the stationary states of an atomic system among the continuous multitude of 

 mechanically possible motions. In this connection it may be pointed out that 

 the principle of the mechanical transfqrmability of the stationary states allows 

 us to overcome a fundamental difficulty which at first sight would seem to 

 be involved in the definition of the energy difference between two stationary states 

 which enters in relation (1). In fact we have assumed that the direct transition 

 between two such states cannot be described by ordinary mechanics, while on 

 the other hand we possess no means of defining an energy difference between two 

 states if there exists no possibility for a continuous mechanical connection between 

 them. It is clear, however, that such a connection is just afforded by Ehrenfest's 

 principle which allows us to transform mechanically the stationary states of a 

 given system into those of another, because for the latter system we may take one 

 in which the forces which act on the particles are very small and where we may 

 assume that the values of the energy in all the stationary states will tend to coincide. 

 As regards the problem of the statistical distribution of the different stationary 

 states between a great number of atomic systems of the same kind in temperature 

 equilibrium, the number of systems present in the different states may be deduced 

 in the well known way from Boltzmann's fundamental relation between entropy 

 and probability, if we know the values of the energy in these states and the 

 a-priori probability to be ascribed to each state in the calculation of the pro- 

 bability of the whole distribution. In contrast to considerations of ordinary statistical 

 mechanics we possess on the quantum theory no direct means of determining these 

 a-priori probabilities, because we have no detailed information about the mechanism 

 of transition between the different stationary states. If the a-priori probabilities 

 are known for the states of a given atomic system, however, they may be deduced 

 for any other system which can be formed from this by a continuous transforma- 

 tion without jjassing through one of the singular systems referred to below. In fact, 

 in examining the necessary conditions for the explanation of the second law of thermo- 

 dynamics Ehrenfest ') has deduced a certain general condition as regards the 

 variation of the a-priori probability corresponding to a small change of the external 

 conditions from which it follows, that the a-priori probability of a given stationary 

 state of an atomic system must remain unaltered during a continuous transformation, 

 except in special cases in which the values of the energy in some of the stationary 

 states will tend to coincide during the transformation. In this result we possess, 

 as we shall see, a rational basis for the determination of the a-priori probability 

 of the different stationary states of a given atomic system. 



') P. Ehrenfest, Phys. Zeitschr. XV p. 660 (1914). The above interpretation of this relation is 

 not stated explicitely bj' Ehrenfest, but it presents itself directly if the quantum tlieorj' is taken in 

 the form corresponding to the fundamental assumption I. 



D. K. D. Vidensk. Selsk. Skr., naturvidensk. og m.-itheni. Afd., 8. Række, iV. 1. 2 



