450 The Theory of Aether and Electrons in the 



This equation may be satisfied either (1) if r is parallel to K, 



in which case it reduces to 



K* - mri* = 0, 



so that n has the value Km"*, or (2) if r is at right angles to K, 

 in which case by squaring both sides of the equation we obtain 



the result 



(V - mn*) z = #tfK\ 



which gives for n the approximate values KW~* el/2m. 



When there is no external magnetic field, so that K is zero, 

 the three values of n which have been obtained all reduce to 

 icw~V which represents the frequency of vibration of the 

 emitted light before the magnetic field is applied. When the 

 field is applied, this single frequency is replaced by the three 

 frequencies cm~, cm"i + eK/2m, icm'i - eK/2m ; that is to say, 

 the single line in the spectrum is replaced by three lines close 

 together. The apparatus used by Zeeman in his earliest experi- 

 ments was not of sufficient power to exhibit this triplication 

 distinctly, and the effect was therefore described at first as a 

 widening of the spectral lines.* 



We have seen above that the principal oscillation of the 

 electron corresponding to the frequency *cra~ is performed in a 

 direction parallel to the magnetic force K. It will therefore 

 give rise to radiation resembling that of a Hertzian vibrator, 

 and the electric vector of the radiation will be parallel to the 

 lines of force of the external magnetic field. It follows that 

 when the light received in the spectroscope is that which has 

 been emitted in a direction at right angles to the magnetic 

 field, this constituent (which is represented by the middle line 

 of the triplet in the spectrum) will appear polarized in a plane 

 at right angles to the field ; but when the light received in the 

 spectroscope is that which has been emitted in the direction of 

 the magnetic force, this constituent will be absent. 



We have also seen that the principal oscillations of the 

 electron corresponding to the frequencies Km-* eJ/2m are 



* Later observations, with more powerful apparatus, have shown that the 

 primitive spectral line is frequently replaced by more than three components. 



