344 



60 



In § 5 it has been mentioned that we possess, quite independent of the estimate 

 which is based on the calculation of the amplitudes of the harmonic vibrations in 

 which the motion may be resolved, another source of information about the inten- 

 sities in the fact that the polarised components in which an unpolarised spectral 

 line is split up will, when taken together, show no characteristic polarisation in 

 any direction. This allows of an instructive application in case of the Stark effect 

 oi H„. In fact, adding the values for R'^ and belonging to the parallel compo- 

 nents, we get 1,70 and 0,66 respectively, while adding the /?'-'s and /?"'^'s for the 

 perpendicular components, we obtain 2,19 and 1,78. From this it follows that the 

 intensities of the perpendicular components compared with those of the parallel 

 components must, for the hydrogen line under consideration, be expected to be 

 considerably smaller than it would follow from a direct comparison with the values 

 of R''^ and R"'^. Especially the component corresponding to a transition between 

 two circular orbits perpendicular to the direction of the electric force, (003 — 002), 

 will be much less intense than the values of and R"^ would indicate. In an 

 even more striking way a consideration of this kind applies to the ultra-violet 

 hydrogen line (2-^1), for which the values of the /I's in the stationary states are 

 still smaller. Thus, under the influence of an electric field, this line will split up in 

 two parallel symmetrical components of equal intensity, (101 001) and (011^001) 

 (R'-' = 0,33, = 0), and one perpendicular component (002 -001 = 1, /?"-=!), 

 and since the sum of the intensities of the former must be equal to the intensity of 

 the latter, we see that the tendency for a transition between the two circular orbits 

 [002] and [001] is again much less than it might have been expected from a direct 

 consideration of the values of R' '^ and R"^. In the discussion in § 7 of the fine struc- 

 ture and in § 8 of the Zeernan eflect of the hydrogen lines we shall meet with 

 analogous phenomena as regards the transitions between circular orbits. In the case 

 of the Stark effect of Hß, Hy and H,^ there are so many components that il is impos- 

 sible to draw any further conclusion from the fact that the sum of the intensities 

 of the parallel and of the circular components must be the same. 



The fact that the tendency for a transition between two stationary states in 

 which the electron describes a circular orbit is less than would be expected from 

 the corresponding values of the Rs (R' = R" = 1) stands probably in close connec- 

 tion with the fact, to be mentioned in the following (see page 61), that the ten- 

 dency for other transitions to final states in which the electron describes a circular 

 orbit (for such transitions R" is always equal to zero) is larger than would be 

 expected from a consideration of the amplitudes of the corresponding harmonic 

 vibration in the motion of the electron. Thus both these facts clearly indicate a 

 tendency of the estimate of the probability of transition between two stationary 

 states based on a consideration of the motion in these states (and in the states 

 lying "between") — in contrast to other mechanical states of the system — to give 

 exaggerated results in cases where these motions show singularities. On the whole it 

 will be seen, from the following discussion, that the experiments on the Stark 



