﻿and its Relation to the Quantum Theory. 843 



hydrogen ion. The difficulties confronting modification of 

 the law of force between negative electrons as an alternative 

 method of explaining the dilemma of the helium atom are 

 also discussed. 



Part II. assumes no knowledge of the quantum theory and 

 is an outline of the mathematical method used in finding the 

 orbits in the model of helium in which the two electrons are 

 arranged with axial symmetry. This method consists in 

 developing the perturbations as power series in a constant 

 of integration, and is readily adaptable to other problems 

 in the dynamics of atomic structure. A simple check on 

 the accuracy of solution is furnished by the theorem that 

 the average absolute values of the kinetic energy and half the 

 potential energy are equal. 



Part III. deals with applications of quantum conditions to 

 the determination of the energy for the model of helium 

 possessing axial symmetry. Various theories for determining 

 the stationary states prove to lead consistently to the same 

 values for the constants of integration. 



The writer wishes to express his gratitude for the encourage- 

 ment and assistance given him by Dr. E. C. Kemble in the 

 problems studied. 



Part I. — The Dilemma of the Helium Atom. 

 Resume of Existing Models of normal Helium. 



Probably the greatest success the quantum theory has yet 

 achieved is found in the Bohr atom, in which the electron is 

 allowed to move only in certain quantized non-radiating 

 orbits. However, the quantitative success of the Bohr 

 theory in explaining spectral lines and ionization potentials 

 has been confined to atoms containing only a single electron, 

 viz., the hydrogen atom and an abnormal helium atom which 

 has been robbed by ionization of one of its two electrons 

 normally present. In generalizing the theory to apply to 

 atoms with more than one electron, it is natural to begin with 

 the simplest possible case, namely, the normal helium atom, 

 which contains only two electrons. 



Numerous attempts have been made to construct quantum 

 theory models of normal helium. In Bohr's own model 

 (fig. 1) the two electrons revolve about the nucleus at the 

 extremities of a diameter *. In the Langmuir semicircular 



* Phil. Mag. vol. xxvi. p. 492 (1913). 

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