Dynamics of the Electron. 



79 



(Eigenzeit) of motion of the electron. This conclusion * is 

 reached in a general way from his theory of the equivalence 

 of the forms for equation of motion of material particles 

 when referred to systems moving with uniform velocity past 

 each other. Minkowski f practically uses the same hypo- 

 thesis as I have done (Effective force is equivalent to the 

 Impressed force), but in case of the electron he begins by 

 implicitly ascribing a rest-mass to the electron. But the 

 method adopted by me is fundamentally different, as will 

 appear in due course. Elsewhere, Minkowski J deduces it 

 from the Principle of Least Action, combined with the 

 principle of conservation of mass in a space perpendicular 

 to the axis of motion. Besides, the investigation has a direct 

 bearing on the theory of Electromagnetic momentum as 

 developed by Lorentz and Abraham. 



Let us now concentrate our attention on a single electron 

 moving with a velocity v. The force components at an 

 external point due to the motion of the electron are given 

 by the equations (1). Generalizing, or rather recasting 

 Maxwell's theorem of stresses into new forms, Minkowski 

 has shown that the force components (f x ,fy,f z ,fi) can be 

 put into the forms 





BX, 

 3* 



BXy 



By 



♦$ 



,BX ? 

 + BZ 



BY, 



, 3Y y 

 + By 



+£ 



, BY* 



+ 3* 





,BZ, 



+ f 



, BZ, 

 + 3/ 



dL* 



3« 



BLj, 

 3y 



+ t 



, BL, 

 + 3« 



"1 



(2) 



where 





* A. Einstein, Jahrbuch der Radio aktivitat, vol. iv. 1907. 

 t H. Minkowski, "Raum und Zeit," § iv. Phys. Zeit. 1911. 

 1 H. Minkowski, Math. Ann. vol. lxviii. Appendix. 



(3) 



