Oonwav — On the MoUoti of an Electrified Sphere. 13 



Wo thus timl f(iv tho oloctroiuoti\'o intensity inside tlic expression 





where 



jjf = 



•IE- /, 5 V? 9 «.' \ ^^ 1 I 1 , 1 + /.• 2 



C- ?'■'■■ 7 lV,,r /.:^ ( t " 1 - /,: 1 - IcV 



and 



where it = Ta and Z; = «/c. 



It will be noticed that M and M' are Abraham's expressions for 

 longitudinal and transverse mass.* 



If we suppose now a surface-density of amount 



pSpaS(T~'a + ([SpaVa'^a, 

 we find an internal electromotive force of amount 



where 



277 (1 -k-) jl, I vk J 



^• = — F—U-^°g 1—^-^1' 



TT I 



(1 - k-f (1 1 + /.• 2 



2' = — AT-j-^'^gr^^i-^^ 



For example, if we require the distribution of electricity due to a field 



ffl' 'lo' ^® fi'^*^ ^h^ linear equation : 



apijo - et \<y>^<y~^<y + I «!?i!? ~ "*^ ) "^ K t" or + eq + Kwi/o = U. 



This contains two scalar unknowns p and q, and a vector unknown a, so 

 that another equation is necessary. In the next section this will be found. 



VII. — DynaiMical Results. 



As a basis for our results we can assume with Lorentzt that the total 

 force on the conductor is that due to the aethereal forces on each element 

 of electricity. If in addition we have Newtonian forces, including reversed 

 effective forces, then the whole system of forces, electrical and non-electrical, 

 must be in equilibrium. The electromotive intensity on the elements gives 



* Cf. Abraham, Theorie lUr EUctrinliit, ii., p. 191. 

 tCf. Lorontz : Theorij of Electrons, p. 19. 



