320 On Electromagnetic Effects due to the Motion of the Earth. 
would be a force on a magnet, due to an electrified body moving along with the 
magnet. It appears to me that this is not the case. For consider the action of 
a current on a quantity of electricity, when both are carried through space. When 
a current producing an electromagnetic potential, whose components are F, G, H, 
moves with a velocity of translation whose components are a, y, z, the components 
of electromotive intensity are 
=p (Pe eB 
"~— G \E + ay 7 dz 
dG dG. dG, dG» 
dH du: ,¢@H dH 
R=-G=-( G+ “dy jt) 
If a pot move with a velocity whose components are E ”» i, then the com- 
ponent of electromotive intensity at it are P=cn—b¢, &c., where a, b, c, are the 
components of magnetic induction at the point. Putting in for a, b, c, we get 
val «z _ dH 
a — 
bi Ge a 
a, jd _ (ak 
= it STE Cat 
=] GCE + Gn HE) +E en i 
Oe <(RE + n+ He) +8 1 toe 
: eGhal  gefal 
Ry =F (PS + Gn Hs) 48S + Cag OTE 
Hence the whole electromotive intensity at the point has components :— 
eo Gn +H) ) +E) + 59 +E) 
Q=F ( FE+Gr + HD) +52 bm) +o eS 
R=7( FELGn+H2) +57 é- ae) + ie y)+— = 2). 
If the two move with the same velocity so that g=a,—y and =z the compo- 
nents become 
PS (Be+ Gy-+1) 
¢ 
=5(Pet Gy + Hz) 
Ras ae + Gy+He). 
en fff Sdecdy de 
~@ 
G=p if de dy da 
1st Sf do: dy de 
Now as— 
