Electric and Magnetic Fields on Spectral Lines. 



511 



equal to the mean value of the potential energy due to the 

 displacements. Consequently (11) forms a complete analogy 

 to Planck's original relation 



JJ =n7iv 



between the energy U of a monochromatic vibrator and its 

 frequency v. This analogy offers another way of representing 

 the present theory — a way more similar to that used in my 

 former paper*. Considering, however, the widely different 

 assumptions underlying the relation (11) and Planck's 

 relation, it may seem more adequate not to seek the basis of: 

 our considerations in the formal analogy in question, but 

 directly in the principal condition (1) and in the laws of the 

 line-spectra. 



In dealing with the more complicated structure of the 

 spectra of other elements, we must assume that the atoms of 

 such elements possess several different series of stationary 

 states. This complexity of the system of stationary states, 

 compared with that of the hydrogen atom, might naturally 

 be anticipated from the greater number of electrons in the 

 heavier atoms, which render possible several different types of 

 configurations of the particles. 



According to (1), (2), and (3) the energy of the ?/th state 

 in the rth series is, omitting the arbitrary constant, given by 





(13) 



The present theory is not sufficiently developed to account 

 in detail for the expression (13). However, a simple inter- 

 pretation may be obtained of the fact that in every series 

 <j> r (n) approaches unity for large values of n. 



Suppose that in the stationary states one of the electrons 

 moves at a distance from the nucleus which is large com- 

 pared with the distance of the other electrons. If the atom 

 is neutral, the outer electron will be subject to very nearly 

 the same forces as the electron in the hydrogen atom. Con- 

 sequently, the expression (13) may be interpreted as indicating 

 the presence of a number of series of stationary states of the 



* Note added during the proof. — In the Phys. Zeitschr. of Feb. 1, 

 E. Gehrcke has attempted to represent the theory of the hydrogen 

 spectrum in a way somewhat different from that in my former paper. 

 Like the procedure in my paper, Gehrcke does not attempt to give 

 a mechanical explanation of Planck's relation between the frequency of 

 the radiation and the amount of energy emitted ; but he does also not try 

 to give a mechanical interpretation of the dynamical equilibrium of the 

 atom in its possible stationary states, or to obtain a connexion to 

 ordinary mechanics in the region of slow vibrations. 



2M2 



