47 



331 



TluTc exists, however, one case in which il seems possible on the basis of 

 the ai)ovc considerations to obtain direct information about the relative intensities 

 with which dilTerenl spectral lines are emitted, viz. if we consider the components 

 in which a spectral line, emitted by an atomic system which is degenerate, is split 

 up due lo Ihe inlluence of some agency on the atom. Kxaniples arc allorded by 

 the fine structure of the hydrogen lines which is due to the inlluence of the 

 relativity modifications, and by the Stark efïect of the hydrogen lines which is due 

 to the influence of an external homogeneous electric field of force on the 

 hydrogen atom. In order to lix the ideas let us consider especially the case of the 

 Stark ellect. Under the influence of the external force a given hydrogen line (/»'-> n") 

 will be split up in a number of components, corresponding to transitions for which 

 the initial states will be characterised by diderent combinations /j, n\, /j, n'., 

 /».. =- n'., (/)', — /j'^ -(- n'3 = n') and the final states by corresponding combinations 

 /j", n'J, n" { n' n" -\- n" = n"). Since the values of the total energy in the difl'erenl 

 initial states are approximately equal, it seems in the first place allowable to con- 

 clude that in the vacuum tube the numbers of atoms present in these 

 states will be approximately ])roportional to the different a -prior i 

 probabilities of these states. In fact, this assumption presents itself natural- 

 ly, in analogy with the corresponding property of a statistical distribution of a large 

 number of atoms which is in temperature equilibrium; although of course the state 

 of equilibrium in the luminescent vacuum tube will, as mentioned, not in general 

 be a temperature equilibrium. As it will be seen in the following sections, the 

 assumption in question seems to be confirmed in a general way by the observations 

 In the case of the Stark edect the atom forms a non-degenerate conditionally perio- 

 dic system, for which the ditrerent stationary states will be a-priori equally j)robable 

 (see Bohr, loc. cit. Part II, p. 25), and we shall consequently expect that the different 

 initial states n\, /»',, /i', are of approximately equal occurrence in the luminous gas. 



Moreover the different frequencies (n', — n',')<«, 4- ■ • •("', — occurring in 

 the motion of the electron in the different corresponding initial states, as well as 

 in the different final states, (and also in the diff"erent slates characterised by 

 /,,. /i{ /IÏ -|- /(«/' — /jj.')} {k = 1,2,3) for a same value of / ) are approximately the 

 same, and equal to {n' — n")(u, so that the relative intensities with which, on ordi- 

 nary electrodynamics, radiations of these frequencies would be emitted from these 

 states are simply proportional to the squares of the amplitudes C of the harmonic 

 vibrations of these frequencies, occurring in the motion in these stales. 



We are therefore led to expect that it will be possible to form an idea 

 o I Ihe relative intensities with whicii the different components 

 of the Stark effect will appear, by comparing the intensity of each 

 component with the values of the scjuares of the am|)litudes of Ihe 

 corresponding harmonic vibrations occurring in 1 li c motion of Ihe 

 system in Ihe initial state and in the final stale and in I he niechani- 



