OF ELECTROSTATIC WITH ELECTROMAGNETIC FORCE. 
645 
experiment, undertook the whole work of the comparison of the currents by means of 
the galvanometer and shunts. He has also tested the resistances, and in fact done 
everything except the actual observation of equilibrium, which I undertook myself. 
The electrical balance itself was made for me by Mr. Becker. 
The electrostatic force observed was that between two parallel disks, of which one, 6 
inches diameter, w T as insulated and maintained at a high potential, while the other, 4 
inches diameter, was at the same potential as the case of the instrument. 
In order to insure a known quantity of electricity on the surface of this disk, it was 
surrounded by the “ guard-ring ” introduced by Sir W. Thomson, so that the surface of 
the disk when in position and that of the guard-ring were in one plane, at the same 
potential, and separated by a very narrow space. In this way the electrical action on 
the small disk was equal to that due to a uniform distribution over its front surface, 
while no electrical action could exist at its sides or back, as these were at the same 
potential with the surrounding surfaces. 
The large disk was mounted on a slide worked by a micrometer-screw. The small 
disk was suspended on one arm of a torsion-balance so that in its position of equilibrium 
its surface and that of the guard-ring were in one plane. 
If E is the difference of potential between the two disks in electromagnetic measure, 
the attraction between them is 
Wa* 
where a is the radius of the small disk, b its distance from the large one, and v is the 
velocity representing the ratio of the electromagnetic to the electrostatic unit of elec- 
tricity. 
The electromagnetic force observed was the repulsion between two circular coils, of 
which one was attached to the back of the suspended disk, and the other was placed 
behind the large disk, being separated from it by a plate of glass and a layer of Hooper’s 
compound. A current was made to pass through these coils in opposite directions, so as 
to produce a repulsion 
2A 
=2 ( 2 ) 
where n and n' are the number of windings of each coil, y is the current, and 
where 
^={E,tan* y -2(F,— *)}££* 
c=sm y= 
2 */ a,a 0 
(3) 
(4) 
<z, and a 2 are the mean radii of the coils, and V the mean distance of their planes, and 
E e and F c are the complete elliptic functions for modulus c=sin y. 
2 A. 2 o! 
When V is small compared with a '!, -g- becomes very nearly y 
4 t 2 
