• 



380 96 



the axis, and transitions for which n decreases or increases by one unit, the emitted 

 radiation being circularly polarised perpendicnlar to the axis, and that for both 

 types of transitions must either decrease or increase by one unit. From this 

 it follows directly with reference to (128) and (129) that, as mentioned in Bohr's 

 paper, the effect of the magnetic field on the fine structure of the hydrogen lines 

 will consist in the splitting up of every fine structure component into one undis- 

 placed component polarised parallel to the direction of the field and two symme- 

 trical components at a distance from the undisplaced component, which 

 appear as circularly polarised in opposite directions when viewed in the direction 

 of the field and as linearly polarised pei'pendicular to the field when viewed in a 

 direction perpendicular to the field. 



As regards the intensities of these components we may in the first place 

 obviously conclude that the latter two components are of equal intensity, since, if 

 the effect is viewed in the direction of the field, they must not show characteristic 

 polarisation when taken together. Further when viewed in a direction perpendicular 

 to the field the intensity of each of the perpendicular components must be equal 

 to half the intensity of the parallel undisplaced component, since we must equally 

 assume that, when viewed in this direction, the ensemble of components into 

 which the unpolarised fine structure component is split up does not exhibit char- 

 acteristic polarisation. The theoretical efTect of a magnetic field on the fine struc- 

 ture of the hydrogen lines may therefore be described as the splitting up of every 

 fine structure component into a Lorentz triplet. 



We have thus met with an illustrative application of the considerations on 

 page 49 at the end of § 5, and it is seen that the problem of the Zeeman effect of 

 the fine structure of the hydrogen lines does not involve a new intensity problem if 

 Ihe intensity distribution in the undisturbed fine structure is known. It will there- 

 fore be of special interest in this case to compare the relative intensities of the 

 Zeeman effect components with the amplitudes of the harmonic vibrations occurring 

 in the states of the perturbed motion, since, owing to the circumstance that we have 

 beforehand some information about these intensities, such a comparison will give us 

 valuable information about the way in which the estimate of the relative intensities 

 of spectral components, based on the values of these amplitudes, may be expected 

 to fail if the numbers characterising the stationary states are small. For this pur- 

 pose we have in the case of two special lines, viz. the helium line 4686 Å (4 3) 

 and the hydrogen line //„ (6562 A), (3 2), calculated the squares of the relative 

 amplitudes of the corresponding harmonic vibrations which occur in the initial 

 states and in the final states involved in the different transitions giving rise to the 

 (lifierent components of the Zeeman etîect of the fine structure. The result of 

 these calculations will be found in tables XIV and XV. 



The first column contains the symbols (/j^, n;, n^, n:,) characterising the 

 transitions corresponding lo the fine structure components of the undisturbed 

 hydrogen atom. 



