﻿based on Free Electrons. 1061) 



§ 3. It is consistent with the hypothesis of discrete charges 

 to suppose a unit at the centre. The adjustment of radii for 

 steady motion is possible with a positive centre when n > 4, 

 not when n — 2 or 3, for the mutual repulsion is not then 

 adequate to balance the central attraction, and so give a 

 position of equilibrium near which an electron in the ring- 

 must lie. The inequality of radii is increased by the presence 

 of the central unit. If the latter is displaced axially while 

 the positive and negative rings are supposed to remain in 

 one plane the position is clearly stable for the central charge, 

 because the attractive elements are the nearer. 



For a negative centre the adjustment of radii is possible 

 for all values of n ; for n>4 the inequality of radii is 

 reduced, for n — 2, 3, or 4 it is reversed and the negative 

 ring is outside. With the two rings in one plane the 

 position would, for axial displacement of the central unit, 

 be stable for n = 2, 3, or 4, unstable for other cases. A more 

 complete treatment in which account is taken of the relative 

 movement of the planes of the two rings, shows that the 

 negative electron at the centre is always axially unstable, the 

 positive always stable. Cf . § 33. 



A positive structure is found for the cases n = 2 or 3, some- 

 what unexpectedly, by taking two positive units on the axis, 

 one above the other below the plane of the rings, with a 

 separation wide enough to make the attraction of the pair on 

 an electron of the ring less than that of a unit at the centre. 

 This proves the beginning of a series which continues up to 

 the value n = & and there stops. In the range from w = 5 

 to n = 8, containing important elements, B, C, N, 0, there 

 are two positions : one where the attraction of the pair on an 

 electron is less than that of a unit at the centre, the other 

 with closer axial units and an attraction greater than that of 

 a unit at the centre. 



This completes the forms of the fundamental structures, 

 for which the symbols R„(0), R„(-f ), R n ( + , +) may be 

 used — rings with vacant centre, positive centre, or, in a few 

 cases, two axial units. 



§ 4. As subsidiary to the main structure it is proposed to 

 consider the case of electrons describing nearly circular orbits 

 about the centre of R n ( + ), either inside the inner or outside 

 the outer ring. The central unit alone can maintain as many 

 as four electrons in one circular orbit, with only a small 

 residual attraction for four. The central component of force 

 due to the ring fluctuates between the two signs, but its 

 mean value gives a reinforcement of the central attraction ; 



