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CURRENT ELECTRICITY The electrical phenomena so far considered have been almost entirely such as depend on the attractions and repulsions be tween charges on conductors. The movement of these charges along the conductors will now be considered.

Cruickshank (1745-180o) soon afterwards found that metallic salts in solution can be decomposed in the same way. For exam ple, with a solution of copper sulphate, copper is deposited on one wire, and sulphuric acid and oxygen appear at the other. Wollas ton (1766-1828) showed that the same decompositions on a very small scale could be produced by electricity from a frictional ma chine, and in 18o' Pfaff (1773-1852) showed that a Leyden jar could be charged by means of a Voltaic pile having a very large number of elements. Thus the identity of frictional and Voltaic electricity was established.

Humphry Davy (1778-1829) studied the action of Voltaic piles, and concluded that chemical action on the zinc accompanies the generation of electricity, and is in some way the cause of it. Davy and Grothus explained the decomposition of water and other bodies by supposing that hydrogen atoms in water molecules are positively charged, and the oxygen atoms negatively. At the negatively charged wire hydrogen atoms are separated, giving up their positive charges to the wire. The oxygen atoms set free com bine with hydrogen atoms in other molecules, and the oxygen atoms from these with hydrogen atoms in still other molecules, and so on, until oxygen atoms appear at the positive electrode. Thus we may imagine a row of water molecules extending from the negative to the positive electrode. If now the hydrogen in each molecule moves into the next one in the row, the result is that we get free hydrogen at one end and free oxygen at the other.

This view was opposed by La Rive (1801-1873), who showed that metals could be made to pass from a salt solution through pure water to a negatively charged electrode. La Rive consid ered that salts in solution were partially dissociated into oppo sitely charged particles, and that the negative particles moved through the liquid to the positive electrode and the positive parti cles to the negative electrode. These electrolytic decompositions led Berzelius 0779-1848) to propose a theory of chemical affinity according to which the atoms in the molecules of compounds are oppositely charged and are held together by electrical attraction.

This subject was taken up by Biot (1774-1862) and Savart (1791-1841) in France, and then by Ampere (1775-1836). Am pere one week after the news of Oersted's discovery arrived in Paris, showed that two parallel wires, carrying currents in the same direction, attract each other, but repel when the currents are in opposite directions. During the next few years Ampere investi gated the subject experimentally and mathematically, and in 1825 published an account of his researches in a memoir which has ex cited the admiration of mathematicians and physicists ever since. He showed that the forces, between currents and magnets, and between one current and another, could be represented by sup posing that each element of a circuit exerts a force on a magnetic pole and on every other current element.

A current element of length ds at a point 0 carrying a current i produces a magnetic field of strength ids sin at a point P, where r=OP and 0 is the angle between the current element and OP. The direction of this field is perpendicular to the plane con taining ds and OP. The force on a current element in a magnetic field of strength H is equal to Hids sin where 4) is the angle between ds and H. This force is perpendicular to H and ds. Am pere assumed that the force between two current elements is along the line joining them. This assumption is not now believed to be correct, but his theory nevertheless gave correct results for the force exerted by one circuit on another. Ampere called the theory of the mutual action of currents electrodynamics.

In 1826 Georg Simon Ohm (1787-1854) published a paper on the flow of electricity through conducting wires in which a result since known as Ohm's Law was established. Ohm argued that the flow of electricity along a wire was analogous to the flow of heat along a rod, one end of which was hotter than the other. The quantity of heat flowing per second is proportional to the difference of temperature, so Ohm suggested that there must be an electrical quantity, analogous to temperature, concerned. He showed that this quantity, which he called electroscopic force, increases by equal increments on passing from one copper plate of a Voltaic pile to the next. This shows that Ohm's electroscopic force is the same thing as electrostatic potential difference. Ohm showed that the current through a wire is equal to the electroscopic force act ing on the wire multiplied by a constant. This constant is now called the conductivity of the wire and its reciprocal the resistance. The resistance is proportional to the length and varies inversely as the cross section of the wire. The resistance of a wire of unit length and unit cross section is called the specific resistance of the material of the wire.

The mathematical theory of electromagnetic induction of cur rents was developed by Neumann and Weber (1804-1890) . It was shown by Neumann that the mutual potential of two circuits is equal to the number of unit tubes of magnetic force, due to one of them, which pass through the other one multiplied by the cur rent in it. According to Faraday's law, the currents induced de pend on the variation of this quantity, so that the induced currents can be calculated from the mutual potential energy. Weber sup posed that a current in a wire consists of a flow of positively charged particles in one direction, together with an equal flow of negative particles in the opposite direction. He deduced an ex pression for the force exerted by one such particle on another one at any distance, and showed that the mutual action of circuits including the induced currents could be explained in this way. Weber's law of force gave correct results, in many cases, but it has been replaced by other conceptions in the modern theory. Weber's idea that a current consists of a flow of particles of electricity reappeared at a much later date in the modern electron theory.

It was argued by Peter Roget (1779-1869), and later by Fara day and La Rive, that the electrical energy supplied by such a cell or element of a Voltaic pile must come from the chemical affinity between the acid and zinc which combine in the cell. If the current merely came from the contact between two metals, Faraday said, it would be a "creation of power like no other force in nature." Magnetism and Light.—In 1845 Faraday placed a block of glass between the poles of a powerful magnet and then passed a beam of plane polarized light through the block along the direc tion of the magnetic field. He found that the plane of polariza tion of the light was rotated as it passed through the glass. By this discovery the sciences of electricity and magnetism were linked with optics. Faraday discussed the nature of light waves, suggesting that they might turn out to be transverse vibrations travelling along his lines of electric and magnetic force. He thus brilliantly foreshadowed the electromagnetic theory of light, which was afterwards worked out by Clerk Maxwell largely as the result of a translation of Faraday's ideas into mathematical form. Faraday, in 1845, also discovered that all substances have mag netic properties in greater or less degree. Some bodies tend to move, in a magnetic field, towards the stronger parts of the field ; these Faraday called paramagnetic bodies. Other bodies, notably bismuth, he found tend to move into the weaker parts of the field ; these he called diamagnetic bodies. Faraday's experimental work ended in 18J5 when he retired. He died in 1867. His col lected scientific papers, published in four volumes, form a note worthy monument to the greatest of all experimental philosophers.

In 1847, Weber showed that diamagnetism could be explained by supposing that currents are induced in the molecules of dia magnetic bodies when they are placed in a magnetic field. Ampere had previously suggested that the magnetic properties of iron atoms may be due to currents flowing round small circuits in the atoms. Weber supposed that paramagnetic atoms have such cur rents always, but that diamagnetic atoms normally have no cur rents but acquire them when put in a magnetic field. The induced currents produce a field opposite to the inducing field so that the resultant field in diamagnetic bodies is less than in non-magnetic bodies. In paramagnetic bodies there is no resultant field when they are not magnetized because the atomic circuits are orientated at random. When put in a field, the atomic circuits tend to turn so that their fields are in the same direction as the inducing field, so giving a resultant field greater than that in a non-magnetic body. (See MAGNETISM.) Electricity and the Conservation of Energy.—The prin ciple of the conservation of energy was finally placed on a solid foundation about 1841 by the labours of James Prescott Joule of Manchester. He applied it to electrical circuits, and showed that the chemical energy, used up in a battery sending a current through a wire, was approximately equivalent to the heat generated in the circuit by the flow of the current. He showed that the heat generated in a wire was proportional to the square of the current in it.

Helmholtz (1821-1894) in 1842 showed that the chemical energy used up in a battery may not be exactly equal to the electrical energy developed, because some heat energy may be absorbed from surrounding bodies. In 1847 Helmholtz published a great memoir, on the conservation of energy, in which he applied the principle to electrostatic and magnetic problems among others. He calculated the electric and magnetic energies by assuming that the work required to produce the final state was stored up in the system. He showed that the energy of a system of charged conductors is equal to IL EV where E is the charge and V the potential of a conductor. The potential is the function, used by Poisson and Green, which is equal to the work required to bring a unit charge from a great distance to the conductor. Helmholtz also considered systems involving currents, and showed that the existence of Faraday's induced currents followed from the prin ciple of the conservation of energy.

Kelvin also worked out the theory of the propagation of elec trical signals along long wires, such as submarine cables, and in 1857 Kirchhoff worked out the propagation of an electrical dis turbance along a wire in air, and showed that the velocity of prop agation, in centimetres per second, should be equal to the ratio of the electromagnetic unit of electricity to the electrostatic unit. This ratio had been found experimentally, by Weber and Kohl rausch in 1856, to be equal to 3.1 X which is nearly equal to the velocity of light in centimetres per second. Thus it appeared, as Kirchhoff pointed out, that the velocity of propagation of an electric disturbance along a wire in air is equal to the velocity of light in air.