( 568 ) 
and those for the state (d', 9’) 
Div D= 
Div H'= 0 
(II) 
Rot H' =Anov And 
An V2 Rot = — D'. 
In the ordinary theory of electromagnetism, the force acting ona 
partiele, moving with velocity », is 
4nV*y+[v. A], 
per unit charge !). 
In the modified theory, we shall suppose that a positively electri- 
fied particle with charge e experiences a force 
kia VA DR Bn tert re a ER 
on account of the field (d, DH), and a force 
hsl ban Von! 4e [oc Spel tete 
pd 
on account of the field ®' 6’), the positive coefficients « and £ 
having slightly different values. 
For the forces, exerted on a negatively charged particle I shall 
write 
he we Pi da V2> +o, Hide). de ee 
and 
kot ta V20' fo BTS o-oo 
expressing by these formulae that e is acted on by (d, 9) in the 
same way as € by (d', '), and vice versa. 
§ 7. Let us next consider the actions exerted by a pair of 
oppositely charged ions, placed close to each other, and remaining 
so during their motion. For convenience of mathematical treatment, 
we may even reason as if the two charges penetrated each other, so 
that, if they are equal, ¢ = — g. 
) [y. H} is the vector-product of » and J). 
