( 593 ) 



If this were the only force, the electron could vibrate with a 

 frequency ??„, determined by 



. ƒ 



(7) 



In order to account for the absorption, one has often introduced 

 a resistance proportional to the velocity of the electron whose com- 

 ponents may be represented by 



rfx dy dz 



— r/ — , — <7 — , — </ — , (8) 



• dt '' dt ^ dt ^ ' 



if by 1/ we denote a new constant. 



We have finally to consider the forces due to the external mag- 

 netic field. We shall suppose this field to be constant and to ha\e 

 the direction of the axis of :. If the strength of the field is H, the 

 components of the last mentioned force will be 

 eH'/y eKdx 



c dt c dt ^ ' 



It must be observed that, in the formulae (2) and (3), we may 



understand by -^ the magnetic force that is due to the vibrations 



in the beam of light and that may be conceived to be superimposed 



on the constant magnetic force H. 



§ 4. The equations of motion of the electron are 



d'x ^ dx eH</y 



dr dt c dt 



d*Y dy e'H.dx 



dr dt c dt 



d' Z _ , dz 



"* t:? = 6 (^■-- + " '^^--) — -^ ^ ~ ." 77 • 



d t a I 



These formulae may however be put in a form somewhat more 

 convenient for our purpose. 



To this effect we shall divide l)y e, expressing at the same time 

 X, y, z in ^p^:, ^Py> l^-- Tins may be done by means of the relations (4). 

 Putting 



m f ; 9 , 



AV = "*' .W^^-^' ^'=^ (^^^ 



we tind in this way 



rri ^-^ = '^.c + « %: — / 'V. — 9 -^- + -^TT- ^— , 

 « < f A' e < 



ö«' ■ dt cNe dt 



4J* 



