On Electromagnetic Effects due to the Motion of the Earth. 321 
when uv w are the components of the current, and 
7? —(E—a)? + (n—y)?+-(€—2)? 
if we call wavy wz=0 
and— SS fie 
LH Hj) 
we get— 
This result may be more rapidly obtained by using the quaternion notation 
thus :— 
The electromotive intensity due to the current moving is 
ay “dy dy -dH sees 
— ee es — == = est 
Si dt (ey be dy "5 d, (Sp4) 
. 6 0 d . d . d 
using’ — —¢7—+y—+z— aS aN Operator. 
(os SpA a + Tay + aE Pp 
Similarly the electromotive intensity at the moving point is— 
G,—Vp'B and 8=va/% 
where— p'=tit+nj+lk and Nai, Be. Ape 
dé “dn dad 
Hence— 6,=Vo' (VAM) =A’ (Sp’2) — (Sp'A’)% 
also A’=-A hence— 
E=G, + GAG) + (S(o' — p)A) a 
so that if p'=p } 
G=A(SoX) = AW) 
where P=Soy = IS S(eS) dedyd 
saa ff fu, anay 
and consequently 0=S(06) 
Expressed thus it is evident that the resulting electromotive force round a closed 
circuit would vanish, and that the electromotive intensity at each point of space is 
the same as that due to electricity of density »o at each element of current. The 
total quantity of electricity required for this is zero, in the case of a closed 
circuit, for 
MD (Sp6) de dy dz=fffude dy dz=/ff'v de dy de=/if'w de dy dz-=0 
when the integration is extended round closed circuits. From this it is evident 
that an electric current in a conductor would have no electromotive intensity on 
a point outside it, and moving with its own velocity ; for, just as electricity enclosed 
in the conductor would have no effect outside, similarly the current in the conductor 
would induce on its surface exactly such a charge as would neutralise the action 
due to the motion of the current on all points moving with the same velocity, 
3H2 
