DIELECTRIC PROPERTIES OF INSULATING MATERIALS 665 



dielectric constant and loss factor with frequency which is observed in 

 the different classes of materials to which the various items in the 

 table refer. In some cases the original formulae, as they appear in the 

 literature, have been expressed in terms which do not show an obvious 

 equivalence to (41), (41a) and (416), but by re-expressing them in the 

 form (41) and then determining eo and eo, by letting co = and oo , 

 respectively, the list of expressions given in Table I is obtained. It is 

 interesting that theories based on such widely dissimilar physical 

 mechanisms as rotating polar molecules (Item 1, Table I) and a block- 

 ing-layer of high resistance at an electrode/dielectric interface (Item 

 3(6), Table I) should yield an identical form of variation with frequency. 

 For the first two polarizations listed in Table I, the alternative 

 expressions obtained by assuming three alternative relationships be- 

 tween polarizability and dielectric constant are given. By means of 

 Table II the quantities (^o — ^co) and t' can be obtained from (eo — e<x,) 



TABLE II 

 The Relationship between {ko — k^) and (eo — «a>) and between t' and t 



(fco - feco) t' 



^, • 1>T . , • 13 , .• 3 3(€0 — €co) €„, "t" 2 



Llausius-Mosotti Relation — - • -. , ^. . ; — — - ■ ■ — r 



47r (€0 -h 2)(ecD -|- 2) to + 2 



Gases —- • (to — «co) t 



47r 



■2 



Wyman's Empirical Relation -— • — "" t 



47r 8.5 



and T in Table I. The resulting expressions can then be substituted 

 for (^0 — ^co) and r' in equation (26) yielding expressions for the polariz- 

 abilities of the different types of polarization listed in Table I. The 

 molar polarization can then be obtained by multiplying (26) by 

 (47r/3)(M/p). However, in general it is not likely that any useful 

 purpose is to be served by calculating the molar, polarization for inter- 

 facial polarizations; a more significant quantity would be the polariza- 

 tion per conducting particle, when the polarization is of the type {M), 

 Table I, and the number of conducting particles per unit volume can 

 be estimated. 



We have pointed out that a number of theories which have been pro- 

 posed for the explanation of the variation of dielectric constant with 

 frequency may be expressed in the forms (41a) and (416) when the 

 expressions listed in Table I are substituted for (eo — eco) and r, but 

 we have not yet indicated how these formulae agree with experimental 

 data. For such materials as ice (see Fig. 3, for example) and for 



