On Electro-magnetic Action of an Electrified SiJliere. 251 



element of an electric current. This may seem like begging the 

 question, but it is only doing explicitly what Mr. Thomson does 

 implicitly. It is evidently impossible that the electro-magnetic 

 action of moving electricity can be due entirely to the electro- 

 magnetic action of the displacement currents in the dielectric, 

 for in the case of a plane moving parallel to itself there are none 

 of these displacement currents, and yet that is the only case that 

 has been experimentally verified. 



To show that my assumption leads to equations satisfying the 

 condition, and leading to practically the same results as Mr. 

 Thomson's, does not require much work. 



Consider an elementary volume dx ds. cos 0, where ds is an 

 element of the surface of the sphere, and d the angle the radius 

 makes with x. The displacement in this volume is = ^ the 

 superficial density while after the time dt it is zero on my 

 assumption. Hence calling the displacement D, we have — 



— — dt= -I .dxds. cos Q. 

 dt 



Hence D= — ^.— -.cZs.cos0. 



dt 



Now -Tj, =p the velocity of the sphere which is supposed to be 



moving along x. Hence the components of t) are /, g, h, and ob- 

 serving that ds = a^dfjid(() where cos 6 = fi and a is the radius of the 

 sphere, while 4nra^ .3 = 6 the total quantity of electricity on the 

 sphere. 



/ dxdy dz— ~-f~ u^diid^t 



g dxdy dz= - ^/z cos fdfidcf} 

 47r 



h dxdy dz= —. — fi sin fdfji.d<}). 



Hence the components of the electro-magnetic potential are at 

 a point at a distance — 



G,=.-£ffltS^df^d<p. 



n.^-^fffi^^dfxdd^. 



SciEN. Proc. R.D.S,, Vol. Ill,, Pt. v. X 2 



