Properties of the Electric Field. 169 



motion of the tubes which have their ends on the plates ot the 

 condenser, a and ft increase respectively by Ajrcoxh and 

 4m<Dyh as we cross one plate and decrease by the same 

 amount as we cross the other. Thus the conditions by which 

 a, ft, 7 are determined will be that, except in the plates of the 

 condenser, they are derived from a potential, that they every- 

 where satisfy the solenoidal condition, that 7 is continuous, 

 while a and ft increase by kiraslix, ^.Trooliy respectively as we 

 cross a plate of the condenser. Hence this distribution of mag- 

 netic force is exactly what would be produced if we supposed 

 that each moving charge e of electricity produced the same 

 effect as a current (ore, where r is the distance of the charge 

 from the axis of rotation. 



Hitherto we have only considered non-magnetic substances. 

 We shall now proceed to discuss the differences which occur 

 when the tubes of electrostatic induction are moving through 

 iron or some other magnetic substance. 



If a, b, c are the components of the magnetic induction, 

 a, ft, 7 those of the magnetic force, the energy in unit 

 volume is 



.— {a* + bft + c*), 



and if the magnetism is entirely induced and //. is the mag- 

 netic permeability, this equals 



From this expression for the kinetic energy we can deduce 

 the components of momentum and electromotive intensity due 

 to a moving tube of electrostatic induction in the same way 

 as we deduced equations (2) and (3). Doing so, we find for 

 U, V, W, the components cf momentum, the expressions 



\J=fi(gy—hP) =gc-hb, 



Y = fjL(ha.—fy) = ha—fc, 

 W=l*(f/3- 3 *)=fb-ga. 



And for X, Y, Z, the components of the electromotive force 



X = /J, (ivft — vy) = wb — vc, 



Y = /jb(uy — wa) =uc — wa, 

 Z = /jl{vu — ufi) =va — ub. 



Thus when a tube of electrostatic induction is moving with 



