C 145 ] 



V. The Initial Accelerated Motion of Electrified Systems of Finite Extent, and 

 the Reaction Produced by the Resulting Radiation. 



By GEORGE W. WALKER, A.R.C.Sc., M.A., Superintendent of Eskdalemuir 



Magnetic Observatory. 



Communicated by Sir JOSEPH LARMOR, Sec.R.S. 

 Received December 17, 1909 Read January 27, 1910. 



CONTENTS. 



Section Page 



1. Introductory 145 



2. Fundamental equations 148 



3. Initial motion of a charged conducting sphere 151 



4. Second order approximation 154 



5. Initial motion of a charged conducting sphere moving with any speed after longitudinal 



acceleration is imposed 157 



6. Initial motion of a charged conducting sphere moving with any speed, after transverse 



acceleration is imposed 163 



7. Comparison with experiment 167 



8. Initial motion of an insulating charged sphere 173 



9. Fundamental equations for a moving dielectric 176 



10. Vibration of a charged conducting sphere under a periodic force 179 



11. First order vibrations of an insulating charged sphere 180 



12. Slow rotation of a charged sphere LS6 



13. Induced electrification and electric vibrations on a conducting sphere moving with uniform 



speed 191 



1. INTRODUCTORY. As far as I am aware, the problem of the electrodynamics of 

 accelerated motion of finite bodies has not been seriously attacked. Attention has 

 been mainly directed to the question of very small charged bodies, and even in this 

 case the results are not as exact as one could desire, in view of the important bearing 

 they have on the theory of the constitution of matter. 



Among results which have been generally accepted two call for special attention. 

 The first of these is the equation of linear motion of a small charged sphere 

 determined by LORENTZ (' Tbeorie Electromagne'tique,' p. 124). In the usual notation 



this equation is 



(m + m')xkx = X, 



VOL. CCX. A 463. U 2.3.10 



