85 



where £„ and m are the values of the energy and frequency and / is the value of the 

 quantity defined by (5), all corresponding to the state of the undisturbed system 

 which would appear if the magnetic force vanished at a slow and uniform rate, 

 while S is the additional energy due to the presence of the magnetic field and 3 

 the angular momentum of the system round the axis of the field multiplied by 2^ 

 and taken in the same direction as that of the superposed rotation. Since (82) has 

 exactlj' the same form as relation (66), and since in the stationary states we have 

 I ^ nh and S = nh, we are therefore from a consideration, quite analogous to 

 that given in § 2 on page 59, led to the conclusion, that, in the presence of 

 the magnetic field, only two types of transitions between stationär}' states are 

 possible. For both types of transitions the integer n may change by any number 

 of units, but in transitions of the first type the integer n will remain constant and 

 the emitted radiation will be polarised parallel to the direction of the field, while 

 in transitions of the second type n will decrease or increase by one unit and the 

 emitted radiation will be circularly polarised in a plane perpendicular to the field, the 

 direction of the polarisation being the same as or the opposite of that of the super- 

 posed rotation respectively. Remembering that, with neglect of small quantities pro- 

 portional to the magnetic force, the angular momentum of the system round the 

 axis of the field remains unaltered in transitions of the first type and changes by 

 '1/2- in transitions of the second type, it will be seen that this conclusion is in- 

 dependently supported by a consideration of conservation of angular momentum 

 during the transitions, like that given in Part I on page 34. 



With reference to formula (80), it will be seen that the above results are in 

 complete agreement with the experiments on the Zeeman effect of the hydrogen 

 lines, as regards the frequencies and polarisations of the observed components. 

 On the other hand, the observed intensities are directly accounted for, independent 

 of any special theory about the origin of the lines. In fact, from a consideration of 

 the necessary "stability" of spectral phenomena, it follows that the total radiation of 

 the components, in which a spectral line, which originally is unpolarised, is split up 

 in the presence of a small external field, cannot show characteristic polarisation 

 with respect to any direction. In case of the Zeeman effect of the hydrogen lines, it 

 is therefore necessary beforehand to expect that the intensity of the radiation, 

 summed over all directions, corresponding to each of the three components in 

 which every line is split up must be the same. From the point of view of the 

 quantum theory of line spectra, it will be seen that by means of considerations 

 of this kind we may inversely obtain a certain amount of direct quantitative in- 

 formation as regards the probabilities of spontaneous transition between different 

 sets of stationary states, holding also in the region where the integers characterising 

 these states are not large and where consequently the estimate of the values of 

 these probabilities, based on the formal relation between the quantum theory and 

 the ordinary theory of radiation, gives results which are only of an approximative 

 character. This point will be discussed more closely in Kramers' paper on the relative 



D. K. D. Vidensk. Selsk. Skr,, nalurvidensk. og matliem. .\fd. 8. Række, IV, 1. .12 



