686 MR. G. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
From equations (26) to (31) we have at once 
h 
x 
e 2 = e 3= A 
y z u « 
(40). 
(41). 
From (40) it follows that the lines of electric force are radii drawn from the origin. 
From (41) it appears that the lines of magnetic force are circles having their centres 
on the axis of x, and their planes perpendicular thereto. Since the electric force is 
radial, there will be a definite amount of electric displacement outwards through any 
closed surface, however small, which encloses the origin. Hence the field given by 
our solution can be produced by the motion of a definite point-charge at the origin. 
If q is this charge, we can find the value of A corresponding to it from the 
consideration that the surface integral of the normal electric displacement, taken over 
any surface enclosing the origin, is equal to q. For the closed surface we may take an 
infinite cylinder of radius c coaxial with x. Hence 
K r +x 27 rAe 2 dx _ KA 
^ 47T j « {.r 3 /« + c 3 }* \/« 
(42). 
7V/<5 
Thus A = t go that 
K 
V — 
(43), 
and the values of the electric and magnetic forces now become 
E x E2 Eg (£ 1 t x 
x y z 
kv/s {1 + y ’+ 
(44). 
H, = 0, 
H i = = J 2 2 
Z V v u 1 a J 
(45). 
These values are the same as those obtained by Heaviside and J. J. Thomson. 
If r denote the radius vector from the origin, and 6 its inclination to the axis of x, 
then we have for the resultant forces 
E = 
2 ( 1 — II? jv 2 ) 
Kr 2 {1 — sin 3 6 ifi/v 2 }* 
(46). 
