MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
703 
Let the angle between E and F be 0, that between F and u 0, and that between E 
and u 0. Then the following relations will be found useful : — 
Fisr. 1. 
By 5 5 
SuE = SuF 
so that 
E cos 0 = F cos 0. 
Again by (38) after multiplying vectoriallv by u 
aVEu = YFu 
so that 
whence 
E sin 0 — — F sin xp, 
. « COS 0 . sin 0 
cos ffl = — 7 ===— . . - - - — , sm 0 = . 
V sr COS" 0 + Sill" 0 V or COS' 0 + Sill 2 0 
But by (36) since R = 0 
so that 
H = KYuE 
Ku 
H = KhE sin 0 — — F sin 0 
a 
Lastly by (38) after multiplying vectorially by E 
YEF - — YEu . SuF = 0 
so that 
u 
sin 0 = — sin 0 cos xp. 
Since 0=0 — 0 this is the same as 
to¬ 
ot sin 6 — — cos 0 sin 0. 
Also 
cos 6 = cos (0 — 0) = — 
« COS 2 -0 -f sin 2 0 
v sc 2 cos 2 -0 + sin 2 0 ‘ 
The expressions for E and H hold good for a point just outside any equilibrium 
surface. But they plainly hold good for any point between a pair of parallel plates 
bearing complementary charges. 
