﻿1088 Mr. R. Hargreaves on Atomic Systems 



there is clear evidence in that scheme. With rings of 

 positive and negative elements P and N, if all the N's are 

 displaced through an angle 2irjn, a new configuration of 

 steady motion is reached. At first this instability appeared 

 significant as providing the occasion for such a transition, 

 but on reflexion a wider view is suggested. The instability 

 is to be regarded as indicating that the whole motion consists 

 in the passage from one of these configurations to others in 

 succession. 



. Now, the equations set up for oscillation about the two- 

 ring position are not adequate to deal with this finite 

 transition — a problem of the motion of 2n bodies under 

 attractive and repulsive forces in less specialized positions. 

 The forecast I make of the motion (without calculation) is 

 that if N is displaced tangentially towards P, there will be 

 a gradual increase in the rate of approach, and N will be 

 carried a little beyond P and describe a loop about it before 



Fig. 4. 



N 



proceeding to the next special position midway between two 

 P's. In the loop phase or near the passage through the 

 apsidal position each N is under the almost exclusive control 

 of the next adjacent P. As a consequence, kinetic and 

 potential energies ;tnd acceleration are all on a greatly- 

 increased scale in ihis part of the motion, much as in the 

 apsidal phase of: motion in a hyperbola or elongated ellipse. 

 The distance between N and P is here of the order a x — a^ 

 say p(a l ~-a 2 ) or pat at the apse. The acceleration at this 

 apse is then e 2 /m 2 p' 2 a 2 £ 2 , whereas in the steady motion it is 

 Ne 2 /?/?^ 2 ; thus as N cc n, and fee??, -2 when n is great, the 

 first acceleration will vary as n 4 /m 2 and the second as njm^ 

 a v^ry wide disparity. 



The system has been treated by mechanical rather than 

 electromagnetic methods, since electrostatic force has been 

 used and a constant inertia. This treatment, however, 

 should give an approximate value of acceleration ; and since 

 radiation varies as the square of acceleration, it would 

 appear that in the brief space belonging to the loop phase, 

 radiation would be on a vastly greater scale than in the rest 



