MR. Ct. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
707 
When u = v we have 
N = - ^ cos 3 xp, 
47r 
or, in terms of cr, since by § 17 cos 6 
N = 
Thus apparently when xp = 0, N = — oo . On the other hand, when i p was put 
zero before u was made equal to v, we found N = 27rcr 3 /K. The reason of the 
discrepancy appears to be as follows :—If the surface is one of two parallel planes of 
absolutely infinite extent, and the motion is along the normal, the only possible 
direction of E is also along the normal. But if the surfaces are not infinite, e.g., a pair 
of circular parallel plates, at all ordinary points there is a definite direction, at right 
angles to the motion, along which the electric force must lie. And if the charge is 
supposed confined to an infinitely thin layer there will consequently be a finite 
amount of displacement through an infinitely small area, thus producing infinite 
electric force. When, as in the case of a moving ellipsoid, we are able to take 
a proper account of the distribution the discrepancy disappears. 
Tangential Pull. —The tangential force per unit area is 
T 
or, in terms of cr, 
When xp = 0, or when xp = , T = 0. 
When u — v, T = cot xfj. 
There is thus a discrepancy when xp = 0 and u — v. The explanation is the same 
as for the normal pull. 
KE 2 - . _ KE 3 v? . a cos 2 \!s + sin 2 
cos u sin 6 = —-^sin \p cos xp -——^rr , 
477 47T ir r T or COS 3 + Sill" f 
T = 
t o~ vr 
sin COS -vp 
K v 2 « cos 2 1 p' + sin 2 xfr 
--- sin xp when u = v, 
— ^ Y„°" cot 3 xp , 
Iv 
Stress between a Pair of Moving Charges. 
19. The theory of the mechanical force experienced by a moving charged particle 
can be readily applied to calculate the stress between two charges which are both 
moving parallel to x with velocity u. Let there be a charge q at the origin and a 
charge q at the point x, y, z. Then by (43) the value of the “convection potential” 
due to q' is 
