

98 Prof. J. W. Nicholson on Atomic Structure 



so that 



^i , w _ L u 2_ x? , » « n I x 



and therefore for a// values of w 1? by division, 



1 J 2 ^ » «" l 1 S °? 2 * w "" 1 



Excluding w = 2, already dealt with in the other paper*, 

 this compels a to be equal to /3, so that the angular momenta 

 are equal. Then r 1 =r 2 , and the electrons are continually 

 equidistant from the nucleus. 



For orbits in one plane, therefore, under any law of 

 electronic repulsion, the electrons are equidistant from the 

 nucleus ; and thus they move in the same circular or elliptic 

 path, or keep pace with each other in two equal paths with 

 the same major axis, as in the diagram given in the Phil Mag. 

 paper -j*. 



By analysis already given, and capable of extension J, 

 the same conclusion can be inferred for non-coplanar paths, 

 of which the figure gives an illustration, showing such possible 

 paths of each electron and of the nucleus round the axis of 



ff 



/?xz$ 



the atom. It is evident that it applies to any law of force 

 whatever which can be expressed in a power series. The 

 details of the analysis can easily be filled in by the reader. 

 We conclude, finally, that for any law of force between 

 electrons, the two in a helium atom must be equidistant from 

 the nucleus throughout any of Bohr's steady states. 



* Phil. Mag. April 1914. t Page 657. 



J ' Monthly Notices,' March 1914. 



