Polarization and Magnetization Electrons. 415 



'corresponding to the complementary polarization n, and the 

 well-known magnetization- current crotm. As stated above 

 the current 



rot k 



originates from a second order influence of the motion of 

 polarized matter. It is neglected because of its smallness in 

 the deductions of Lorentz and of Cunningham *. In the paper 

 of Born cited above it is not separated from the magnetiza- 

 tion-current. Perhaps its action might be detected experi- 

 mentally if a rotating sphere of insulating material were 

 surrounded by a fixed circuit about its equator and placed in 

 a strong homogeneous electric field with the lines of force 

 parallel to the equator's plane. An oscillating rotation of 

 the sphere should induce an oscillating current in the 

 circuit. 



§ 8. Remarks concerning Covariancy. 



In the introduction allusion was made to the covariancy 

 of the result of the variation. Indeed, a reader familiar 

 with Einstein's theory of general relativity may easily con- 

 vince himself that equations (3) and (4) are invariant in the 

 general sense. From the definition of N?c a in § 3 it is clear 

 that Niu a is s/gx a contravariant vector, where s/ g is the 

 well-known factor in that theory ; for in the numerator N^V 

 is a definite' scalar number and dx a a contravariant vector, in 

 the denominator \/gdYdt would have been a scalar. 



~Niv a being i/g x a contravariant vector, we see that 



r<*Nw b —rl>l$w a ' 

 is Vg x a contravariant anti-symmetrical tensor, and 8Nw a : 



is seen to be \/gX the contravariant vector-divergency of 

 the tensor and therefore s/gX a contravariant vector 

 itself. 



The same may be said, mutatis mutandis, of the second 

 variation 8 2 JSiv a . 



Knowing the character of F ah and M« 6 as sj g x contra- 

 variant tensors, it is easy to deduce the ordinary transforma- 

 tion-formulae for the polarization and the magnetization. 

 This, however, will not be done here. 



* Lorentz, Eac. d. Math. Wiss. ; Cunningham, < Principle of Rela- 

 tivity.' 



