642 BELL SYSTEM TECHNICAL JOURNAL 



amplitude and charge extended over all of the hound charges in a unit 

 volume of the material determines the dielectric constant of the mate- 

 rial. The energy dissipated as heat by the motions of these bound 

 charges in the applied electric field represents the dielectric loss per 

 second, a quantity which is proportional to the a.-c. conductivity 

 after the d.-c. conductivity has been subtracted from it. The ima- 

 ginary part of the complex dielectric constant is proportional to the 

 dielectric loss per cycle. 



While the physical meaning of the dielectric constant and dielectric 

 loss can be conveniently described, as above, in terms of the amplitudes 

 and energy relationships of bound charges in their motions in an 

 applied electric field, a more useful basis for the discussion is that 

 provided by the concept of polarizability. In the present application 

 the polarizability is equivalent to the product of charge and amplitude, 

 but it has the advantage of being a quantity which is defined and dis- 

 cussed in the general theory of electricity as well as in that of dielec- 

 trics. The dielectric constant is then found to be related closely to 

 the polarizabilities of the assemblages of charged particles which the 

 dielectric contains. 



The polarization of an assemblage of charges is a quantity defined in 

 electrostatic theory as the vector sum 



p = HeSi, (1) 



where Sj is the distance of the i^^ charge, d, from a point chosen as 

 origin, and the summation is extended over all of the charges in the 

 assemblage, for which d is a typical charge. (If the assemblage has no 

 net charge {Y^^i = 0), the origin may be arbitrarily located without 

 affecting the value of p.) 



The polarization is a vector quantity. It can be written as the 

 product of a scalar quantity p, which represents the magnitude or 

 electric moment of the polarization and a unit vector pi which gives 

 the direction of the polarization ; thus p = ppi. As it will not be neces- 

 sary to distinguish between the properties of isotropic and anisotropic 

 materials in this article the direction of the polarization need not be 

 emphasized. The notation will therefore be simplified, in general, by 

 using the magnitude or scalar part of such vector quantities as the 

 polarization, the electric field intensity and the displacement of charged 

 particles. 



To illustrate the application of equation (1) let us consider a very 

 simple configuration consisting of two charges -f e and - e (see Fig. 1). 

 The vector polarization of this configuration is p = e(si — S2) = ppu 

 where p is the magnitude or electric moment of the polarization and 



