508 • BELL SYSTEM TECHNICAL JOURNAL 



as shown in the preceding paper. The current density in the dielectric 

 is then 



^+.^)£o.- (8a) 



= (7' + iy")E,e''-'\ (86) 



where 7' = e'co/Air and y" = e'w/Aw. It is evident that 7' + iy" (=7) 

 is the complex conductivity. 



The dielectric constant and conductivity for alternating currents 

 are determined by measurements, made with bridges or by other 

 means, which give the admittance or impedance of the condenser con- 

 taining the dielectric at the particular frequency at which the measure- 

 ment is made. This admittance ^ may be expressed in terms of the 

 equivalent parallel capacitance (Cp) and conductance (Gp) and an 

 alternative expression for (8) is then 



dq 0.9 X 1012 .^ , .^ . ,, ^, .„. 



• J = -^ (Gp + tCp<^) Foe"-', (9) 



where Gp is expressed in mhos (or reciprocal ohms) and Cp in farads 

 and 0.9 X 10^^ is the ratio of the farad to the electrostatic unit of 

 capacitance and also of the mho to the e.s.u. of conductance. 



By comparing (9) with (8), (8a) and (8&) we obtain expressions for 

 7', e" and e' in terms of the quantities Cp and Gp as directly measured 

 on a bridge or similar arrangement. However, the expressions ob- 

 tained are briefer if we make use of the fact that, when expressed in 

 farads, the capacity Co of the empty condenser is 



^' " Ayrd X 0.9 X W ' ^^^^ 



Then it is evident that 



e' = CpICo, (11) 



e" = Gp/Coc^, (12) 



y' = Gp/AwCo (13) 



= €"a;/47r = e"//2. (13a) 



^ Measurements on a series bridge give directly the equivalent series resistance 

 Rs and capacitance C. These data can be converted into equivalent parallel con- 

 ductance and capacitance by the general relationships 



