648 BELL SYSTEM TECHNICAL JOURNAL 



Na = Nk/L. And if m is the mass of a molecule, Nm = M, where M 

 is the molecular weight, and Lm = p, where p is the density; so that 



N _ M 

 L' p 



and the polarizability per mol may be written as Mk/p. 



From equations (3) and (4) (or 4-b) it can be shown that the polariz- 

 ability is related to the dielectric constant by the familiar relation 



3^ 



47r 



e - 1 



6 + 2 



(5) 



which however is only valid when (3) is valid — and for some materials 

 (3) is apparently not valid. 



For gases the term (47r/3)P in (3) is so small as compared with E 

 that F is approximately equal to E and 



k = K = '-^- (6) 



47r 



The polarizability and susceptibility are then equal. The physical 

 reason for this is that the ratio of intermolecular space to the space 

 occupied by molecules is much larger in a gas than in a solid or liquid 

 and the direct force exerted by the charges on the condenser plates on 

 a charged particle in the dielectric is then much greater than the in- 

 direct force which they exert through the polarization induced in other 

 molecules. 



It is customary to call the quantity (47r/3)^ the volume polarization, 

 and it is often denoted by the letter p. The volume polarization may 

 be thought of as 47r/3 times the polarization induced in the dielectric 

 per unit volume per unit applied field. The convenience of using 

 {4Tr/3)k instead of k comes from the occurrence of the factor 47r/3 in 

 the relation (5) between dielectric constant and polarizability. 



On dividing equation (5) by the density we obtain a quantity which 

 is called the mass polarization, as it is 47r/3 times the polarizability 

 per gram : 



1 



P 



-2]='4~- m 



+ 2\ 3 



And on multiplying (7) by the molecular weight of the material we 

 obtain 



pe+2 3p 3 L 3 



