Into the other hole in, (Plate CCXLIV. Fig. 7.) is in troduced a small cylinder m x t, the lower part of which, x t, is formed of gum lac, and carries a pith ball t. At six inches from the bottom of the glass cylinder there is pasted round its circumference a band of paper z q, di vided into 360 degrees, so as to be on a level with the needle a g.
In order to adjust this instrument for use, the hole 771 is made to correspond to the zero of the scale z o q. The index o i of the micrometer is then placed upon the zero of its graduated circle oh, and the whole micrometer is turned in the tubef h, till, in looking past the vertical silver wire P 1, and the centre of the ball, the needle a g shall correspond with the zero of the scale z q. The other ball t is then introduced, so that it may touch the ball a, and so that a line joining the centre of the silver wire, and the ball t, may also point to the zero of the scale z q.
tance. In the third experiment, when the distance of the balls was 8e, the force of torsion was 567° ; so that. at a quarter of the distance, the repulsive force was nearly eight times as great. Hence it follows, that the repulsive force of two small globes electrified either posi tively or negatively, is in the inverse ratio of the squares of the distance of time centres of the two globes.
In the preceding experiments, the wire was 28 ches long, and of a grain in weight, and the force necessary to twist it through an angle of 300°, when at the distance a P, or four inches from the wire, is of a grain, as calculated from the formula: given by Cou lomb in his Memoir on the force of Torsion. blence real force in the preceding experiments were, When the instrument was thus adjusted, Coulomb applied it in the following manner to determine the law of the repulsions of the two balls t, a. Having provided a brass pin AB, Fig. 11. with a large head, he stuck it into a handle AC of sealing-wax, and having electrified it he introduced it through the hole nz, Fig. 7. and touch ed the ball t in contact with a. The electricity of the pin was thus communicated to the two balls, which of course possessed the same kind of electricity ; and as soon as the pin was withdrawn, the balls mutually repelled each other to a distance which is measured by observing the degree on the circle z 0 9, which is pointed out by a line joining the silver wire and the ball a. If the index o of the micrometer is now turned in the direction p n o, the silver wire I P will be twisted, and we shall produce a force proportional to the angle of torsion, which is re quisite to make the ball a return to the ball t. By this
means he observed the distance at which different angles of torsion bring back the ball a to the ball t ; and in comparing the forces of torsion with the corresponding distances of the balls, he obtained a measure of their repulsive force.
Exp. 1. The two balls being electrified with the head of the pin, and the index of the micrometer being set to zero, the ball a was repelled by the ball t to the distance of 36 degrees.
Exp. 2. The silver wire being twisted by turning the index of the micrometer 126 degrees, the ball a ap proached to t, and stopped at the distance of 13 de grees from it, having moved backwards through an arch of 18°.
Exp. 3. Having again twisted the silver wire through arch of 567°, the two balls approached, and stopped at the distance of 8°.
Now, as the force of torsion, or the force which is capable of keeping a thread twisted to a certain degree, so as to hinder it from turning round its axis, and re covering its natural state, has been shewn by Coulomb to be proportional to the angle of torsion, or the arch through which it has been twisted, we have in the first experiment a force of torsion equal to 36^ ; and in the second experiment, when the distance of the balls was 18°, the angle, and consequently the force of torsion, was 126'1-18=144° ; su that the repulsive force, at the distance of 36° •,‘ as 36° : and the repulsive force, at the distance of 18°, was 144°, or quadruple at half the dis M. Coulomb has remarked, that with a silver wir:. so fine as that which he used, and which requires only a force of part of a grain to twist it through an angle of 5", it is impossible, with every precaution, to ascertain the position of the needle to within 2° or 3° when the force of torsion is nothing. lie recommends therefore, after electrifying the balls, to twist the wire 30° or 40°, which, joined to the observed distance of the two balls, will give a force of torsion so great as to re move any sensible error arising from the uncertainty of 2° or 3° already mentioned. He recommends also the use of a wire nearly double in diameter to that which he used, as it was liable to break with the least agitation. A wire of this thickness should also be stretched for two or three clays by a weight equal to half of that which is necessary to break it, and should never be twisted through an arch or more than 300°.