values and the experimental evidence about the constitution of the atom obtained from 

 other sources, it is necessary to introduce further assumptions about the laws which 

 govern the stationary states of a given atomic system and the transitions between 

 these states. 



Now on the basis of a vast amount of experimental evidence, we are forced 

 to assume that an atom or molecule consists of a number of electrified particles in 

 motion, and, since the above fundamental assumptions imply that no emission of 

 radiation takes place in the stationary states, w-e must consequently assume that 

 the ordinary laws of electrodynamics cannot be applied to these states 

 without radical alterations. In many cases, however, the effect of that part of the 

 electrodynamical forces which is connected with the emission of radiation will 

 at any moment be very small in comparison with the effect of the simple electro- 

 static attractions or repulsions of the charged particles corresponding to Coulomb's 

 law. Even if the theory of radiation must be completely altered, it is therefore a 

 natural assumption that it is possible in such cases to obtain a close approxima- 

 tion in the description of the motion in the stationary states, by retaining only the 

 latter forces. In the following we shall therefore, as in all the papers mentioned 

 in the introduction, for the present calculate the motions of the particles 

 in the stationary states as the motions of mass-points according to 

 ordinary mechanics including the modifications claimed bj' the theory of rela- 

 tivity, and we shall later in the discussion of the special applications come back to 

 the question of the degree of approximation which may be obtained in this way. 



If next we consider a transition between two stationary states, it is obvious 

 at once from the essential discontinuity, involved in the assumptions I and II, that 

 in general it is impossible even approximately to describe this phenomenon by 

 means of ordinary mechanics or to calculate the frequency of the radiation absorbed 

 or emitted by such a process bj- means of ordinary electrodynamics. On the other 

 hand, from the fact that it has been possible by means of ordinary mechanics and 

 electrodjmamics to account for the phenomenon of temperature-radiation in the 

 limiting region of slow vibrations, we may expect that any theory capable of describing 

 this phenomenon in accordance with observations will form some sort of natural 

 generalisation of the ordinary theory of radiation. Now the theory of temperature- 

 radiation in the form originally given by Planck confessedly lacked internal 

 consistency, since, in the deduction of his radiation formula, assumptions of 

 similar character as I and II were used in connection with assumptions which were 

 in obvious contrast to them. Quite recently, however, Einstein') has succeeded, 

 on the basis of the assumptions I and II, to give a consistent and instructive deduc- 

 tion of Planck's formula by introducing certain supplementary assumptions about 

 the probability of transition of a system between two stationary states 

 and about the manner in which this probability depends on the densitj' of radia- 



') A. Einstein, loc. cit. 



