708 
MR, G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
Hence, if P denote the mechanical force on q so that P = qF, we have by (69) 
^ “ Kv/« 
D _ * 
K 
P 3 - 
qq'V a. 
K 
n 
[~ + l f + 2 2 
_A_ 
l 
[f +f + *\ 
-1 
( 87 ). 
This set of forces is equivalent to a repulsion 
/ /1 u~ 
! C 1 1 - - 
V" 
K? ,2 ( 1 — l — sin 2 9 
together with a force perpendicular to the axis of x, and towards it, of amount 
if 
fjqq'u- (1-- ) sin 9 
r s 1 1 - - sin 2 9 
where r is the radius from q to q, and 6 the angle it makes with the direction of 
motion, and k/jl has been put for l/v' 2 . Taking the two charges as a complete system, 
the last force gives rise to a couple 
iiqcq'v? sin 9 cos 9 
tending to make r coincide with x. 
The resultant force is perpendicular to the surface T = constant, which passes 
through the point x, y, z. It is, therefore, normal to the ellipsoid a? 2 /a + y~ + 2 2 = c~, 
where c is a proper parameter. 
When the charges move at the speed of light, the disturbance due to q is entirely 
confined to the plane of yz, and the stress vanishes unless the charge q lies in this 
plane. 
In terms of r and 0 the component of P perpendicular to x is, in any case 
, • J, n* y 
qq Sill 9{1-^J 
Kr 2 jl - ^J-sin 2 | ° 
which vanishes when u = v, even when sin 6=1. There is, therefore, no stress at 
all between a pair of charges moving parallel to each other at the speed of light. 
