and the Spectrum of Helium, 103 



therefore helium does not possess a nucleus charge 2e, or 

 Bohr's theory of series is incorrect. But since the whole 

 argument can be extended to atoms with nuclei 3e and 4e. 

 we conclude that this theory cannot give the helium spectrum 

 from any atom, and is incapable therefore of further deve- 

 lopment in the interpretation of spectra. The fact that this 

 incapacity is associated with a similar one in connexion with 

 the sequence of chemical properties of the elements is very 

 decisive. 



It might perhaps be urged that only the total angular 



momentum in the atom is a multiple of — and not that of 



in 



any individual electron, as supposed, after Bohr, in all the 



preceding work. In that case the problem is one of " periodic 



orbits," but as such it can hardly, by its solution, lead to a 



definite picture of the atomic processes which can be called 



a theory of spectra. For the essential feature of the angular 



momentum principle is that it makes the atom definite, by 



only admitling a certain number of possible radii or angular 



velocities, whether constant values with an actual existence 



or mean values associated with non-circular orbits. If, as in 



Bohr's fundamental assumption, bound electrons do not 



radiate energy in their stationary states, and thus experience 



no drag on their motion, the total angular momentum of the 



atom must remain constant. A knowledge of this constant 



does not go far in fixing the atomic structure when there is 



more than one electron. More conditions must be imposed 



in order to obtain a definite atom, except in special cases of 



the simplest periodic orbits which are possible. These are 



the cases investigated in this paper, in which the angular 



momentum is shared in a simple way between the electrons. 



They must be the cases of most frequent occurrence in actual 



atoms, and the fact that they do not show the spectra which 



theory requires is in itself sufficient to show that spectra will 



not be obtained from the less likely though more indefinite 



cases. No generalization of the theory on these lines can 



therefore hope to be successful, and we must conclude that 



it cannot develop in the manner which its earlier success 



appeared to foreshadow. At the same time, the connexion 



between the Rydberg constant and Planck's constant is so 



close that it is difhVult to believe that it is not -eal. But 



such a reality does not contain a corresponding reality for 



the process by which the form of the hydrogen spectrum is 



derived. It can be derived, for example, in its entirety, also 



from the theorv of Ritz. 



