﻿hased on Free Electrons. 1091 



The quasi-hyperbolic type is transient, and points to inter- 

 change with the status of free electrons. 



Setting aside the cases of R„( + , + ), where stability has 

 not been examined, the most permanent forms of structure 

 are R„(0), R„( + ), and R„( -f ) with one satellite, two forms 

 neutral, one with a single positive residue. Less permanent 

 is the type with one negative residue (viz. two satellites), and 

 in a still less degree that with a double negative residue 

 (viz. three satellites). 



§ 24. In respect to any atomic scheme there are two 

 crucial tests to be faced — the question of stability which 

 belongs to the domain of mathematics, and that of comparison 

 with assured facts in the domains of Physics and Chemistry. 

 As regards the problem of stability, examined with reference 

 to the present scheme and that of multiple core, although 

 the methods used are largely approximative, I believe the 

 results to be substantial in their bearings on both schemes 

 and in the main correct. The existence of instability in both 

 schemes, though of differing types, demands a discrimination 

 as to the fatal or admissible character of the instability, and 

 in the latter case as to the function which it may be held to 

 discharge. This again carries with it the suggestion that 

 the activity of groups of atoms and free electrons as displayed 

 in the world of phenomena may be dependent on some degree 

 of instability. 



The application of the second test, with the task of inter- 

 preting an abstract mathematical theory, is one that calls 

 for a wide and intimate knowledge of experimental work, 

 'and especially of results of recent research which seem to 

 probe the nature of the atom. To such knowledge I can lay 

 no claim ; and consequently I have felt much uncertainty in 

 interpreting the present scheme, and some hesitation in 

 criticizing what appear to be weak points in other theories. 

 For this there is no remedy but an appeal to readers who 

 may agree with my opinion that the multiple-core scheme 

 involves an essential irrationality, may be prepared to 

 consider the present alternative scheme, and can bring to 

 the matter a fuller knowledge of the relevant branches of 

 Physics. 



Mathematical Theory. 



§ 25. The first problem examined was that of oscillation 

 confined to radial displacements. The limitation is realized 

 by supposing this displacement the same for all elements 

 lying on one ring, and also supposing all elements to have 



