75 



motion of the electron in the hydrogen atom, clue lo the relativity modifications 

 and an external electric field. 



In the deduction of formula (78) there is looked apart, not only from Die effect 

 on the motion of the electron due to the small modifications in the laws of mechanics 

 claimed by the theory of relativity, but also from the effect of possible forces 

 which might act on the electron, corresponding to the reaction from the radiation 

 in ordinary electrodynamics. If, however, for the moment we exclude all stationary 

 states for which the angular momentum round the axis of the system would be 

 equal to zero (n^ = 0), the total angular momentum of the electron round the 

 nucleus will during the perturbations always remain larger than or equal lo ''2-, 

 just as in the stationary states considered in the theory of the fine structure; and, 

 according to the considerations on page 66, we shall therefore expect that the effect 

 of the neglect of possible "radiation" forces will be small compared with the effect 

 of the relativity modifications. On the other hand, if the intensity of the electric field is 

 of the same order of magnitude as that applied in Stark's experiments, the elTect of 

 these modifications must again be expected to be very small compared with the 

 total effect of the electric force on the hydrogen lines, since the perturbing effect 

 of this force on the Keplerian motion of the electron will be very large com- 

 pared with the corresponding effects of the relativity modifications. If, on the 

 contrary, we would consider a state of the atom for which n^ was equal lo zero, 

 the orbit would be plane and would during the perturbations assume shapes, for 

 which the total angular momentum round the nucleus was very small, and in which 

 the electron during the revolution would pass within a very short distance from 

 the nucleus. In such a state the effect of the relativity modifications on the motion of 

 the electron would be considerable, but quite apart from this a rough calculation shows 

 that the amount of energy, which, on ordinary electrodynamics, would be emitted 

 during the intervals in which the angular momentum during the perturbations of 

 the orbit remains small, is so large that it would hardly seem justifiable to calculate 

 the motion and the energy in these states by neglecting all forces corresponding to 

 the radiation forces in ordinary electrodynamics. We need not, however, enter more 

 closely on these difficulties, because, on the general considerations in Part I aboul 

 the a-priori probability of the different stationary states, we are forced to conclude 

 that, for any value of the external electric field, no state which would corres- 

 pond to 7Î3 = will be physically possible; since any such state might be 

 transformed continuously, and without passing through a degenerate system, into 

 a state which obviously cannot represent a phj'sically realisable stationary state 

 (compare pag. 27). In fact, if we imagine that an external central field of force, 

 varying as the inverse cube of the distance from the nucleus, is slowly eslablished, 

 it would be possible to compensate the secular etïect of the relativity modifica- 

 tions and to obtain orbits in which the electron would pass within any given, how- 

 ever small, distance from the nucleus. As regards the other stationary states fixed 



