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LXXXVIII. Does an Accelerated Electron necessarily 

 Radiate Energy on the Classical Theory ? 



To the Editors of the Philosophical Magazine. 



GrENTLEMEN, 



IN your March number Dr. Milaer discusses the question of 

 the radiation from an accelerated electron in connexion 

 with a generalization of a solution of Maxwell's equations 

 obtained by Schott. This solution gives the field of a 

 Lorentz electron of large mass moving up from infinity and 

 then back again along a line of force in a uniform electric 

 field, and Dr. Milner adopts it to give the field of two 

 electrons with equal and opposite charges movin >■ first 

 towards one another and then separating after coming 

 simultaneously to rest, the motion again being along a line 

 of force in a uniform electric field. 



In the electromagnetic field thus presented by Milner, 

 there is quite clearly no irreversible radiation of energy either 

 away from or into the field, a fact which at first sight appears 

 to contradict the generally accepted notion that an electron 

 in accelerated motion is radiating energy. A closer exami- 

 nation will, however, soon prove that there is in fact no 

 discrepancy. 



The case for radiation may be presented in the following 

 form : — When the velocity of a moving electron is altered 

 the necessary modification in the surrounding field is effected 

 by means of a thin spherical shell of disturbance spreadino- 

 out symmetrically from the instantaneous position of the 

 electron, sweeping up the old field as it proceeds outwards 

 and leaving behind the new. As this shell gets farther and 

 farther from the electron its field approximates more nearly 

 to the type associated with radiation, and the energy of this 

 radiation, which never sinks below a finite positive limit, 

 represents a proper loss by radiation of the intrinsic (localised 

 velocity) energy of the electron. 



It is quite clear from this presentation that there is no 

 sense in the expression " radiation from the electron " unless 

 the radiation shell created at any instant can in fact get 

 away from the electron, that is unless the velocity and 

 acceleration of the electron are small compared with the 

 velocity of radiation. The limits have been calculated and 

 amply cover all conceivable physical cases, so that there 

 would appear to be full justification for the practical gener- 

 alization of the notion of radiation from moving electrons. 



