Electrodynamics for Moving Ponderable Media. 57 



In the case of a magnetic rotation alone J = 0, but the 

 expression for the angle of rotation cannot be put so simply. 

 We have 



^^-^) = {4^V + 4K + 4Le 2 p-{4^ 2 e 2 + 4K-4L6 2 } i , 



so that up to the first power in L, the rotation 6 is 

 7T e 2 L 2tt 2 e 2 L/ 



t(w;V + 4K)^ r 1 (4K + wV 2 )" 



These expressions for the rotation are thus independent 

 of the sign of w, i. e., are the same whether the medium 

 moves in the same direction as the wave of light, or in the 

 opposite direction. For a direction of the wave of light 

 oblique to that of the motion of the earth, these same 

 expressions for the rotation should be obtained in accordance 

 with the hypothesis by means of which the constitutive 

 relation (18) was obtained, though the analysis in any 

 particular case would be rather heavy. 



Manchester University,, 

 August 1913. 



Note added December 1913. 



I find that there is some difference of opinion as to what 

 is the correct interpretation of Minkowski's own work in § 8 

 of his paper. It seems clear that he himself regarded his 

 system of equations as true for any variable velocity. 

 According to the interpretation given in § 1 above,. 

 Minkowski's equations are to be considered as proved only 

 for a uniform velocity. 



The matter may, however, be considered in the following 

 way. The theory of relativity restricts the relations between 

 the various vectors to be such as are invariant in regard to 

 the particular transformations of the theory, and Minkowski's 

 work thus suggests constitutive relations which are true for 

 any variable motion. These, combined with the equations of 

 the field obtained from some theory of the constitution 

 of matter, Avould then form a scheme of electrodynamical 

 equations which are universally valid. 



In this case equations (9), (10) of § 3 would be universally 

 true and would correspond to a theory of the constitution of 

 matter as is developed in Minkowski's (posthumous) paper, 

 with the particular definition of magnetization involved in 

 that theory. 



