81 



365 



under which the spectrum was produced. In fact, we must naturally expect that in 

 the vacuum tube containing the luminous gas tliere will always be electric fields 

 acting on the atoms, but under dillerent experimental conditions these fields will 

 not be equally strong, and especially in the case where an interrupted spark dis- 

 charge is applied, the intensity of such fields may become considerable. 



In order to discuss in detail the intensities with which for a given value of 

 F the new components may be expected to appear it will first of all be 

 necessary to consider in detail the different transitions between stationary states 

 giving rise to these components. The motion of the system in a stationary state 

 n.^; n) will be given by the formulae (83), (90), (94) and (96) in § 4, if we intro- 

 duce for /!J and /" in these formulae their values n,, n.^—n, ii and n =^ n^^n., 

 respectively. A transition between an initial state {n\, n'^; n') and a final state (n", n"; n") 

 will be characterised by the symbol {n\,n'„; u' — ► /i", u'J ; n")- If <o^, ^«^2 and co^ have 

 the same signification as in § 4 it may be shown by a closer examination of 

 the perturbed system, as that which w'ill be given in the later paper mentioned 

 above, that the general relation discussed in J; 5 between the frequencies which an 

 atomic system will emit during a transition between tvv'o stationary states, and the 

 frequencies occurring in the motion of the systen), will in the present case exist therein 

 that the frequency of the radiation emitted during a transition {n\,n\; n' — n", n'J; n") 

 will be equal to the mean value of the frequency (n', — /i") -j-(n', — n' — n'^ — n")(o^ 

 f (ii' — n")w.j occurring in the motion in the states corresponding to = n" -f 

 Å{n[~n'l), Il -\- Il = n'J +i (n'g— n','), /" = n"-|- /(n' — n"), where / takes all possible 

 values between and 1. Now the motion of the perturbed system may be resolved 

 in a number of linear harmonic vibrations parallel to the electric force, the fre- 

 quencies of which are of the type t^Wi + ^2"'2 -» '^'^^ ^ number of circular harmonic 

 lotalions perpendicular to the electric force and of frequencies Ti(M,-f- r.,<«i.,+ <tf3 , as 

 it is seen from (94) and (96). We shall therefore expect that, just as in the theory of 

 the Stark effect, two kinds of transitions will be possible, uiz. transitions for which 

 n' — u" = and which give rise to radiations polarised parallel to the electric force, 

 and transitions for which n' — n" = ± 1 and which give rise to radiations of cir- 

 cular polarisation perpendicular to the electric force.') Further from (83), (90) and 

 (94) it is seen that the motion of the electron parallel to the electric force consists 

 partly of vibrations of frequencies [r,w,-raj2 which also occurred in the undisturbed 

 motion, and the amplitudes of which in first approximation are not affected by the 

 electric force, partly of vibrations of frequencies r^w^ and ri<y,-r2w., the ampli- 

 tudes of which are proportional to ^ o. From this we may conclude that two types 



') This conclusion will be seen to be supported by a consideration of conservation of angular 

 momentum round the a.xis of the field during the transitions, as that mentioned in note 2 on page 4:). 

 In this connection it may be of interest to observe that the effect of the external electric field in 

 producing new components has intimate relation to the possibility for these forces to change the total 

 angular momentum of the electron round the nucleus during a transition between two stationary states 

 icompare Rubinowicz, 1. c . 



I). K. 1). Vl.leiisk. Selsk. Ski ., iialurviilcusk. niiilhein. Aid.. S. K;i'kke. III. :i. 47 



