69 



in general, are considerably larger than [he ampliludes of Ihe rotations in the opposite 

 direction, and we shall accordingly expect that the probability of spontaneous 

 transition will in general be much larger for transitions, in which the angular 

 momentum decreases, than for transitions in which it increases. This expectation 

 is verified by Paschen's observations of the fine structure of the helium lines, 

 which show that, for a given line, the components corresponding to the transitions 

 of the former kind are by far the strongest. On Paschen's photographs, how- 

 ever, especially in the case of the application of a condensed discharge to the 

 vacuum tube containing the gas, there appear, in addition to the main com- 

 ponents corresponding to transitions for which the angular momentum changes by 

 hl2K, a number of weaker components, corresponding to transitions for which the 

 angular momentum remains unchanged or changes by higher multipla of /i 2-. This 

 fact obtains a simple interpretation on the considerations in Part I on page 34 

 about the influence of small external forces on the spectrum of a conditionally 

 periodic system. Thus, in the presence of small perturbing forces, the motion will 

 generally not remain in a plane, and in the trigonometric series representing 

 the displacement of the electron in space, there will occur small terms corres- 

 ponding to frequencies (t^w-i^-j- r^w^), where ^2 may be different from one. In 

 the presence of such forces, we shall therefoi-e expect that, in addition to the regular 

 probabilities of the above mentioned main transitions, there will appear small 

 probabilities for other transitions.') A detailed discussion of these problems will be 

 given in a later paper bj' Mr. H. A. Kramers, who on my proposal has kindly 

 undertaken to examine the resolution of the motion of the electron in its constituent 

 harmonic vibrations more closely, and who has deduced explicite expressions for 

 the amplitudes of these vibrations, not only for the motion of the electron in the 

 undisturbed atom, but also for the perturbed motion in the presence of a small 

 external homogeneous electric field. As it will be shown by Kramers, these calcula- 

 tions allow to account in particulars for the observations of the relative intensities 

 of the components of the fine structure of the hydrogen lines and the analogous 

 helium lines, as well as for the characteristic way in which this phenomenon is 

 influenced by the variation of the experimental conditions. 



§ 4. The effect of an external electric field on the hydrogen lines. 

 As mentioned in the introduction, a detailed theory of the characteristic effect 

 of an external homogeneous electric field on the hydrogen spectrum, discovered by 



') Note added during the proof. As remarked in Part !, tliis consideration obtains a strilving 

 confirmation by the observation of the appearance of new series of lines in the ordinary series spectra 

 of helium and other elements, when the atoms are exposed to an intense external electric held. As it 

 ■will be discussed more closely in Part 111, it is possible in this way to account in detail for the mani- 

 fold results, regarding the appearance of such series in the helium spectrum, which have been published 

 quite recently by J. Stark (Ann. d. Phys. LVI, p. 577 (1918)) and by G. Lif.bkrt (ibid. LVI, p. .')8il and 

 p. Ü10 (1918)). 



I). K. D. Vldensk. SelsU. Ski-., nalurviilensk. og matlieni. AW., 8. It:ukkc, IV. 1. 10 



