368 



84 



///. Comparison of the theory with the observations on the fine structure. 

 We shall now proceed to compare the estimate of the relative intensities, ob- 

 tainable from the preceding considerations, with Paschen's observations. As men- 

 tioned at the end of the first section of this chapter it is necessary, in order to 

 account for these observations, to pay attention to the disturbances which the tine 

 structure undergoes as a consequence of the presence of external forces, and we 

 shall therefore in the following discussion from the beginning take the intensities 

 of the "new" components, discussed in the second section, into account. The first 

 problem with which we meet will therefore be to compare these intensities for a 

 given value of the intensity F of the external electric field with the intensities of 

 the original components. Now the latter intensities were already estimated in the 

 preceding section on the basis of the formulae (123), the numerical results being 

 given in tables IX and X. It is, however, not possible to compare the numbers in 

 these tables directly with the numbers obtained from (126) and (127) because in 

 the formulae ( 123) are given the relative values of the amplitudes of the circular 

 harmonic rotations which the electron in the undisturbed hydrogen atom performs 

 in the plane of its motion. On the other hand, in order to take into account 

 that the electi'on moves in space and that the position in space of the plane 

 of its motion is arbitrary, it will obviously be sufficient to multiply the numbers 

 n'^R"^ and /?"/?"- in tables IX and X by the factor ^/:;, the numbers thus obtained 

 representing an estimate of the relative intensities of that part of the original 

 components which may be considered as polarised parallel to the direction of 

 the electric force, or that part which is polarised perpendicular to this direction, 

 which two parts are equal on account of the original components being unpolari- 

 sed. It must, however, be observed that we could also have obtained an estimate 

 for the intensities of the original components by considering the ditTerent transitions 

 {n\, n'^; n' n", n'g'; n") between stationary states of the perturbed system which 

 contribute to these components, but this would complicate our tables without 

 necessity, and moreover we shall have the opportunity to come back to this 

 other method of estimating the intensities of the original components in § 8, 

 where the influence of a magnetic field on the fine structure of the hydrogen lines 

 will be discussed. 



In the tables XI, XII and XIII we have given a scheme of the estimate which 

 according to the preceding considerations can be obtained for the intensities of the 

 new and of the original components in case of the fine structure of the helium 

 lines 4686 Å (4 ^ 3) and 3203 Å (5 ^ 3) {N = 2) and of the hydrogen line Ha, 6563 Å, 

 (3->2) {N = 1). In the calculation of the tables we have taken F=l i.e. the 

 intensities of the new components refer to an intensity of the perturbing electric 

 field of 300 Volt/cM. 



The first column contains the symbols (li^, n., ■ n^, n.,] characterising the tran- 

 sitions between two stationary states of the hydrogen atom to which the new and 

 the original components correspond. 



