[ «>5 J 



XXXV. Does an Accelerated Electron necessarily Radiate 

 Energy on the Classical Theory ? By S. R. Milker, D.Sc, 

 Acting Professor of Physics, The University, Sheffield*. 



THIS question is of fundamental importance in modern 

 theory, and it would, I imagine, at the present time 

 receive an affirmative answer from most physicists. It is 

 true that certain adverse experimental results, such as the 

 normal absence of radiation from electronic motions in the 

 atom, call urgently for theoretical explanation ; but it seems 

 to be accepted that the necessity in the classical theory for 

 radiation from accelerated charges is so firmly based that it 

 can only be removed by far-reaching and revolutionary 

 changes, such as the quantum theory supplies. Some 

 apology seems necessary for attempting to open the question 

 again at this date ; and I should not have ventured to do so, 

 but for the result of the consideration of a certain concrete 

 case of accelerated electronic motion which is amenable to 

 an accurate mathematical treatment. This example shows 

 that it is possible to obtain, even on the classical theory, a 

 solution for a particular case of the accelerated motion of 

 charges, which satisfies completely both Maxwell's equations 

 and the mechanical laws which characterize a conservative 

 system, without any irreversible radiation of energy. A 

 study of it enables us, I think, to prove that a certain step 

 made in the deduction on the classical theory of the general 

 necessity for radiation is not invariably a valid one, and to 

 show that a comparatively minor modification of the boundary 

 conditions of the solution is sufficient to do away with 

 radiation in at any rate one case of accelerated motion. 



A remarkable solution of Maxwell's equations for a 

 particular type of accelerated electronic motion has been 

 given by Schott t- It is remarkable in that it is the onlv 

 case, other than that of uniform motion, which up to the 

 present has been solved in finite terms. 



Consider a point-charge moving along the (positive) axis 

 of x, and, f being its distance from the origin at time t, let 

 it move in such a way that 



£»=*»+«*», (1) 



where k is constant. At t = — x> the charge is at £= -|-g© 

 moving towards the origin with the velocity of light <•. it 



* Communicated by the Author. 



f ' Electromagnetic Radiation,' pp. 63-69. 



Phil. Mag. S. 6. Vol. 41. No. 243. March 1 921. 2 E 



