97 



racter of the motion of the electron within a lime interval of the same order of 

 magnitude as o\x, only if we look apart from small quantities of the same order as 

 //-'; and we must therefore be prepared to find that the frequencies of the vibra- 

 tions of small amplitudes will not be defined with the same degree of approxima- 

 tion as the frequencies of the vibrations of large amplitudes. Thus, while the fre- 

 quencies of the latter vibrations are defined with neglect of small quantities pro- 

 portional to Xß'^, the frequencies of the small vibrations under consideration are 

 obviously defined only with neglect of small quantities proportional to iji. In in- 

 timate connection with the general want of definition of the energy in the stationary 

 states for perturbed systems of the type in question, we must accordingly be pre- 

 pared to find that, in contrast to the strong components, for which we may expect 

 that by far the larger part of the intensity is contained within a spectral interval 

 of a width proportional to lu', the new components will be diffused over spectral 

 intervals of a width propoi-tional to /î/i. ') Thus, in case the effect of the external 

 electric field is large compared with that of the magnetic field, we might expect at 

 first sight that, on each side of every of the Stark effect components polarised 

 parallel to the electric force, there would appear a weak component which would be 

 circularly polarised and be displaced from this component by an amount twice that 

 of the displacement of the strong components into which the perpendicularly 

 polarised Stark effect components are split up as a consequence of the small 

 magnetic field. We must be prepared, however, to find that these weak components 

 will be so diffuse, that they are not separated from the weak perpendicular com- 

 ponent which has the same frequency as the strong parallel components on each 

 side of which the weak components under consideration would lie, and which 

 appears as a consequence of the above mentioned want of sharpness as regards the 

 polarisation of the strong components. On the other hand, if the effect of the mag- 

 netic field is large compared with that of the electric field, any weak component 

 of the type under consideration, which corresponds to transitions in which the 



') Compare Note on page 61. With reference to the general validity of relation (1), it will be seen 

 that the assumption, that the weak components possess this degree of diffusion, implies the assumption, 

 that the corresponding transitions (the probability of occurrence of which is very small compared wilh 

 the probability of the transitions responsible for the strong components) will generally take place 

 between two states of the perturbed atom, which do nut both belong to the well defined ensemble of 

 stationary states in which at any moment the great majorit3' among a large number of atoms will be 

 present. Thus, in case the effect of the external electric field is large compared with that of the mag- 

 netic field, we may expect that, in both states involved in the transitions in question, the positions of 

 the plane in which the electrical centre moves will coincide with positions of this plane in states 

 belonging to the ensemble just mentioned, while the angular momentum of the electron round the 

 axis of the electric field will generally change bj' an amount which will not be equal to an entire 

 multiple of /i/2-. On the other hand, if the effect of the magnetic field is the larger, the angular 

 momentum of the electron round the axis of this field will, in the transitions in question, change by 

 two times ii'2-, while we may e.xpect that the plane in which the electrical centre moves will generally, 

 in at least one of the states involved in these transitions, differ from tlie positions of this plane in the 

 ensemble of stationary states referred to. 



