366 



82 



of transitions will be possible for which n remains unaltered, viz. transitions for 

 which n,^ — n and therefore also changes by one unit, and which give rise to 

 radiations corresponding to the original components of the fine structure; and 

 transitions for which n^ — n and therefore also n., remains unaltered or changes 

 by two units, giving rise to radiations which correspond to the new components. 

 In the same way it is easily seen from (83), (90) and (96) that also the transitions 

 for which n changes by one unit may be divided into transitions for which n,^ 

 changes by one unit and which contribute to the original components, and transi- 

 tions for which n, remains unchanged or changes by two units and which con- 

 tribute to the new components. According to the considerations in § 5 we shall further 

 expect tliat it wmII be possible, from the numerical values of the amplitudes of the 

 corresponding harmonic vibrations occurring in the initial states and in the final 

 states, to obtain an estimate for the relative intensities with which for a given 

 hydrogen line (n' — n") all these components will appear. Let us consider the 

 estimate which in this way may be obtained from (94) and (96) for the intensities of 

 the new components assuming that the direction of the perturbing electric field is 

 perpendicular to the direction in which the spectrum is viewed. The radiations giving 

 rise to a new component characterised by {n\, n'„ — /i", n") will originate from different 

 transitions {n[, n[ ; n' n", n") where n[, n\, n", /I'J have the same values, but where 

 n' and n" may assume different pairs of values. For ii' — n" = these transitions 

 give rise to radiations polarised parallel to the electric force; for n' — n" il they 

 will give rise to radiations polarised perpendicular to this direction. The new com- 

 ponents might therefore in general be expected to show characteristic polarisation if the 

 direction of the electric force was the same at all points in the luminescent vacuum 

 tube which contribute to the formation of the spectroscopical image. In order to obtain 

 an estimate for the intensities of the radiations corresponding to these transitions 

 we shall, in analogy with the procedure followed in § 6, for each transition {n\, n\ ; u' 

 n'l,n"; n") calculate the square of the relative amplitude of the harmonic vibration 

 of frequency {n\ — n'l)ü}^-\- {n'^ — n' — n'^' — n")a»2+(n!; — n^ß^s occurring in the mo- 

 lion in the initial state and in the final state, where just as in the preceding sections 

 under relative amplitudes are understood the actual amplitudes divided by the 

 length of the half major axis of the Keplerian orbit which the electron at any 

 moment may be considered to describe. Now this half major axis is equal to xl"' so 

 that from (94) and (96) the values of the relative amplitudes may directly be found. 

 The expressions obtained in this way are all seen to contain the factor "^^J^ > which 

 by means of (124) and (86) may be written in the form 



where Ä- is a constant the value of which may be simply calculated from the 

 experimental data, owing to the fact that we, with reference to formula (105), can 

 write k in the form 



'6eFxF 

 4P 



