92^ 



symmetrical doublet the members of which will show circular polarisation in op- 

 posite directions, when viewed in the direction of the axis, and will be displaced 

 from the position of the original component by an amount corresponding to a 

 frequency difference equal to o,,. 



A simple application of the last result is afforded by the problem of the 

 simultaneous effect on the hydrogen lines of a homogeneous electric 

 and a homogeneous magnetic field which have the same direction. 

 Thus, if the intensities of the fields are so large that we may look apart from the 

 small modifications claimed by the theory of relativity, we shall from the above expect 

 that the effect in question will differ from the ordinary Stark effect of the hydrogen 

 lines, only therein that every component polarised perpendicular to the field is split up 

 in two symmetrical components corresponding to the outer members of a Lorentz 

 triplet. This seems to agree with some observations of the effect of two such fields 

 on the hydrogen line Ha, published by Garbasso.^) The problem in question might 

 also have been treated by means of the method of separation of variables, because, 

 as may be easily shown, the perturbed system — if the relativity modifications 

 are neglected — allows of separation of variables in parabolic coordinates, just as 

 in the presence of the electric field only. If, on the other hand, the relativity modific- 

 ations are taken into account, the method of separation of variables cannot be ap- 

 plied, but, with reference to the considerations at the end of the last section, it will 

 be seen that it is possible, also in this case, to predict at once the modification in 

 the effect of an electric field on the fine structure of the hydrogen lines, which 

 would result from the simultaneous presence of a parallel magnetic field. Passing 

 to the limiting case where the intensity of the electric field is equal to zero, it will 

 thus be seen at once from the preceding, that the effect of a homogeneous 

 magnetic field on the fine structure of the hydrogen lines will consist 

 in the splitting up of every component in a normal Lorentz triplet. As far as 

 the frequencies of the components are concerned, this result has been predicted by 

 Sommerfeld and Debye, who have treated the problem under consideration by 

 means of separation of variables in polar coordinates (compare page 84). In con- 

 nection with the fixation of the stationarj' states in this problem, it may be remarked 

 that we must assume that no stationary state will exist for which the angular 

 momentum round an axis through the nucleus parallel to the magnetic field would 

 be equal to zero. In fact, as seen in § 4, we must assume that, in case of a hydrogen 

 atom exposed to a homogeneous electric field, no such states will be possible; and 

 by imagining that the electric field decreases slowly to zero, while at the same 

 time a magnetic field parallel to the electric field is slowly established, it would 

 be possible, without passing through a degenerate system, to obtain a continuous 

 transformation of the stationary states of the perturbed atom during which the 

 angular momentum of the electron round the axis would remain unaltered. With 



') A. Garbasso, Phys. Zeitschr. XV, p. 123 (1914). 



