2212. To use the torsion balance: Turn the torsion head around until the two pith-balls m and n just touch each other. Remove the glass rod a, and communicate the charge to be measured to the gilt ball m. Replace the glass rod in the jar. The two gilt balls will touch each other momentarily, and half of the charge will pass from m to n. As both balls possess similar charges, they will immediately repel each other; the ball n, being driven around, twists up the wire to a certain extent. The force of torsion in the wire will eventually balance the force of repulsion, and the ball n will come to rest when the balls are separated by a certain distance. In any wire, the force of torsion is proportional to the amount of twist, or, in this case, to the angle of torsion; hence, the force exerted between the two balls can be measured by the angle described by the ball n.
2213. By means of the torsion balance, it is proven that the force exerted between two bodies statically charged with electricity varies inversely as the square of the distance between them.
Thus, suppose two electrified bodies one-fourth inch apart repel each other with a certain force; at a distance of one inch the force would only be one-sixteenth as great. This law is equally true for the force of attraction between two bodies with dissimilar charges.
2214. In either case, whether of attraction or repulsion, the force at any given distance is equal to the product of the two quantities of electricity on the bodies. But a unit quantity of electricity is that charge which, when placed in air at a distance of one centimeter from another equal and similar charge, will be repelled with a force of one dyne. (For values of the centimeter and dyne, see Arts. 2255 and 2262.)
Therefore, if a certain body were charged with 4 unit quantities of electricity and another with 3 unit quantities, then the force exerted between them would be 13 times greater than if each had contained a charge of one unit.
