77 



is polarised perpendicular lo the field. This resull may l)e simply interpreted on 

 the basis of the general formal relation between the quantum theory of line 

 spectra and the ordinary theory of radiation. In fact, it was shown in Part I 

 that, for a conditionally periodic system possessing an axis of symmetry, we 

 shall expect only two types of transitions to be possible. In transitions of the 

 lirst type n^ remains unchanged, and the emitted radiation is polarised parallel to 

 the axis of symmetry, while the transitions of the second type, in which «g varies 

 by one unit, give rise to a radiation of circular polarisation in a plane perpendicular 

 to this axis (see page 34). In order to show that this agrees with the empirical rule 

 of Epstein, it may be noted in the first place that, for any component which might 

 be ascribed to a certain transition in which n.j changes by a given entire number 

 of units, there exists always another transition which will give rise to a radiation 

 of the same frequency but in which n.^ remains unchanged or changes by one 

 unit, according to whether the given number is even or uneven. Next it will be 

 seen that, in case of the effect of an electric field on the hydrogen spectrum, we 

 cannot detect by means of direct observations the circular polarisation of the 

 radiation corresponding to transitions of the second type; because, for each transi- 

 tion giving rise to a radiation of circular polarisation in one direction, there will 

 exist another transition giving rise to a radiation which possesses the same fre- 

 quency but is polarised in the opposite direction. Besides on the problem of the 

 polarisations of the different components into which the hydrogen lines are split up 

 in the presence of the electric field, the general considerations in Part I allow also to 

 throw light on the question of the relative intensities of these components, by 

 considering the harmonic vibrations into which the motion of the electron in the 

 stationary states can be resolved. Compared with the problem of the relative in- 

 tensities of the components of the fine structure of the hj'drogen lines, the present 

 problem is simpler in that respect, that the stationary states may be assumed to 

 be a-priori equally probable. Since the different components, into which a given 

 hydrogen line is split up in the electric field, correspond to transitions between pairs of 

 states which for all components have very nearly the same values for the total energy, 

 these states may therefore be expected to be of approximately equal occurrence in 

 the luminous gas. According to the considerations in Part I, we shall consequentlj' 

 assume that for a given hydrogen line the relative intensities of the different Stark 

 effect components, corresponding to transitions between different pairs of stationary 

 states characterised by n^ = n[, n, = n'„, n,, ^ n'„ and n^ = n',', n„ = n'.^, n^ = n" 

 respectively, will be intimately connected with the intensities of the radiations of 

 frequency (n'^ — n'[) (u^-\- (n'.^ — /I'J) «g-j- (/i', — n'^) cu^, which on ordinary electro- 

 dynamics would be emitted by the atom in the two states involved in the transition 

 in question; Wj, co^ and ^3 being the fundamental frequencies entering in the ex- 

 pression (31) for the displacement of the electron. In order to test how far such 

 a connection is actually brought out by the observations, it is necessary to determine 

 the numerical values of the amplitudes of the harmonic vibrations into which the 



D. K. I) Vidensk. Selsk Skr., iiiilunidensk. og malliein. Aid., 8. Hiekke. IV. 1. 11 



