value of jc{tc), where e^CoR « tc « t, will be designated by 70 

 and called the initial conductivity. Using this terminology we see that 



