Polarization and Magnetization Electrons. 413 



Turning to the second part of M> 6 we require the value of 

 8w a . This we get from the known values of SNw* and 

 8N = SNw (4 > (form. (7)). It turns out to be 



dt K /r B# c 



Now write down 



i^N (r a 8iv h — i*8iv") = J<?N (p<*Siv b —p h hw a ) 



— J<?N (r (A) Bw a . w h — r (4) Sw 5 . tc») , 



and we see that the latter part : 



-i*N {W^ ~ (>.V)^)^-^ (4) (^ - (p.V)w*)«* j , 



gives <z polarization again with the corresponding Rontgen- 

 vector. 



This last correction, 



brings the polarization into complete agreement with the 

 value given in (6) for the electrons' exact displacements. 



These second-order polarization corrections are very inti- 

 mately connected with the magnetization, and always come 

 into play whenever magnetized matter is moving. This is 

 well known. 



It remains to investigate the nature of the part 



^e~N(p a Sw h — p h hw a ). 

 If we write 



±eK<j>«Swi-pl8w«) = ieN{p»^ -p* ~\ 



m*(rr& -*>%), 



we notice that both expressions vanish for a value 4 of one 

 ot: the index-numbers a or b. We recognize that 



2c e V dt p dt) 



nre the components of the magnetic momentum of an atom. 

 Thus, writing m x , m y , m z for the magnetization we evidently 

 have 



