PART II.

STATIC ELECTRICITY.

CHAPTER I.

ELECTRICAL ATTRACTIONS AND REPULSIONS.

AFTER having unfolded the general phenomena presented by electricity, and having familiarised ourselves with the study of this agent, let us examine more closely its properties, commencing by those that relate to static electricity.

Let us first occupy ourselves with the repulsions and attractions manifested by electrised bodies. It is easy to perceive, by means of the apparatus that we have employed in demonstrating the existence of these repulsions and attractions, that the energy with which they occur is greater in proportion as the two bodies between which they are exercised are nearer together. Thus, in the case of attraction, we first see the two electrised balls approach each other slowly, then acquire a more rapid movement, and finally rush upon each other. It is the same with regard to repulsion; we see the two balls, when they are charged with the same electricity, avoid each other with the more vivacity, the more we endeavour to bring them near to each other.

This influence of distance is subjected to a law which was discovered by Coulomb. It consists in this, that two electrised bodies attract or repel each other with a force which is inversely proportional to the square of the distance that separates them; that is to say, that if the distance becomes half, the force becomes quadruple; if it becomes the third, the force becomes nine times greater; and so on.

Electric Balance.

The demonstration of this law is founded upon the employment of an instrument contrived by Coulomb, and with

which it is necessary to become acquainted, in order to be able conveniently to study static electricity. This instrument is the electric balance, or rather the

torsion balance (Fig. 37.). It consists of a cylindrical or cubical glass cage, surmounted in its upper part by a vertical tube from 15 to 20 inches high the cage itself may be 12 or 15 inches in diameter, or even more. The top of the tube is closed by a brass piece, which, like the lid of a tobacco-box, may turn tightly round the cap; which is also of brass, and fixed to the tube itself. A circular division enables us to measure how many degrees the movable piece has been turned, and which may thus describe several circumferences of the circle.

Fig. 37.

This piece carries interiorly a vertical metal pincer adapted exactly to its centre, and to which is fixed, by one of its extremities, a very fine silver or platinum wire, which is stretched at its other extremity by a brass weight. The wire must be sufficiently long, that its lower extremity may reach to about half of the height of the glass cage; it is generally about two feet. The brass weight by which the wire is stretched, is traversed by a horizontal needle of glass or gumlac, one of the branches of which is very short, and the other, which is from 3 to 5 inches long, according to the size of the cage, carries at its extremity a little gilt ball of elder pith, or a small metal disc of tinsel. A circular division, traced round the glass cage, serves to measure the angular spaces traversed by this needle. The deviation that it assumes, when not urged by any force, depends on the position that is given to the movable lid that sustains the wire to which it is suspended. Care is taken that the 0° of the division that is traced on the cage shall coincide with the direction assumed by the needle, when the lid itself is at the 0° of the division, traced on its own circumference. In this manner the starting points, or the 0° of the two divisions, correspond. Finally, an insulating

stem of glass or gum-lac, carrying a ball or disc perfectly similar to the ball or disc at the extremity of the movable needle, is introduced vertically by an opening made in the cover of the cage: the place of the opening of the cage and the length of the stem are so combined, that the ball or disc which is at its extremity shall be in contact with the ball or disc of the needle, when the needle itself is in the direction corresponding to the 0° of the division.

The insulating stem may be easily taken away and returned to its place, by means of the piece, to which it is fixed by its upper extremity, and which at the same time serves to adjust it to the opening formed in the cover of the glass cage.

Determination by the Electric Balance of the Law that Electric Attractions and Repulsions obey according to Distance.

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To make the experiment, we begin by removing the insulating stem, then giving to the ball, by which it is terminated, either vitreous or resinous electricity, by touching it with an electrised body. It is immediately to be restored to its place it at once divides its electricity with the ball of the movable needle. The latter is then repelled, and the needle describes a larger or smaller arc of the circle, according to the energy of the repulsion. After a few oscillations, it settles in a certain position, at 36° for example, from the point of departure, namely from the 0° of the division. If the needle stops at this distance, and does not describe a greater arc, it is because, at 36° of distance, there is equilibrium between the two forces, the repulsive force existing between the fixed electrised ball and the movable one, and the torsion force of the metal wire, to which the needle is suspended, and which tends to bring it back to its starting point. Since the needle acquires a fixed position, after having described an arc of 36°, this proves that the force, with which the wire, when twisted to an angle of 36°, tends to untwist itself, is precisely equal to that with which the two balls repel each other at the distance of 36°.

Let us now inquire what would be the force that would

produce equilibrium, and that consequently would be equal to that with which they were repelled if they were at a smaller distance, at 18°, for example, instead of 36°; namely, at a distance one half less. For this purpose, let us turn the metal lid, to which the upper extremity of the wire that carries the needle is fixed, so as to compel this needle to approach nearer to its starting point; to compel, consequently, the movable ball to approach the fixed one. We shall see that, in order that there may be an arc of only 18° between the two balls, the lid above must be turned 126°, which causes the wire to be twisted 126° from above; but since the needle is not at the 0° of its division, but remains fixed at 18° beyond, it follows that the wire is twisted 18° below and 126° above, which makes in all a torsion of 144°. The force, then, that produces equilibrium, or that is equal to that with which the two balls are repelled when they are 18° apart, is the force with which a wire, twisted to 144°, tends to untwist itself. We operate, in the same manner, to determine the force with which the two balls are repelled when the arc by which they are separated is no more than 9°. We should find that it would be necessary to twist the wire from above 567°, which makes 576° of torsion in all, by adding the 9° that it is twisted below; for the needle is maintained 9° beyond its 0° of torsion: thus the force with which the wire tends to untwist, when it is twisted to an angle of 576°, is equal to that with which the two balls are repelled when they are only 9° apart.

Experiment had proved to Coulomb that the forces of torsion are proportional to the angles of torsion; in other words, that the force, which must be employed to twist a wire to a certain angle, or that with which it tends to untwist, is proportional to this angle; that is to say, that if the angle becomes double, triple, half, or quarter, the force in like manner becomes double, triple, half, or quarter of what it was. Thus the forces that produce equilibrium, or that are equal to the forces with which the electrised balls are repelled at the distances 36°, 18°, 9°, are to each other as the angles of torsion 36°, 144°, 576°. But these angles are to

each other as 1:4: 16; whence we may conclude that, if the distances are to each other as 1:4, the repulsive forces are to each other as 1:4: 16. It is therefore correct to say that the force with which two electrised bodies repel each other, is inversely proportional to the square of the distance by which they are separated.

In the same manner we prove that the force with which two bodies that possess different electricities attract each other, is inversely proportional to the square of the distance by which they are separated.

In this case, after having given to the ball of the movable needle, by means of the other ball, a certain electricity, we must take away this latter, and give it the contrary electricity. But, before restoring to its place this ball that is intended to remain always fixed at the 0° of the division, it is necessary to give the movable needle another position, which prevents the contact taking place immediately between the ball that terminates it and the fixed ball that has a contrary electricity; for, without this precaution, as these two balls would be touching, the two electricities would be neutralised immediately, and no effect would take place. For this purpose we turn the metal cover, to which the torsion wire is fixed; and, in this manner, we induce the movable needle to remain at 40° or 50° from the 0° of its division, when it is not acted upon by any force, and when the wire consequently is without torsion. It is then we introduce the ball, which is to remain fixed at the 0°, and which is charged with a contrary electricity to that which has already been given to the movable ball before it was made to change its place. There is immediate attraction between the two balls; but they are prevented from coming into contact in consequence of the torsion of the wire resulting from the displacement of the movable ball; they remain, therefore, at a certain distance from each other, a distance at which there is equilibrium between the force of torsion that tends to separate them, and the attraction that reigns between them and that tends to bring them together.

We augment or diminish the torsion so as to maintain