to the Motion of Electrification through a Dielectric. 329 



upon what basis to work. First the Faraday-law {p standing 

 for d/dt), 



— curl E=/AopH, (11) 



requires no change when there is moving electrification. But 

 the analogous law of Maxwell, which I understand to be really 

 a definition of electric current in terms of magnetic force, (or 

 a doctrine), requires modification if the true current is to be 



C+/>D + pu; (12) 



viz. the sum of conduction-current, displacement-current, and 

 convection-current pu, where p is the volume-density of elec- 

 trification. The addition of the term pu was, I believe, pro- 

 posed by Gr. F. Fitzgerald *. 



[This was not meant exactly for a new proposal, being in 

 fact after Rowland's experiments; besides which. Maxwell was 

 well acquainted with the idea of a convection-current. But 

 what is very strange is that Maxwell, who insisted so strongly 

 upon his doctrine of the ^wasi'-incompressibility of electricity, 

 never formulated the convection-current in his treatise. Now 

 Prof. Fitzgerald pointed out that if Maxwell, in his equation 

 of mechanical force, 



F = VCB-eV'I'-mVO, 



had written E for — V"^, as it is obvious he should have done, 

 then the inclusion of convection-current in the true current 

 would have followed naturally. (Here C is the true current, 

 B the induction, e the density of electrification, m that of 

 imaginary magnetic matter, "^ the electrostatic and 12 the 

 magnetic potential, and E the real electric force.) 



Now to this remark I have to add that it is as unjustifiable 

 to derive H from O as E from "^ ; that is^ in general, the 

 magnetic force is not the slope of a scalar potential ; so, for 

 — V^ we should write H, the real magnetic force. 



But this is not all. There is possibly a fourth term in F, 

 expressed by 47rVDG, where D is the displacement and G the 

 magnetic current ; I have termed this force the "magneto- 

 electric force," because it is the analogue of Maxwell's " elec- 

 tromagnetic force" VCB. Perhaps the simplest way of 

 deriving it is from Maxwell's electric stress, which was the 

 method 1 followed t- 



Thus, in a homogeneous nonconducting dielectric free 

 from electrification and magnetization, the mechanical force 

 is the sum of the " electromagnetic " and the " magnetoelec- 



* Brit. Assoc, Southport, 1883. 



t " El. Mag. Ind. and its Prop." xxii. ' Electrician,' Jan. 15, 1886, p. 187. 



