﻿Mr. A. Bramley on Radiation. 725 



latter the intensities are both inversely proportional to the 

 square of the distance, while in the former they are inversely 

 as the first power, so that at great distances from the moving 

 charge the part of the field which depends on the accele- 

 ration will become very great in comparison with the other 

 part. 



The energy of the field is : 



» = ^ 1 H 2 + E- , + 2(HH 1 ) + 2(EE 1 )4-H ] 2 + E 1 2 }, 



where the terms with suffixes depend on the acceleration. 

 We shall consider the latter part only. 

 Since the energy per unit volume is i(E 1 2 + H 1 ) 2 we have 



for the volume density pWl+ ? ^) for E 1 =H 1 .- . 



The stream of energy passing any point per unit of area 

 is equal to c[E . H], the direction of the stream being along 

 the perpendicular to the plane of the orbit. 



Now 



,[E.H] =1 |- 2 . M 



16tt 2 • uc 2 ' 1-/3 2 ' (r 2 + R 2 + £ 2 -2rR cos 0{) 



in the direction of the axis of Z. 



This flow of energy is zero when the electron is stationary 

 and has a maximum value whenj#=l, attaining an infinite 

 value as the motion of the electron equals that of light. 

 This shows that the high speed electrons are the most 

 efficient radiators of energy. This energy also varies in- 

 versely as the square of the distance, as in the case of all 

 radiant energy. 



We are now in a position to calculate the force acting on 

 an element of volume due to the radiation emitted from that 

 particle. 



F=E+*|>H], 



F R = E R+ J[H .^-H 5 .^], 

 = 0. 



1 f e — u . a 1 1 I — 



~c]±7r' ug VW? ' (?- 2 + R 2 -K 2 ~2rKcos B^p J ~ 



