654 BELL SYSTEM TECHNICAL JOURNAL 



In this discussion it will be sufficient to consider that the different types 

 of polarization designated by ^i, ^2 • • • kw differ from one another only 

 in having different sets of values for the constants of equation (12), 

 designated by the subscripts 1,2,3 • • • w, for example, the character 

 of the polarizability k\ is specified by the set of constants m\, ri,fi and «i. 

 In the first place it is evident that when the frequency of alternation 

 of the voltage applied to the dielectric lies in the radio and power range 

 it is possible to select any number of sets of values of m, r,/ which will 

 make the terms mco^ and roo negligible in comparison with / in the 

 denominator of (12). Let nti, ri, /i be an example of such a set of 

 constants and let there be fii particles per unit volume to which these 

 constants apply. Then for this type of polarization equation (12) 

 reduces to 



i,=^'- (15) 



This type of polarization is independent of frequency and will be 

 referred to as an instantaneous polarization or an optical polarization. 

 The main representatives of the instantaneous or optical polarizations 

 are the electronic and atomic polarizations, which experience dis- 

 persion in the visible and infra-red but which are independent of fre- 

 quency in the electrical range, and the contribution of this polariz- 

 ability to the dielectric constant is therefore frequently calculated from 

 refractive index measurements. 



A second type of polarization results if we assume that the dielectric 

 we are considering contains a class of particles for which mw^ in equation 

 (12) is negligible by comparison with roo and with/, but in which rw is 

 of the same order of magnitude as/ in the electrical range of frequencies. 

 Let W2, ^2, /2 be a typical member of this class, the number of such 

 particles per unit volume of the dielectric being W2. Then for this class 

 of particles equation (12) becomes 



(16) 



{iriu -f- /s) 



This expression represents the type of variation with frequency to 

 which the name anomalotis dispersion is given, and in the preceding- 

 paper the type of polarization which produces it was called an absorp- 

 tive polarization. 



It can readily be seen also that neglecting the ms term in (10) or 

 the mP term in (11) leads to the same expression for k, i.e., equation 

 (16), as does neglecting the wco^ term in the denominator of (12). 

 So for any member, {ri, ji, ^2), of the class of particles which produces 



