702 
MR. G. F. C. SEAR.LE ON PROBLEMS IN ELECTRIC CONVECTION. 
But by (76) when VO vanishes, 
so 
that 
Hence 
E x = Fj, Eo = -F £ , E 3 = -^F 3 
E= v/l - Z 3 (l -a 2 ) F . . . 
-p, 4 it a v/l — P (1 — a 2 ) 
JlIj - T _ tj 
K - M* 
1 - ^l 2 
v~ 
[October 23, 1896. 
The direction cosines of E are 
(83) . 
(84) . 
cd m n 
v/f- P (1 - a 2 ) 5 V 7 ! -! 3 ’ V 7 1 - P (1 -^2) ’ 
We have now obtained the value of E as far as it depends upon the moving 
electric charges. If VO does not vanish we have simply to add on the electric force 
whose components are 
E x = 0, Eo 
/.m dQ „ fiu clPl 
TT~ } Eg = ~ • 
a dz a. dy 
The magnetic force near a moving charged surface is compounded of two parts, one 
due to 'F, the other due to O, and these are quite independent. I shall now calculate 
the value of H when VO is zero. If in any case VO is not zero, we have simply to 
add on the part of H which is due to O. 
Now when VO vanishes (and therefore also R) equations (77) give 
so that 
H, = 0, H, = — ~F a . H 3 = ~ F s 
H = K + K , = — F v/ l - P 
« ■ X 
. (85). 
But making use of (83) and (84) we have 
H = K u 
\/l - P 
V/l -P (1 - a 3 ) 
E = 47T?(0" 
v 7 l - P 
u~ 
V - 
. . ( 86 ). 
Now when It = 0 we have by (39) that H is perpendicular to both u and F. 
Again, by (36) H is perpendicular to E and u. Hence E, F, and u are co-planar, 
and since F has already been proved to be normal to the surface, E lies in the plane 
containing the direction of motion and the normal to the surface. 
