DIELECTRIC PROPERTIES OF INSULATING MATERIALS 661 



Equation (39) is the complex dielectric constant expressed in rectangu- 

 lar form for a dielectric having a polarizability (per unit volume) given 

 by (21) and in which the internal field {F) is such that the Clausius- 

 Mosotti relation (equation (8)) applies. 



For gases the derivation of the expression for the complex dielectric 

 constant from that for the polarizability is simpler, though the same 

 in principle, as the above. From {22b) or (6) we see that e = 1 + 47r^ ; 

 and on substituting (30) for 4x^ and rationalizing we obtain 



, to - io. . (eo - 6^)cor' 

 e = Coo H To — t ;s— • (4U ) 



1 + W^T 1 + COT 



And when the relation between polarizability and dielectric constant 

 is that proposed by Wyman, cf. (9) or (22c), we again obtain (40) on 

 substituting (31) for (47r/3)^ in (9) and rationalizing. 



It will be noticed that the difference between (40) and (39) is that t' 

 appears in the former and r in the latter, r being given by (35). This 

 shows that the factor (eo + 2)/(eco + 2) has its origin in the fact that 

 for the conditions to which (39) applies F — E + (47r/3)P, while for 

 the conditions to which (40) applies F = E, or is a linear function of E. 

 T is the relaxation-time for the dielectric constant, while t' is the re- 

 laxation-time for the polarizable units in the material; when F = E 

 these two relaxation-times are equal. 



For materials of high dielectric constant the factor (eo + 2)/(ecD + 2) 

 produces a considerable difference between r and r'; for example, for 

 water or ice r is about 23r'. In a recent paper, R. H. Cole ^^ has 

 shown that when the volumes of certain polar molecules are calculated 

 from r by means of Debye's expression for the relaxation-time better 

 agreement with the volume estimated from van der Waals' equation is 

 obtained when Onsager's relation between polarization and dielectric 

 constant is used instead of the Clausius-Mosotti relation. In par- 

 ticular, for water the van der Waals coefficient gives 13 X 10~^^ c.c. 

 for the volume of the molecule, while r' gives 0.5 X 10~^* c.c. on the 

 Clausius-Mosotti relation but 12 X lO"^"* c.c. on the Onsager relation, 

 and 4 X 10"^* c.c. for a modified Onsager relation. And if Wyman's 

 relation is used, r = 23r', and the volume should be 23 times that 

 calculated on the basis of the Clausius-Mosotti relationship, or about 

 11 X 10-24 c.c. 



Both equation (39) and equation (40) can be expressed in the form 



e = e' - ie", (41) 



" R. H. Cole, Jour. Chem. Pkys., 6, 385 (1938). 



