8 



where the motions in successive stationary states comparatively differ very little 

 from each other, will tend to coincide with the frequencies to be expected on 

 the ordinary theory of radiation from the motion of the system in the stationary 

 states. In order to obtain the necessary relation to the ordinary theory of radiation 

 in the limit of slow vibrations, we are therefore led directly to certain conclusions 

 about the probability of transition between two stationary states in this limit. This 

 leads again to certain general considerations about the connection between the 

 probability of a transition between any two stationary states and the motion of the 

 system in these states, which will be shown to throw light on the question of the 

 polarisation and intensity of the different lines of the spectrum of a given system. 

 In the above considerations we have by an atomic system tacidly understood 

 a number of electrified particles which move in a field of force which, with the 

 approximation mentioned, possesses a potential depending only on the position of 

 the particles. This may more accurately be denoted as a system under constant 

 external conditions, and the question next arises about the variation in the stationary 

 states which may be expected to take place during a variation of the external 

 conditions, e. g. when exposing the atomic system to some variable external field 

 of force. Now, in general, we must obviously assume that this variation cannot 

 be calculated by ordinary mechanics, no more than the transition between two 

 different stationary states corresponding to constant external conditions. If, how- 

 ever, the variation of the external conditions is very slow, we may from the neces- 

 sary stability of the stationary states expect that the motion of the system at any 

 given moment during the variation will differ only very little from the motion in 

 a stationary state corresponding to the instantaneous external conditions. If now, 

 moreover, the variation is performed at a constant or very slowly changing rate, 

 the forces to which the particles of the system will be exposed will not differ at 

 any moment from those to which they would be exposed if we imagine that the 

 external forces arise from a number of slowly moving additional particles which 

 together with the original system form a system in a stationary state. From this 

 point of view it seems therefore natural to assume that, with the approximation 

 mentioned, the motion of an atomic system in the stationary states can be cal- 

 culated by direct application of ordinary mechanics, not only under constant ex- 

 ternal conditions, but in general also during a slow and uniform variation of these 

 conditions. This assumption, which may be denoted as the principle of the 

 „mechanical transformability" of the stationary states, has been introduced 

 in the quantum theory by Ehrenfest') and is, as it will be seen in the following 

 sections, of great importance in the discussion of the conditions to be used to fix 



') P. Ehre.\fest, loe- cit lu these papers the principle in question is called the "adiabatic hypo- 

 thesis" in accordance with the line of argumentation followed bj- Ehrenfest in which considerations 

 of thermodynamical problems play an important part From the point of view taken in the present 

 paper, however, the above notation might in a more direct way indicate the content of tlie princfpie 

 and the liinits of its applicability. 



