656 MR. CLERK MAXWELL ON A COMPARISON OE THE ELECTRIC UNITS 
Thus, if 
j3 = CCOSy (2 — W), 
i’=i sin x( z - Vl! )> 
cos ~ (z— Vi), 
/=ilv“ s x( z - v <)- 
( 21 ) 
I have in the next place to show that the velocity V is the same quantity as that 
found from the experiments on electricity. 
For this purpose let us consider a stratum of air of thickness b bounded by two 
parallel plane conducting surfaces of indefinite extent, the difference of whose potentials 
is E. 
The electromotive force per unit of length between the surfaces is P= ^ E. 
The electric displacement is/=^P. 
The energy in unit of volume and the tension along the lines of force per unit of area 
is \ P f. 
The attraction X on an area 7 ra? of either surface is 
=mv\ 
( 22 ) 
If this area is separated by a small interval from the rest of the plane surface, as in 
the experiment, and if this interval is small compared with the radius of the disk, the 
lines of force belonging to the disk will be separated from those belonging to the rest of 
the surface by a surface of revolution, the section of which, at any sensible distance from 
the surface, will be a circle whose radius is a mean between those of the disk and the 
aperture. This radius must be taken for a in the equation (22)*. 
Let us next consider the magnetic force near a long straight conductor carrying a 
current y. The magnetic force will be in the direction of a tangent to a circle whose 
axis is the current ; and the intensity will be uniform round this circle. If the radius is 
b, and the magnetic intensity j3 , the integral round the circle will be 2T$/3=4vry by (A). 
* [Note added Dec. 28, 1868. — I have since found that if a x is the radius of the disk, and a 2 that of the 
aperture of the guard-ring, and b the distance from the large fixed disk, then we must substitute for ^ the more 
approximate expression , where a is a quantity which cannot exceed (a 2 — aj. — J. C. M.] 
b z 26 ( 6 + a) tt 
