412 Dr. A. D. Fokk'er on the Electric Current from 



one may see at a glance that the first three of the com- 

 ponents of the variation e8Niu a are the components of 



rot[p.w]+p, (8 a) 



and that the fourth becomes 



-divp (8b) 



The first variation thus furnishes a polarization-current p 

 and the corresponding Ront gen-current rot[p .w] ; besides it 

 shows a polarization-charge. 



§ 7. The interpretation of the second variation. 



The second variation too is connected by a differential 

 operator to a tensor, M a& : 



7\M* b 



where 



M ab = ±(er a SNiv b — er b 8Nw a ). 



We divide this into two parts : 



M« 6 = i£?6N (r<*w b - r b w«) + ^N(V«Sw 6 - r b 8w a ) , 



the first of which is nothing but a correction to the polari- 

 zation-tensor V ab . We can put it into the form 



^SN (r a w b — r b w a ) = %e8N(p a w b — p b u «), 



and as in the preceding section we find contained in it a 

 polarization 



heSNp", 



and the corresponding Rontg en-vector. At a closer inspection, 

 taking SN from (7) we see 



The latter part is in good agreement with a term of the 

 exact expression (6) for the displacements. The former part 

 implies a correction that is grasped in its meaning as follows. 

 Imagine that we want to know the polarization and that we 

 therefore choose an arbitrary closed surface, taking the sum 

 of the electric momenta of the atoms within and dividing by 

 the volume. Then our correction amounts to saying that an 

 atom will be reckoned to lie within the surface only when 

 the centre halfway between nucleus and electron lies 

 within. 



