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XI. The Initial Accelerated Motion of a Rigidly Charged 

 Dielectric Sphere. By G. H. Livens, B.A., Lecturer in 

 Mathematics, Sheffield University *. 



IN a previous paperf the problem or the motion of a perfectly 

 conducting sphere was solved, and it was seen that the 

 analysis and results were capable o£ expression in a manner 

 quite independent of any "material" mass that the sphere 

 might possess. The same method is now applied to the 

 initial accelerated motion of a dielectric sphere with a rigid 

 uniform charge of electricity. The notation of the previous 

 paper is adopted, and in addition we use K for the specific 

 inductive capacity of the medium of which the sphere is 

 composed. 



We proceed in an exactly analogous manner and assume 

 for the field external to the sphere 



v e 2 cos , , 



sin 6 , - mi , m /./n 



where / is in general a function of (ct — r + a). Inside the 

 sphere we have a field which is, in general, composed of both 

 converging and diverging waves. 

 We assume 



cV=^[*W'+fc'')+^i'-<k')L 



where fa is a function of (c't — r) and fa a function of (c f t 4- r), 

 and K = c 2 /c' 2 defines c' as the velocity of radiation in the 

 dielectric. 



* Cornnmiricated by the Author, 

 t Phil. Mag. May 1911, p. 640. 



