690 
MR,. Gr. F. C. SEARLE ON PROBLEMS IN ELECTRIC CONVECTION. 
charged line. To find A we must equate to q the surface integral of the normal 
electric displacement taken over unit length of a cylinder of any form, enclosing the 
charged line, the generating lines of the cylinder and the charged lines being parallel. 
The most convenient surface is that formed by the two infinite planes x = a and 
x = — a respectively. 
Thus 
i = 4 1 f 
1“ 
2 Aft dy 
ft- 
+ y 2 
or 
A = 
_ q s/ c 
Hence 
A. 
x 
y 
K 
2q 
kV« (+ f 
Equations (29) to (31) give us 
H, = H 3 = 0, 
H 3 - 
\/ * 
KA 
y/ ci 
E s = 0 
iquy 
-lx- 
+ y 
(59). 
( 60 ). 
If P is written for cc 3 + y 2 , and 6 is measured from the axis of x in the plane xy, 
the resultant electric and magnetic forces may be written 
E = 
2 q \/« 
u 
Kp ( 1 — sin 2 6 
( 61 ), 
H = 
2 qu \/ a. sin 6 
it- 
sin 2 6 
( 62 ), 
so that the forces vary inversely as the distance from the charged line. When 
u = v, the electric force, and also the magnetic force, is confined to the plane yz just 
as in the case of the point-charge. 
Mechanical Force clue to Electromagnetic Action. 
8. The mechanical force experienced by any very small portion of the electro¬ 
magnetic medium, when reckoned per unit of volume, has the following constituents :— 
(1.) A force E p, where E is the electric force and p the volume density of positive 
electrification. 
