96 



of each of the outer components of the normal Zeeman effect into a number of 

 components, corresponding to the parallel and perpendicular components respectively 

 of a Stark effect produced by an electric field of intensity F cos c. 



The effects just described, however, which are the same as would take place 

 if only the parallel component of the weaker field was acting on the atom, will 

 not be the only effects of the presence of the weaker field on the spectrum. In 

 fact, although the perpendicular component of the weaker field, apart from small 

 quantities proportional to u-, will not have any secular effect on the cycle of shapes 

 and positions which the orbit of the electron would pass through if the atom was 

 exposed to the stronger field only, it will obviously produce alterations in the 

 motion of the electron within this cycle which are proportional to u. Thus, if the 

 weaker field was parallel to the stronger, the motion of the electron in the per- 

 turbed atom would be composed of a number of linear harmonic vibrations parallel 

 to the direction of the fields, the frequencies of which are of the type rajp + tj o^ , 

 and of a number of circular harmonic rotations perpendicular to this direction, the 

 frequencies of which are of the type rtup ^ tjO^ -[^ o, (compare page 59). In the 

 general case, however, where the weaker field is not parallel to the stronger, there 

 irt"ill, in the expression for the displacement of the electron in any given direction, 

 in addition appear a number of harmonic vibrations the amplitudes of which are 

 proportional to fi and the frequencies of which, as a closer consideration of the 

 perturbations learns, are equal to the sum or difference of the frequency' of one of 

 the harmonic ^^brations, in which the motion in this direction could be resolved if 

 the external fields were parallel to each other, and one of the small frequencies of 

 tj'pe tjOj-i-Dj , which appear in the expression for the secular perturbations of the 

 electron in this case. A part of these additional vibrations will again possess fre- 

 quencies of the tv'pes rwp^-tjDi and r(£^p-r tjOj-j- O2 ) i^nd will cause that the motion, 

 instead of consisting of vibrations which are exactly linear and exactly circular 

 as in the case where the external fields are parallel to each other, wall be com- 

 posed of elliptical harmonic vibrations which partly are nearly linear and par- 

 allel to the direction of the stronger field and partly nearly circular and per- 

 pendicular to this direction. On account of this we shall expect that, due to the 

 presence of the perpendicular component of the weaker field, the different com- 

 ponents mentioned above will not be sharply polarised. Further there will, in the 

 motion of the perturbed atom, also appear a number of circular harmonic rotations 

 perpendicular to the stronger field, the amplitudes of which are small quantities 

 proportional to u, and the frequencies of which are of the type rtop -f- tjO^ -p 20^ . 

 From this we shall expect the appearance in the spectrum of a number of new 

 weak components, corresponding to a tj-pe of transition between stationary states 

 which would not be possible if the two external fields were parallel to eachother. 

 When considering more closelj' the frequencies of these new components, it must 

 be remembered, however, that, as mentioned above, the present method of treating 

 the problem of the perturbations assures us of the conditionallj' periodic cha- 



