90 



electric field of axial symmetry, and the conditions which fix the stationary states of the 

 perturbed atom will again be expressed by the relations (61). As regards the question 

 of the probability of spontaneous transition between the stationary states, we get 

 moreover, just as in § 2, from a consideration of the harmonic vibrations into which 

 the motion of the electron can be resolved, that only two types of transitions will 

 be possible; in transitions of the first type n^ remains unaltered, and the accom- 

 panying radiation is polarised parallel to the direction of the common axis of the 

 perturbing fields ; in transitions of the second type n^ decreases or increases by one 

 unit, and the accompanying radiation will be circularly polarised in a plane per- 

 pendicular to this axis. In this connection it may be remarked, however, that the 

 number of components, into which a given hydrogen line is split up in the presence 

 of a magnetic field, will in general be double as large as the number of components 

 which appear in the presence of an external electric field of axial symmetry. In 

 fact, in the latter case the motions of the electron in two stationary states of the 

 perturbed atom, corresponding to the same value of n, will be symmetrical with 

 respect to a plane through the axis, and these states will possess the same values 

 for the additional energy, if it^ is the same while the values of xi^ are numerically 

 equal but have opposite signs. On the other hand, if the atom is exposed also to 

 a magnetic field, this will not hold, because the value of the function ¥m, in con- 

 trast to the value of ^e, will not possess the same sign for two orbits which have 

 the same shape and position relative to the axis, but for which the direction of 

 revolution of the electron is reversed. Considering two states of the perturbed atom 

 for which the values of iij are the same and the values of n^ are numerically equal 

 but have opposite signs, we get therefore, if the atom is exposed only to a magnetic 

 field of axial symmetry, that the values of the additional energy will be equal 

 with exception of the sign; while, if the atom is exposed to a magnetic as well 

 as to an electric field, the additional energy in two such states will in general differ 

 also as regards its numerical value. In contrast to what in general will take place 

 if the atom is exposed to an electric field of axial symmetry, it will thus be seen 

 that, if the hydrogen atom is exposed only to a magnetic field possessing axial 

 symmetry, the ensemble of components into which a given hj'drogen line is resolved 

 will be completely symmetrical with respect to the position of the original line, as 

 regards the frequencies as well as the intensities and polarisations. Moreover it fol- 

 lows from the above, that if we consider a hydrogen atom exposed to an electric 

 field of axial symmetry and imagine that an external magnetic field, which possesses 

 symmetry round the same axis, is gradually established, each component which 

 appears in the presence of the first field only will split up into two components, 

 in such a way that each component polarised parallel to the axis will split up into 

 two components of the same polarisation, while each component polarised per- 

 pendicular to the axis, and which originally showed no polarisation when viewed 

 in a direction parallel to the axis, will split up into two components showing 

 circular polarisations in opposite directions. If the magnetic field is small, the new 



