76 



by (22), which correspond to "3 > 1, we shall according to the considerations in Part I 

 expect that their a-priori probabilities are all equal. ') 



As regards the comparison between the theory and the experiments, it will be 

 remembered that Stark found that every hydrogen line in the presence of an 

 electric field was split up in a number of polarised components, in a way different 

 for the different lines. When viewed parallel to the direction of the field, there appeared 

 a number of components polarised parallel to the field and a number of com- 

 ponents polarised perpendicular to the field; when viewed in the direction of the 

 field, only the latter components appeared, but without showing characteristic 

 polarisation. Apart from the marked symmetry of the resolution of every line, 

 the distances between successive components and their relative intensities varied 

 in an apparently irregular way from component to component. As pointed out by 

 Epstein and Schwarzschild, however, it is possible by means of (78), in connection 

 with relation (1), to account in a convincing way for Stark's measurements as regards 

 the frequenci es of the components. Especially a closer examination of these measure- 

 ments showed that all the differences between the frequencies of the components 

 were equal to entire multipla of a certain quantity, which was the same for all lines 

 in the spectrum and, within the limits of experimental errors, equal to the theoretical 



value ,7— Tn.7 • On the other hand, the theories of Epstein and Schwarzschild gave 



no direct information as regards the question of the polarisation and intensity 

 of the different components. Comparing formula (78) with Stark's observations, 

 Epstein pointed out, however, that the polarisation of the different components 

 observed could apparently be accounted for by the rule: that a transition between 

 two stationary states gives rise to a component polarised parallel to the field, if n, 

 remains unchanged or is changed by an even number of units; while a component, 

 corresponding to a transition in which n^ is changed bj' an uneven number of units, 



') By a simple enumeration it follows from this result, that the total number of different stationary 

 states of the hydrogen atom, subject to a small homogeneous electric field, which corresponds to a sta- 

 tionary states of the undisturbed atom, characterised by a given value of n in the condition I = nh, 

 is equal to n (n -i- 1). This expression is directly obtained, if we remember that n = n^ + "2 "r "3 

 and if we count each state, characterised by a given combination of the positive integers n^, n^, «3, as 

 double, corresponding to the two possible opposite directions of rotation of the electron round the axis 

 of the field. With reference to the necessary stability for a small variation of the external conditions 

 of the statistical distribution of the values of the energy among a large number of atoms in tempera- 

 ture equilibrium (see Note on page 43), it will be seen that the expression n(n -\- 1) may be taken as 

 a measure for the relative value of the a-priori probability of the different stationarj- 

 states of the undisturbed hydrogen atom, corresponding to different values of n. The problem of 

 the determination of this a-priori probability has been discussed by K. Herzfeld (Ann. d. Phys. 

 LI, p. 261 (1916)) who, by an examination of the volumes of the different extensions in the phase space 

 which might be considered as belonging to the different stationary states of the hydrogen atom, has 

 arrived at an expression for the a-priori probability of these states which differs from the above. From 

 the point of view, as regards the principles of the quantum theory, taken in the present paper, a con- 

 sideration of this kind, however, does not, as explained in Part I on page 26, afford a rational means 

 of determining the a-priori probabilitj' of the stationary states of an atomic system. 



