95 



with respect to the axis of the stronger field, exhibited by the periodic cycle of 

 shapes and positions wliich the orbit of the electron would pass through if the 

 atom were exposed to this field only, it is easily seen that the contribution, which 

 the perpendicular component of the weaker field gives to the mean value of 'F 

 corresponding to the latter field, will vanish. From this it follows that the secular effect 

 of the weaker field, with neglect of small quantities proportional to n^, will be 

 the same as if only the parallel component of this field was acting on the atom; 

 and we see consequently that, in the stationary states of the atom in the presence 

 of both fields, the possible cycles of shapes and positions of the orbit of the elec- 

 tron will be characterised in the same way as if the weaker field was parallel to the 

 stronger. The problem, however, of the fixation of the stationary states of a hydrogen 

 atom in the presence of a homogeneous electric field and a homogeneous magnetic 

 field, which are parallel to each other, is very simple. In fact, as it appears from the 

 considerations on page 91, the stationary states will in this case be fixed completely 

 by two conditions, of which the one, in the same way as in the simple theory of 

 the Stark effect, defines the position of the plane in which the electrical centre of 

 he orbit of the electron moves, while the other defines the value of the angular 

 momentum of the electron round the axis of the fields in the same way as in the 

 simple theory of the Zeeman effect. In connection with the problem under con- 

 sideration here, it may be useful for the sake of illustration to note, that, if the 

 perturbing effect of the electric field is large compared with that of the magnetic, 

 the second of these conditions maj' be said to be imposed on the sj'stem by the 

 slow and uniform rotation, which the magnetic field produces on the periodic cycle 

 of shapes and positions of the orbit of the electron, which would appear if the 

 atom was exposed to the electric field only. If, on the other hand, the etTect of the 

 magnetic field is large compared with that of the electric field, the first condition 

 may be said to be imposed on the system by the slow periodic oscillation in the 

 shape and position relative to the axis, which the electric field produces on the 

 uniformly rotating orbit which the electron would describe if the atom was ex- 

 posed to the magnetic field only. 



If we consider a hydrogen atom which is exposed to the simultaneous in- 

 fluence of a homogeneous electric field of intensity F and a homogeneous magnetic 

 field of intensity H, the direction of which makes an angle f with the direction of 

 the electric field, it follows from the above that, if the perturbing influence of the 

 electric field is large compared with that of the magnetic field, the main etTect pro- 

 duced by the latter field on the spectrum may be described as the splitting up of 

 each Stark effect component, polarised perpendicular to the axis of the electric field, 

 into two circularly polarised components, corresponding to the outer members of a 

 Lorentz triplet which would be produced by a magnetic field of intensity Hcos<f. 

 On the other hand, if the perturbing effect of the magnetic field is large compared 

 with that of the electric, it follows that the main effect, produced by the latter field 

 on the spectrum, may be described as the resolution of the middle component and 



13* 



