﻿and its Relation to the Quantum Theory. 845 



complete cycle of values of q. Having thus determined the 

 dimensions, we can compute the energy and compare the 

 calculated value with that found experimentally from ioniza- 

 tion potentials. In no case is the agreement satisfactory, so 

 that apparently none of these models can be correct if the 

 Sommerfeld quantum conditions are accepted. For a more 

 thorough exposition of the difficulties confronting these 

 models the reader is referred to a recent paper by E. C. 

 Kemble in the Philosophical Magazine *. 



Since none of these models can be regarded as thoroughly 

 satisfactory, it is natural to inquire whether there cannot be 

 some other possible model. In making this investigation we 

 must bear in mind that the extreme chemical stability of 

 helium indicates that the arrangement of its two electrons is 

 particularly simple and symmetrical, for an electron revolving 

 in an orbit outside that of its mate would presumably be a 

 valence electron. Symmetry with respect to a point yields 

 the Bohr model, already mentioned. The two simplest cases 

 of symmetry with respect to a plane (figs. 2 and 4) have been 

 investigated by Langmuir, and yield impossible ionization 

 potentials of approximately the same size ( — 4*6 and —8*5 

 volts) f- If is extremely doubtful whether other more 

 complicated, and therefore less probable, orbits symmetric 

 with respect to a plane would yield ionization potentials 

 differing very widely from those of these two simple limiting- 

 cases ±. 



Study of Model with Axial Symmetry. 



The onl} T remaining type of simple symmetry which has 

 not been studied is that with respect to an axis. It 

 therefore seemed desirable to compute the ionization 

 potential of a model possessing this kind of symmetry, 

 which was suggested by Dr. E. C. Kemble §. Since the 

 two electrons I. and II. move in three dimensions so as to 

 always be symmetrically located with respect to an axis, 



* Phil. Mag. vol. xlii. p. 123 (July 1921). 



t Physical Review, vol. xvii. p. 339. 



\ Cf. identity of elliptical and circular energy levels in the hydrogen 

 atom (relativity corrections neglected). In the two Langmnir models, 

 projection of motion on plane of symmetry is a straight line or circle. 

 The most general motion symmetric with respect to a plane would pro- 

 ject into a sort of precessing ellipse, which may be regarded as 

 intermediate between the above two cases. The more general motion 

 might involve impossible singularities, such as continual distortion of 

 shape of ellipse. 



^ Loc. cit. 



