1919] on Ether and Matter 477 



On submitting these equations to Mr. C. T. Preece, INIathematical Lecturer 

 at Birmingham University, he dealt with them thus : — 



i» + ^' = ';-^j/^ + c, 



or choosing the constant suitably — 



\r a J a^ 



The second term represents departure from elliptic motion by the planting on 

 it of a small harmonic disturbance. 



If the disturbance ceases at any point («, y) the particle will continue in an 

 ellipse, such that — 



The effect of the disturbance, while it lasts, is to shut up the ellipse spirally in 

 the direction of its minor axis, leaving the major axis considerable, the excen- 

 tricity of the orbit becoming great. In the limit the semi-minor axis might be 



reduced to k, in which case ^ = a/1 — (-)» ^^^ ^^^ possible range of a' 



would be between a and a/e". So practically e becomes nearly 1 and a 

 remains nearly a ; thus keeping the frequency constant. 



The effect of this narrowing down of the ellipse is to bring the particle 



within the range k /^I"-^ of the central nucleus, or practically ^ ——a, 



\/ 1 +e a 



proximity likely to cause disruption and conferring on the particle a high 



maximum velocity na \/ "T^ , or approximately . 



This looks as if we could thus reckon an exaggerated upper limit to the 

 amplitude of light-wave concerned. With ordinary electric value for w it 

 comes out k — V^6 N a 2;), where z is the size of an electron, and a the size of 

 its orbit ; but if m is allowed to increase with speed, )8 being the ratio vjc, this 

 expression for the minor axis of a disruptive orbit, V(6 Nas;), must be multi- 

 plied by the fraction \^(1 - yS^)/^. It seems anyhow to be of the order 10-^'' 

 centimetre. 



