95 379 



Proceeding to discuss the ellecl of liie iiia^iielic licld on llic specli uni we sec 

 in the first place that the energy in a given stationary state will dilîer from the 

 energy in the corresponding stationary state of the undisturbed atom, which was 

 given by (118), only by a small term pro])ortional to the intensity H of the magnetic 

 field, which represents the ellecl of the superposed rotation on the kinetic energy of the 

 system. This term is simpiv shown to be equal to -i- nhon -i- n/j , , where the 

 upper or the lower sign holds according to whether the direction of the superposed 

 rotation is the same as or the opposite of that of the revolution of the electron 

 round the axis respectively, (considering a transition {n\, n',; n' ~^ n", n"; n") between 

 I he initial state {n\, n') and the final state (/i", n"; n") we see therefore thai the 

 frequency of the emitted radiation will be given by 



where v,„ t/j and 'i^'ve the same signification as in (120), (121) and. (122), while 

 is given by 



vg = ± di'^u"). (l'-^^>) 



4 TT m c ' 



As shown by Sommehfelo and Debye the formulae (128) and (129) offer an 

 interpretation, as regards the frequencies, of the effect of a magnetic field on the 

 hydrogen lines, since, putting ii' — n" = Ü and n' — n" ^ i 1, and disregarding the 

 terms s/, and v^, w-hich refer to the fine structure, we obtain the fre(|uencies of 

 the three components in which the hydrogen lines are split up, these lines showing 

 a normal Zeeman ellect. Further Bohh showed that it is possible, on the basis of 

 the formal connection between the quantum theory of line spectra and the ordinary 

 theory of radiation, to obtain a natural inter|)retation of the characteristic polarisa- 

 tion of the observed three components, as well as of the fact thai no further com- 

 ponents appear; the theory of the Zeeman effect thereby obtaining a remarkable 

 formal analogy with the theory originally devised by Lokentz on the basis of the 

 classical theory of electrodynamics. 



From the considerations in § 2 it is seen that in the presence of a homo- 

 geneous magnetic field the motion of the electron in the hydrogen atom may 

 be resolved in a number of linear harmonic vibrations of frequencies r,Wj i (m^ 

 parallel to the direction of the field, and in a number of circular harmonic rota- 

 tions of frequencies TjWj (o.^^Oh perpendicular to this direction. Now it is easily 

 shown that the frequency emitted during a transition {n\, n',; n' ^ n", n'/. n" ) will be 

 equal to the mean value of the frequency (n\ — — (n!, — n!,')«>2 rîi — 



taken over the multitude of mechanically possible states, lying between the initial 

 state and the final slate, which are characterized by n,; = n'l' \- Å{nh — /i;, ). (/v ^1,2) 

 and n n" -f /(n'— n"), x assuming all values between and 1. With reference to 

 the formal connection between the quantum theory and the ordinary theory of 

 radiation we may therefore conclude thai only such transitions will he possible 

 for which ii remains unciianged, the emitted radiation being polariseil parallel to 



