DIELECTRIC PROPERTIES OF INSULATING MATERIALS 657 



specified by the second term on the right. The quantity t' is called 

 the relaxation-time. 



On multiplying the left-hand side of equation (21) by (47r/3)(M/p) 

 and the right-hand side by (4x/3)(7V/L) we obtain 



Air Mk _ ^ { ki 



.,, ne^ { 1 



fL\\^ ic 



(22) 



which is the molar polarization. 



For dielectrics to which the Clausius-Mosotti relation applies, 

 equation (8) shows that 



^ir Mk M e- \ 



3 p p € -\- 2 



(22a) 



and in fact the expression on the right-hand side of (22a) is frequently 

 called the molar polarization. Reference to equation (6) shows, how- 

 ever, that for gases (22a) reduces to the simpler relation. 



4^Mk M (e- 1) 



TV^7~1 — ^^^^^ 



And for Wyman's relation between dielectric constant and polariz- 

 ability, which has been discussed earlier, the molar polarization be- 

 comes 



4TAIk M e -f 1 



3 p p 8.5 



(22c) 



Equations (22a), (22b) and (22c) are not the only relations between 

 dielectric constant and molar polarization which have been proposed, 

 but they apparently cover moderately well many of the conditions 

 met in practice. For the right-hand member of equation (22) can be 

 substituted whichever of the three expressions (22a), (22b), (22c) seems 

 the most suitable for the type of dielectric under investigation. 



If in equation (21) w is set equal to zero we obtain the zero-frequency 

 (or static) polarizability 



k^ = ki + ne'^lf (23) 



and if w is set equal to infinity we obtain 



^oo = ki. (24) 



Subtraction gives 



ko — k^ — ne^lf. (25) 



Substituting (24) and (25) in (21) gives 



ko - 



TTi 



k = k^-^( ^\ .^'^, ) • (26) 



