DIELECTRIC PROPERTIES OF INSULATING MATERIALS 647 



upon their indirect action through the polarization which they create 

 in other elements of volume. 



The contribution which the polarization of the dielectric makes to 

 the force upon a charged particle in it has been calculated by Lorentz 

 to be (47r/3)P, where P is the polarization per unit volume induced by 

 the applied field. This calculation applies to an array of particles 

 with cubic symmetry and to isotropic materials.^ The internal or local 

 field F is then given by 



F = £ + y P. (3) 



E may be thought of as the force which has its origin in the direct 

 interaction between the charges on the plates of the condenser and the 

 charges in the polarizable complex on which attention has been fixed 

 (such as one of the cubes of Fig. 2), while the term (47r/3)P may be 

 regarded as an indirect force coming from the other parts of the dielec- 

 tric by virtue of their polarized state. 



It is assumed in the theory of dielectrics that the structure of mate- 

 rials is such that P is a linear function of F (or a linear vector function 

 in the case of anisotropic materials) ; then 



P = kF, (4) 



where k is the polarizability per unit volume. It can be seen that 



where A = 47r/3, and consequently that the relation between the 

 polarizability k and the susceptibility (e — l)/4x (= K) is 



K^^^ =^ , ^ ., , {4b) 



4ir \ — Ak ^ ^ 



whenever (3) is a valid expression for the internal field. 



The susceptibility can be calculated without presupposing the 

 validity of equation (3) for the internal field, while the value ofk depends 

 upon whether (J) or some other expression gives the strength of the internal 

 field in the dielectric. 



If L is the number of molecules per cubic centimeter, kJL(= a) is 

 the polarizability per molecule. This molecular constant a is called 

 the polarizability of the molecule. By multiplying a by Avogadro's 

 number N, we obtain the polarizability per mole of the dielectric: 



*H. A. Lorentz, "The Theory of Electrons," p. 138, and Notes 54 and 55. 



