﻿1052 Does an Accelerated Electron radiate Energy ? 



for certain velocities smaller than that corresponding to 

 •2 volt. 



The large increases of the free paths of electrons as the 

 velocity diminishes are the most remarkable of the definite 

 results obtained from these experiments. There can be no 

 doubt that these conclusions about the mean free paths, and 

 the estimates of the loss of energy of the electrons in 

 collisions with molecules, are substantially correct, notwith- 

 standing the possible experimental errors or any uncertainty 

 as to the exact values of the numerical coefficients in the 

 formulae that have been used. 



XCV. Does an Accelerated Electron necessarily radiate Energy 

 on the Classical Theory? 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



BY the kindness of Professor Born I have learnt that the 

 absence of radiation from the system of two oppositely 

 charged point electrons of Lorentz mass accelerated by a 

 uniform electric field, which I proved in a paper with this 

 title in your March 1921 number (p. 405), also follows from 

 a general theory which he worked out so long ago as 1909. 

 Professor Born's paper {Ann.d.Phys. xxx. p. 1, 1909) forms 

 a discussion of the theory of rigidity and of the motion of a 

 "rigid" electron, on the basis of the principle of relativity, 

 and one of his conclusions is given in the following words : — 



" Bemerkenswerth ist, dass ein Elektron bei einer Hyper- 

 belbewegung, so gross auch ihre Beschleunigung sein mag, 

 keine eigentliche Strahlung veranlasst, sondern sein Feld 

 mit sich fiihrt, was bis jetzt nur fur gleichformig bewegte 

 Elektronen bekannt war. Die Strahlung und der Widerstand 

 der Strahlung treten erst bei Abweichungen von der Hyper- 

 belbewegung auf." 



This remarkable result of the early days of relativity 

 seems to be but little known in this country, may I therefore 

 be permitted to direct attention to it here ? By " Hyper- 

 belbewegung " is meant the motion of a particle whose world- 

 line in the four-dimensional universe is hyperbolic, or, which 

 comes to the same thing, the graph of which on an #, t 

 diagram forms an hyperbola. It is the equivalent in the 

 relativity theory of uniform acceleration in Newtonian 

 dynamics. 



Yours faithfully, 



September 30th, 1922. S. R. MlLNEIU 



