﻿Theoretical Aspects of the Neon Spectrum. 205 



In order, therefore, to study the atom, it is. essential that 

 the electrons be given definite position relative to one 

 another. This has been undertaken by Langmuir *, and 

 there is considerable evidence in favour of the postulate that 

 eight of the electrons arrange themselves at the corners of a 

 cube at the centre of which the nucleus is situated. The 

 other two electrons are imagined to lie within this cube, 

 probably on a line joining the mid-points of any pair of 

 opposite sides. If we make use of this hypothesis, and 

 further are in possession of data which will allow us to 

 find the length of the diagonal of the electron cube, 

 then it was shown by the author f that it is possible to 

 calculate the angular velocities of the electrons about the 

 nucleus. 



Siuce the determination of the spectral lines is an ex- 

 tension of the matter given in that paper, it will be advisable 

 here to state the principles on which the calculations of the 

 electron frequencies depend. 



It has already been stated that the two inner electrons will 

 probably lie on a line joining the mid-points of any pair of 

 opposite sides. If this be the case, then the electrical forces 

 acting on the outer electrons due to the other electrons in 

 the outer shell, and to the two inner electrons, will be the 

 same whichever electron we take, provided that the two 

 inner electrons are equidistant from and on opposite sides of 

 the nucleus. 



The next consideration was the axes of revolution. As 

 before, it was desired if possible to get the forces acting on 

 the outer electrons due to centrifugal action the same for all 

 of the electrons. If we take as axes the three lines which 

 pass through the mid-points of the three opposite pairs of 

 sides of the electron cube respectively, then the above con- 

 dition will be satisfied. In the diagram the axes of revolution 

 are illustrated by XX', YY', and ZZ'. The inner electrons 

 being on the axis XX' will only rotate about two axes. 

 It is, of course, quite immaterial which axis the inner 

 electrons lie upon. The forces acting on any outer electron 

 were then considered, and were taken along the three sides 

 of the cube which meet at the point where the electron is 

 situated. Now, since the electron must be in equilibrium, 

 so the force along each of these lines due to electric;) 1 

 attraction and repulsion and also due to the motion in a 

 circular orbit must be equal to zero. 



* General Electric Review, 1919. 

 t Phil. Majr. Feb. 1922. 



