LESSON XXXVII.-MEASUREMENT OF ELECTRICITY. 340. We have seen that there are two kinds of electricity, and that the one never appears without the other. We have also seen that like electricities repel, while unlike attract each other. But to perfect our knowledge of the subject it will be necessary to devise some method of measuring electricity, and of estimating electrical forces. We have spoken of electricity as a thing which can be conceived of as separate, but we must bear in mind that it is never found disassociated from matter. Our method of determining the quantity of free electricity in a body must therefore be different from that of determining the quantity of matter in the body. Let us begin by supposing that we have two similar metallic balls, each insulated by a glass stem, and the one charged with electricity, but the other uncharged. Now if we bring these two balls into contact with each other, the electric fluid will diffuse itself in equal proportions over both balls, so that when we separate them, each will have one-half of the original quantity of electricity. We thus see how a charge can be subdivided. Coulomb was the first to investigate the mutual attractions and repulsions of electrified bodies, and he did it by means of an instrument called the torsion balance. It consists of a delicate horizontal needle (Fig. 110), made of some non-conducting substance, such as shellac, suspended by a very fine wire. There is a small disc of copper fixed at one extremity of this needle. There is likewise a vertical glass rod, terminated by a gilt pith ball, which passes through an aperture at a. This pith ball is capable of receiving an electric charge. At the bottom of the apparatus is a dish containing chloride of calcium, for keeping the air dry, since moisture would conduct away the electricity which it is wished to measure. Surrounding the cylindrical side of the instrument, at the level of the pith ball and needle, there is a graduated scale. Finally the attachment at the top of the fine thread which sustains the needle is capable of moving independently of the tube, and there is a small circle at the top which registers the angular movement which is thus communicated to the suspended thread. Now let the apparatus be so arranged that the copper disc n is just in contact with the pith ball m. Next let the rod a m be taken out, and let the pith ball receive a charge of electricity. The pith ball will touch FIG. 110 and communicate part of its charge to n, and the needle will thereafter be repelled by the pith ball, since both are charged with the same kind of electricity. The needle will therefore settle in some position where the electric repulsion tending to drive it from m will just balance the force of torsion tending to bring it back to m. Now if we suppose that the angle between m and n as read on the scale is 10°, the force of torsion being proportional to the angle (Art. 67), we may call this force 10, and hence the electric force which counteracts it may be called 10 also. But by moving the top round in the same direction as the hands of a watch, we may, by means of the force of torsion, make n approach m. Suppose that we twist the suspension round 35°, we shall find by the scale that m and n are now five degrees apart. Hence the whole torsion will now be denoted by the 35° through which we twisted round the suspension above, plus the 5° between m and n on the scale below; that is to say, there will be 40° of torsion in all, and hence the electric repulsive force will be measured now by 40 instead of 10. Thus, while it takes a force equal to 10 to keep m and ʼn 10° from each other, it takes a force equal to 40 to keep them at the distance of 5°. But 10 and 5 represent very nearly the distances of the two electric bodies from each other, so that the force of repulsion is four times as great at half the distance. We might by a similar method charge the two balls with opposite electricities, and we should then find that when the distance is halved the attraction is increased fourfold. We are thus entitled to conclude that the attractions or repulsions between two electrified bodies vary inversely as the square of their distance from each other. 341. Having thus proved the law of variation with distance, the law of variation with quantity can be proved in a similar manner for if we take out the ball m, and cause it to touch a similarly-sized unelectrified ball, its charge will be reduced to one-half (Art 340). If we now replace it, we shall find that the force as measured by the angle of torsion will be reduced to one-half, In this experiment ʼn retains its full charge; but had we commenced the experiment with this half-charge both of m and n, we should have found the electric force only one-quarter of that due to a full charge of both m and n; that is to say, the half-charge of m acting on the half-charge of n will produce a result only one-quarter as great as before. In fine, the law of electrical force is similar to that for gravity; that is to say, the force of electric attraction or repulsion between two electrified bodies varies directly as the product of the quantities of electricity. Thus, if we denote for the present occasion by unity the force exercised by unit of positive upon unit of negative electricity, at unit of distance, then the force exercised by X 6 units of positive upon 4 units of negative electricity at distance 3 will be denoted by 6 X 4 = 2, and so on. 342. We have said that electricities of like kinds repel one another: the consequence is, that electricity only manifests itself on the surfaces of bodies, and would escape from them if it could; but it is prevented by the surrounding atmosphere, which is a very bad conductor. In proof of this let us take an insulated hollow brass globe, and let it be supplied with two hemispherical brass envelopes capable of fitting tightly upon it, and having glass handles so as to admit of their being separated from the globe. Now in the first place let us electrify the hollow globe, and then let us enclose it in the brass hemispheres. If we now quickly remove the brass hemispheres we shall find them to be strongly electrified, while the sphere will have little or no electricity left in it. It is another consequence of the repulsive force of electricity, that while on a sphere the charge is uniformly distributed, on a pointed conductor there is an increase of intensity towards the point, so that if the body be disposed to part with its electricity it will do so more rapidly if it be pointed than if it be a sphere. If we use the term electric density to denote the quantity of electricity on unit of surface, we shall find that in a conductor, one part of which is spherical and another pointed, the density is very much greater at the point than at the spherical surface. An instrument called the proof plane is often used to test the relative distribution of electricity over the surface of a body. It consists of a small disc of copper foil, insulated by a glass rod. This disc is made to touch an electrified body at its various parts, and forms in fact, for the time being, the outer surface of the body at the point where it touches it. We then, by removing the disc, remove the outer surface of the body at this point along with its electricity, which we can test by means of Coulomb's balance. LESSON XXXVIII.-ELECTRICAL INDUCTION. 343. It has been said that unlike electricities attract, while like repel one another. Now what will happen if we bring near together two insulated conductors, one charged with electricity, and the other not charged? An index to the result will be found in the statement already made (Art. 338), in which a neutral body is regarded as a reservoir of both electricities in a state of union. Suppose now that the conductor in question (Fig. 111) is charged with positive electricity when it is brought near the neutral conductor it will decompose its fluid, attracting that of the opposite kind to itself, that is to say, negative electricity, and repelling that of a like character with itself, or positive electricity. The end of the neutral conductor next the electrified one will thus be charged with negative, and the opposite end with positive electricity. The state of things will be represented by Fig. 111. Now let us suppose that we have an arrangement by which the neutral conductor may be divided into two, and that we perform this separation, we shall find the half nearest the positively charged conductor to have a negative, and the |