As the arc of ten degrees is virtually the same as the chord, the number ten may be regarded as representing the distance of m and n. If the cap, e, is turned from left to right in the figure, it is found that, to reduce the distance to five degrees, it must be turned through thirty-five degrees. The wire is thus twisted through thirty-five degrees at the top and through five at the bottom; its total torsion is forty degrees, that is to say, four times as much as it was at first. Hence at the distance five the repulsion is four times as great as at the distance ten; for it is a known law, that the angle of torsion is proportional to the force of torsion. It may be shown in the same manner that, to make the distance from m to n one-third what it was, the total torsion must be ninety degrees, that is, nine times as great; the second law is thus thereby proved. In order to prove that attractions and repulsions between electrified bodies are proportional to the quantities of electricity which each of them possesses, the ball, m, is again electrified and placed in the cage; after contact it repels the disc, n, through a distance of, let us say, twelve degrees. The ball, m, is now withdrawn and placed in contact with a second brass ball of the same diameter, but insulated and unelectrified. As the electricity is equally distributed over both balls, the ball, n, loses half its electricity, and on again placing it in the cage, the repulsion which was twelve degrees is now only six, which verifies the third law.

393. Conductors and nonconductors.—When a glass rod, rubbed at one end, is brought near an electroscope, that part only will be electrified which has been rubbed; the other end will produce neither attraction nor repulsion. The same is the case with a rod of shellac or of sealing wax. In these bodies electricity does not pass from one part to another-they do not conduct electricity. Experiment shows, that when a metal has received electricity in any of its parts, the electricity instantly spreads throughout its entire surface. Metals are hence said to be good conductors of electricity.

Bodies have, accordingly, been divided into conductors and nonconductors. This distinction is not absolute, and we may advantageously consider bodies as offering a resistance to the passage of electricity which varies with the nature of the substance. Those bodies which offer little resistance are then conductors, and those which offer great resistance are nonconductors or insulators: electrical conductivity is thus the inverse of electrical resistance. We are to consider that between conductors and nonconductors there

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Insulating Bodies.

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is a quantitative and not a qualitative difference; there is no conductor so good but that it offers some resistance to the passage of electricity, nor is there any substance which insulates so completely but that it allows some electricity to pass. The transition from conductors to nonconductors is gradual, and no line of sharp demarcation can be drawn between them.

In this sense we are to understand the following table in which bodies are classed as conductors, semiconductors, and nonconductors; those bodies being conveniently designated as conductors which, when applied to a charged electroscope, discharge it almost instantaneously; semiconductors being those which discharge it in a short but measurable time, a few seconds, for instance; while nonconductors effect no discharge in the course of a minute.

394. Insulating bodies. Common reservoir. Electrification of conductors.-Bad conductors are called insulators, for they are used as supports for bodies in which electricity is to be retained. A conductor remains electrified only so long as it is surrounded by insulators. if this were not the case, as soon as the electrified body came in contact with the earth, which is a good conductor, the electricity would pass into the earth, and diffuse itself through its whole extent. On this account, the earth has been named the common reservoir. A body is insulated by being placed on a support with glass feet, or on a resinous cake, or by being suspended by silk threads. No bodies, however, insulate perfectly; all electrified bodies lose their electricity more or less rapidly by means of the supports on which they rest. Glass is always somewhat hygroscopic, and the aqueous vapour which condenses on it affords a passage for the electricity; the insulating power of glass is materially improved by coating it with shellac or copal varnish.

Dry air is a good insulator; but, when the air contains moisture, it conducts electricity, and this is the principal source of the loss of electricity.

It is from their great conductivity, that metals do not become electrified by friction. But if they are insulated, and then rubbed, they give good indications. This may be seen by the following experiment. A brass tube is provided with a glass handle, by which it is held, and then rubbed with silk or flannel. On approaching the metal to the pendulum, the pith ball will be attracted. If the metal is held in the hand electricity is indeed produced by friction, but it immediately passes through the body into the ground.

Electrifying by contact is due to conductibility. For when an insulated conductor in the neutral state is made to touch an electrified conductor, a portion of the latter passes instantaneously to the former. If the two bodies have the same surface, and the same shape, for instance, two spheres of the same diameter, the electricity is equally distributed on the two; but if the bodies differ in shape or surface the electricity is unequally distributed.

395. Law of the development of electricity by friction.— Whenever two bodies are rubbed together, the neutral fluid is decomposed. The two electricities are developed at the same time and in equal quantities—one body takes the positive, and the other the negative fluid. This may be proved by the following simple experiment devised by Faraday :-A small flannel cap provided with a silk thread is fitted on the end of a stout rod of shellac, and rubbed round a few times. When the cap is removed by means of a silk thread, and presented to a pith ball pendulum charged with positive electricity, the latter will be repelled, proving that the flannel is charged with positive electricity; while, if the shellac is presented to the pith ball, it will be attracted, showing that the shellac is charged with negative electricity. Both electricities are present in equal quantities; for if the rod be presented to the electroscope before removing the cap, no action is observed.

The electricity developed on a body by friction depends on the body rubbed. Thus glass becomes negatively electrified when rubbed with catskin, but positively when rubbed with silk. In the following list the substances are arranged in such an order, that each becomes positively electrified when rubbed with any of the bodies following, but negatively when rubbed with any of those which precede it:

396. Accumulation of electricity on the surface of bodies.Numerous experiments show that when a body is electrified, all the electrical fluid goes to the surface, where it is accumulated as an extremely thin layer, tending incessantly to escape, and flying off, in short, when it is not retained by any obstacle.

This may be demonstrated by the following experiment, which is due to Biot.

A hollow brass globe, fixed on an insulating support, is provided with two brass hemispherical envelopes which fit closely, and can be separated by glass handles. The interior is now electrified, and the two hemispheres brought in contact. On then rapidly removing

them (fig. 312) the coverings will be found to be electrified, while the sphere is in its natural condition, and indicates no electricity. Thus in removing, so to say, the surface of a body, all the free electricity it contained is also removed, which shows clearly that the electricity is on the surface. That electricity resides solely in the surface is further proved by the fact, that two metal spheres of the same diameter, but one of them solid and the other hollow, take the same charge of electricity when applied to the same source. When accumulated on the surface of bodies, electricity tends to pass off to adjacent objects with an effort which is known as the tension. This increases with the quantity of electricity. So long as it does not exceed a certain limit, it is balanced by the resistance presented by the small conducting power of the air when it is dry. If the tension increases, this resistance is overcome, and the electricity springs off to an adjacent body with a sound, and in the form of a bright spark. In moist air the tension is always feeble, for the electricity passes away almost as rapidly as it is supplied, moisture being a good conductor of electricity. In very rarefied air, on the contrary, where there is little resistance, electricity passes off, presenting the appearance of a luminous glow.

397. Influence of the shape of a body on the accumulation of electricity. Power of points.—The manner in which electricity is distributed on the surface of a body varies with its shape. If it is spherical the amount is everywhere the same, which might indeed be predicted, and which may be readily confirmed by means of the proof plane. This is a small thin metal disc fixed at the end of a thin shellac rod. This is held in the hand, and successively applied to different parts of the electrified body, and after each contact is presented to an electrical pendulum. If the body is a sphere the attraction is in each case the same, which shows that the disc has taken the same charge of electricity from each point of the sphere, and, therefore, that the distribution of the electrical fluid is uniform.

This is no longer the case if the electrified body is more or less elongated, as, for instance, a kind of ovoid shape, as shown in fig. 313. In this case the proof plane is the more charged the nearer it is applied to the elongated end; and at this end itself most electricity is removed. This experiment shows that, in good conductors, electricity always tends to accumulate towards the most elongated parts towards the points. This accumulation produces a greater tension, which is sufficient to overcome the resistance of