Conway — On the Motion of an Electrified Sphere. 1 1 



Fiiuu ii knowlodgo of the imiiiial wnipoiienl. oT Uk- clectiio force we 

 liiid that the Burl'aco-dciisity is jiri>piirli(iiial lo 



Sap + — f ^SapShp + Jrt-iSacr j + . . . 



Thus the harmonic distribution of first order involves also one of the second, 

 so that the principal modes of oscillation are different from those of a fixed 

 sphere. 



We can now deal with the case of discontinuous motions, i.e. when 

 any differential coefficient becomes discontinuous. For example, suppose that 

 the sphere is moving with an acceleration ij', and that when t = t^ the 

 acceleration is a. Before the time t^ the surface-density is 





1 + 2<r"-Spa + . . . j, 



then after t =„/a the surface-density is 



- — ; Jl + 'Ic'^Spa +...[ + Sup + . . . 



where a is a solution of 



aci^ + acic + ac" = 



such that when t = to the densities and the currents (which depend on the 

 differential coefficients of the density) are equal. In this case we find 



" = 9-;? ('^0 - To) f -" \ ' Sin \-^— {t-t,) + - sin - 



^TTCI y_ lit Oj\ o 



Ec' -^ ('-'") • v/3/ \\. 2ir 



^" \ / sin t - t.. ] sin — • 



{'do - o-o )c '^" ^ I sin — - [i - fo] sin 



2ira 2a 



VI. — Quasi-Stationary Motion. 



A particular class of motion called quasi-stationary motion has received 

 much attention in modern dynamics of an electron. In this motion the 

 acceleration is supposed to be so small that its differential coefficients 

 and its square and higher power can be neglected. Our formulie become 

 in this case somewhat simpler ; but another method (which can be applied 

 to any other case of motion) seems more direct in this case. 



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