AND ON ON THE ELECTEOMAGNETIC THEOEY OE LIGHT. 
657 
Hence 
0 = 
2 - 
*b' 
(23) 
Let a wire carrying a current y be placed parallel to the first at a distance b, and let 
us consider a portion of this wire of length l. This portion will be urged across the 
lines of magnetic force, and the electromagnetic force Y will be equal to the product of 
the length of the portion, multiplied by the current and by the number of lines which 
it crosses per unit of distance through which it moves, or, in symbols, 
Y=fcW3 ' 
=ty l htnf 
(24) 
If the two wires instead of being straight are circular, of radius a!, and if V the 
distance between them is very small compared with the radius, the attraction will be 
the same as if they were straight, and will be 
Y=2^V (25) 
When V is not very small compared with a!, we must use the equation (3) to calculate 
. 2A 
the value of -g- by elliptic integrals. 
Making X=Y and comparing with equation (6), we find 
<3 
if 
Sit 
(26) 
but, by (19), 
yg— k . 
4?rj w. 
Hence 
v — yV, 
...... (27) 
where v is the electromagnetic ratio and V is the velocity of light. 
But since all the experiments are made in air, for which is assumed equal to unity, 
as the standard medium with which all others are compared, we have finally 
v=Y, (28) 
or the number of electrostatic units in one electromagnetic unit of electricity is numeri- 
cally equal to the velocity of light. 
