336 



52 



transitions will be possible, riz. transitions for which n'g — = giving rise to 

 radiation polarised i)arallel to the field, and transitions for which n'g — n" = ± 1 

 giving rise to radiation polarised circularly in a plane perpendicular to the field. ' ) 

 The components corresponding to the latter transitions will, however, appear as 

 unpolarised when viewed parallel to the field because, due to the symmetry of the 

 atom round the axis of the field, the numbers of the transitions, corresponding to 

 such a component, which give rise to light polarised circularly in one direction 

 and in the opposite direction, will in the mean be the same. 



hi order to discuss the intensities, we have in the following given tables 

 for the estimate of the relative intensities of the Stark effect components of the 

 hydrogen lines H^, Hß, Hy, Hß, as it can be obtained by the method exposed in § 5. 



In the first column the different possible transitions between two stationary 

 states are characterised by their symbols (7?'^, n'^, n'^ -> n", n"). On account of the 

 symmetry of the Stark effect we have only given those transitions which give rise 

 to components lying on one side of the undisplaced line ( J ' 0). Transitions which 

 correspond to the same value of J and which therefore contribute to the same 

 component in the observed effect are collected by brackets. As regards the 

 stationary states involved in these transitions we have, according to the above, 

 assumed that no stationary states exist for which n.^ == 0. Each table is divided 

 into two parts, the first containing the transitions for which /i', — ik = Ü, corres- 

 ponding to "parallel" components, the second containing the transitions for which 

 n'g — n!,' = 4; 1, corresponding to "perpendicular" components. 



The second column contains the value of J = n'{n[ — n'J — '^"("'i — iC), which, 

 as seen from (111), determines the displacement of the component under consider- 

 ation from the undisplaced line; the third, fourth and fifth columns contain the 

 values of = n[ — /i", = n'^ — "'J, r., = "3 — n". 



The sixth and seventh columns contain the values R' and R" of the "relative 

 amplitudes" of the harmonic vibrations of frequency TjCJj^ -r t.,(u.^ + r.jW.,, occurring 

 in the molion in the initial and in the final state respectively; where by 

 relative amplitude is understood the ratio of the amplitude of this vibration to the 

 half major axis of the Keplerian ellipse which the electron at any moment may be 

 considered to describe. This half major axis remains constant during the motion 

 and is equal lo the value for a„ given by (102), /. e. equal to the quantity xP occur- 

 ring in the formulae (70) and (72). The expressions for the values of the relative 

 amplitudes of the linear vibrations parallel lo the field and of the circular vibrat- 

 ions perpendicular to the field in a given stalionm y stale, characterised by a certain 

 combination of the ;j's, are directly obtained by introducing (110) in the formulae 

 (70) which represent the motion of the electron parallel and perpendicular to the 

 direction of the field. In this way we find, denoting, as in § 2, the Bessel coeffi- 

 cient of order p and of argument p by Jp{p), and its derivate with respect to p 

 by J'Ap), 



1) N. Bohr, loc. cit. Part II, p. 77. 



