332 



48 



cally possible states lying "between" these states. In §6 the values of these 

 squares in the initial stales and in the final states will be calculated on the basis 

 of the expressions for the amplitudes deduced in § 3, and it will be shown that, 

 simply from a consideration of these values, it is actually possible to account in 

 main features for the intensities of the different components observed by Stark. 

 In § 7 the same method will be applied in order to estimate the relative intensities 

 of the fine slruclure components of the hydrogen lines, in which case the above 

 consideration needs a slight modification, due to the fact that the a-priori proba- 

 bilities for the different stationary states are no more equal to each other. It uîust, 

 however, be emphasised already here that the melhod in question can only be 

 expected to give a rather rough estimate of the relative intensities, especially when 

 the n's involved in the difierent stationary states are very small numbers. In the 

 theory of the Slark effect we shall, for instance, meet with transitions for which 

 the amplitudes of the corresponding frequency are equal to zero in the initial 

 stale, as well as in the final state, and where, as a matter of fact, the intensity of 

 the corresponding component is different from zero. A closer discussion of these 

 transitions shows, however, that the value of the amplitude of the vibration of 

 corresponding frequency in the mechanically possible states lying "between" the 

 initial stale and the final state is different from zero for these transitions. In order 

 to account for the finer details of the observations, we are therefore naturally 

 induced to try to improve the estimate of the relative intensities of the components 

 by comparing these intensities, not with the squares of the corresponding ampli- 

 tudes in the initial states and final states only, but with some suitable mean value 

 of Ihese squares taken over the mechanical states which lie between these states, and 

 which are characterised by the different values of / between and 1. Especially the 

 logarithmic mean value of these squares, of the type defined by (109) in the 

 note on page 46, would seem to lend itself naturally to such an attempt. A compu- 

 tation of these logarithmic mean values, however, would involve laborious numeri- 

 cal calculations and has not been given in the present paper, because we cannot 

 expect, as mentioned in the note referred to, to obtain in this way an exact 

 determination of the relative intensities (compare page lUO) and also because, at 

 the present stale of the theory, the agreement with the observations obtained by 

 the simpler calculations in this paper may be considered as very satisfactory. 



Although we have thus met with a case where Bohr's considerations about 

 the connection between the quantum theory and the ordinary electrodynamical 

 theory of radiation may be directly applied to estimate the relative intensities 

 of spectral lines, it must be remembered that this estimate is based on the neces- 

 sary continuous connection between the unknown laws governing the intensities 

 with which spectral lines are emitted in the region where the n's in (99) are small 

 and the law which governs these intensities in the region of very large n's. The 

 estimate in question must consequently be expected to become the more uncertain 

 the smaller the numbers n^, ... n« are which characterise the stationary states 



