682 
MR. G. F. C. SEARLE OR PROBLEMS IN ELECTRIC CONVECTION. 
For the sake of greater generality, I shall first suppose that the velocity u of the 
system has the components u 1} u. 2 , ^^ 3 . Then since the motion is steady, we have 
d 
cl 
d 
d 
dt~~ Tx + Ty + “» ~l 
(13). 
Taking the first of each of the two sets of equations represented by (5) and (4) and 
substituting for djdt, we have 
dE, cZEo 
dy dz 
cl H, , dH, , cm, 
1 + 7 + U S 7 
dx 2 dy 3 - 7 - 
“ T7F — / x ( u i t ,v 2 AX, t “3 (h 
(14). 
dH ;! 
% 
dH 2 
dz 
f cl Ej dE, dEA 
• (is)- 
But div E = 47 rp/K and div H = 0 . Using the latter, (14) becomes 
d E 3 
dy 
dE 2 
dz 
dH, , dH, dH, dH, 
ijl ( u 2 — + u° —— — u 1 ~ — u x —— 
r ' 2 dy 6 dz 1 dy 1 dz 
— ^ \ d y (Hi% — H^q) — (H 3 u, H 1 R 3 ) 
if P = [jN Hu. 
Hence 
— dPJdy — dPJdz, 
dz 
A( E 3 - p 3 )-|-(E 2 -r a ) = o. 
The remaining two equations symbolised by (5) may be treated in the same 
manner, and the resulting equations may be symbolised by 
curl (E — pYHu) — 0 
(16). 
Similarly from (4) we find 
curl (H + KVEu) = 0 .(17), 
p disappearing from the equations. 
These two equations take the place of (5) and (4) for the case of steady motion, 
and must be satisfied throughout the field. 
it follows from (16) and (17) that we can write 
E — ^VKu = — v'E 
(18). 
H + KVEu = - vfl 
(19). 
or 
