Polarization and Magnetization Electrons. 405 



I venture to offer a new development of the same idea, 

 which distinguishes itself by the extreme simplicity of the 

 means employed. No use is even made o£ any theorem from 

 the theory of relativity. After completing the deduction, 

 nevertheless, it is easy to show the covariancy of the equa- 

 tions obtained in the sense of the theory of general 

 relativity. 



In addition, one hits on a contribution of the bound elec- 

 trons hitherto not yet signalized, so far as I am aware (§7). 



§ 1. Minkowski's Idea. 



Consider a stream of neutral atoms. For simplicity's sake 

 we shall take them to consist of a positive nucleus and one 

 ■accompanying electron, both of them carrying the elementary 

 charge. The motions of the heavy nuclei will be identified 

 with the motion of matter, and we shall assume that neigh- 

 bouring atoms will be very nearly similar and similarly 

 situated, so that the functions defining the positions of the 

 electrons relative to their nuclei, though not strictly constant, 

 will vary but slowly from one atom to the next. 



Of course the stream of positive nuclei will constitute an 

 electric current, and the stream of electrons another. As a 

 result of the displacements of the latter relative to the nuclei 

 their current will not have the same intensity as the positive 

 current from the nuclei. The combined effect will be 

 the current required in the field equations for ponderable 

 matter. 



It will be clear that if, given the displacements, we succeed 

 in rinding the resulting variation of intensity of the stream, 

 our problem will be solved, as soon as we shall have inter- 

 preted the result in terms of physical quantities such as 

 polarization and magnetization. 



The displacements can be regarded as depending on a varia- 

 tional parameter 6. It turns out that the terms in the result 

 proportional to 6 are connected to the polarization, and that 

 the terms proportional to 2 express the effect of magnetiza- 

 tion mainly. 



§ 2. IJie displacements. 



We imagine a stream of particles moving through a space 

 which will be described by the co-ordinates «r, y, z. Let 

 there be N of them per unit of volume, moving with velocities 

 clv/dt, dy/dt, dz/dt. which, after adding to them as a fourth 



