79 



363 



scd by Ihc |)fiturl)iiig forces on llu' motion oC llic oiigiiially (icf^eiieratc system, it 

 will be seen that tbe circumstance, that in the present case the energy in the sta- 

 tionary states of the perturbed system to the first approximation does not (le|)en(i 

 on the value of the integer n appearing in the third of the conditions (124), is 

 intimately connected with the fact that the two fundamental fre(|uencies (o.. and oi.>, 

 which together with ^w, characterise the motion of the perturbed system, do not 

 ditVer from each other as far as small quantities proportional to F are concerned 

 (see page 33)')- 



With reference to (1) it will be seen from the above that the elTccI of the 

 external electric field on the spectrum of the hydrogen atom consists, as regards 

 the frecjuencies, in the splitting up of every fine structure component 

 in a number of components, because to every stationary state (Hj, n.^) of the 

 undisturbed atom there corresponds a number of stationary states (n^, nl of the 



transformed into one among the stationary states involved in tlie tlieory ol the Stark effect, for whicli. 

 witli the notation of ij A, /.. (= 2- X angular momentum of the electron round the axis of the field) 

 has the same value as I'^, but for which /, = /!] and - /','. 



M From the formulæ (90) and (41) it will, with reference to the considerations on page 15 and 

 16, be seen that (o^ — oj.^ represents the frequency with which the plane of the orbit of the electron 

 under the influence of the electric field rotates uniformly round the z-axis. As it will he proved in the 

 l)apcr referred to above, this frequency may. just as the additional energy, be represented by a series 

 f F /F\2 I 



of the form F| fc, fc, ( j 4- . . ] ; the first term of this series may again be found already from the 



calculations in § 4, bj' means of a consideration of conservation of angular momentum analogous to 

 that applied by Bohr in his discussion of the Stark effect (loc. cit. Part II. p. 72). In fact, a rotation of 

 the plane of the orbit will imply a change of the angular momentum of the electron round the nucleus, 

 considered as a vector, the mean value of which, taken over a time interval laigc compared with 



' but small compared with ^ — , will have a direction perpendicular to the : axis and, « itli the 

 Wj — tt/j 



JO 4_ JO 



' " ' here the first factor ie|)resents the component of 



the angular momentum of the electron perpendicular to the direction of the field. This mean change 

 in angular momentum, however, is directly seen to originate from the fact that the mean position of 

 the electron, taken over a time interval of the order mentioned, will not be placed on the r-axis but 



will, as seen from formula (96), be displaced from this axis by an amount ^ 3// ,n ï in a direction 



perpendicular to the direction of the mean change of the angular momentum. K(|uali/,in« the mean 

 value of the change of angular momentum due to the action of the external force with the amount 

 arising from the rotation of the plane we consequently get 



wlilcli gives 



<"3 "'2— ^ p /3-(- /!l 2 (2ri»/V<'r'»m» ' ' 



which, as it was to be expected, is seen to be a small quantity of the same order as the sniall fre- 

 quency differences between the components into which each line structure component is split up under 

 the influence of the external field and which can be directly found from the formula for J > deduced 

 in the above note. 



