384 



100 



over llie slates lying between the initial state and the final state. Although, as 

 mentioned in § 5 (compare page 63), such a calculation may perhaps permit of 

 accounting in more detail for the observed intensities, a consideration of the Zeeman 

 effect of the hydrogen lines can, however, be used to show that no simple type 

 Ü f m e a n V a 1 u e w i 1 1 b e a b 1 e t o g i v e an e x a c t m e a s u r e f o r t h e r e 1 a t i v e 

 intensities. Let us thus especially consider the hydrogen line (2 -* 1), which in a 

 magnetic field will show the components (02 ; 1 01 ; 1) and (02; 2 ~* 01 ; I). In the 

 states characterised by (0,1 4" -^î 1) tlie square of the relative amplitude of the harmonic 

 vibration of frequency w., is, as seen from (130), given by 1 —^j j^;)2' while in the 

 states characterised by (0, 1 + /; 1 + /) the. square of the relative amplitude of the 

 liarmonic vibration of frequency a»., is equal to 1. Now it is beforehand clear that any 

 simple type of mean value of 1 — (î"3~7|2> taken over all values of / between 

 and 1, never can be equal to 1, which number obviously represents any such mean 

 value corresponding to the second transition. Since nevertheless the corresponding 

 intensities are the same, we are therefore directly led to the above conclusion. If, for 

 instance, we would use the logarithmic mean value defined by (109) which, as men- 

 tioned on page 46, for several reasons oilers itself naturally for an estimate of the 

 intensities, we would for the first transition, as it may be shown by a simple cal- 

 culation, get the value , while for the second transition we would get 1. Even 

 if we may be justified in expecting that in general it will be possible by means of 

 the mean value in question to obtain a closer estimate of the relative intensities of 

 spectral lines, we see from this example that, in case the /i's are small, the errors 

 involved in such an estimate may become considerable in especially chosen un- 

 favourable cases. 



In concluding this paper it may be useful once more to emphasize the in- 

 complete and preliminary character of the underlying considerations. Nevertheless 

 the results obtained as regards the applications to the Stark eflect and to the fine 

 structure of the hydrogen lines must be considered as allording a general support 

 of Bohr's fundamental hypothesis of the connection between the intensity of spec- 

 tral lines and the amplitudes of the harmonic vibrations into which the motion of 

 the electron in the atom may be resolved, the more so because it seemed possible 

 to obtain a natural understanding of certain marked deviations of the observed 

 intensities from the preliminary theoretical estimate of the intensity distribution 

 obtained on the basis of this hypothesis. It seems therefore justifiable to conclude 

 that Bohr's considerations offer a sound basis for a further development of the 

 theory of intensities of spectral lines. 



