galvanometer will be deflected, showing that the points P and Q are no longer equipotential. The effect of the magnetic field is to distort the lines of flow and the equipotential lines in the sheet in the way shown in Fig. 475, which corresponds to the case of a sheet of bismuth in which the lines of force of the magnetic field are passing from above the page to below, the direction of the main current in the sheet being as shown

by the arrows. In the case of other metals, such as gold, the direction in which the equipotential lines and lines of flow are deflected, and hence the direction of the current in the galvanometer, is the opposite to that in the case of bismuth.

This phenomenon is referred to as Hall's phenomenon, from the name of the discoverer. We shall see later that a conductor conveying a current, when placed in a magnetic field, experiences a mechanical force tending to move it at right angles to the lines of force of the field. But

P

G

FIG. 475.

this effect on the conductor conveying the current must be carefully distinguished from the Hall effect, which refers to the current in the conductor.

The magnitude of the Hall effect is excessively small, and it is only with very strong magnetic fields and a very delicate galvanometer that it can be detected at all.

CHAPTER IX

JOULES LAW

493. Joule's Law.-We have defined the E.M.F. between two points, A and B, on a conductor through which a current is flowing as being equal to the work done in transporting the unit quantity of electricity from one of these points to the other. We have also seen that, if Ris the resistance between the points and C is the current passing, the E.M.F. between the points is given by E=CR. Now a current C will transport C units of electricity past each point of the conductor in the unit of time, hence the work done in a second in driving the current from the point A to the point B is given by EC or RC.C, that is, RC2. If the current continues for a time, the work done will be represented by the equation WRCt. The work thus done appears as heat developed in the conductor through which the current is flowing.

In order to get the amount of heat developed in the conductor in thermal units we have to divide this result by the mechanical equivalent of heat, that is, by 4.19× 107 (§ 250). Hence the quantity of heat, H, developed in a wire of which the resistance is R c.g.s. units by a current of C c.g.s. units in seconds is given by

If the electrical quantities are measured in the practical units, since a current of C c.g.s. units is equal to 10 C amperes, and a resistance of R c.g.s. units is equal to 10-R ohms, the heat developed in a conductor of which the resistance is 0 ohms, by a current of A amperes, in a time seconds, will be 0.2387 OA't calories. The work done in one second by a current of one ampere when passing through a resistance of one ohm, that is, when passing between two points between which there exists a difference of potential of one volt, is 107 ergs, or in thermal units 0.2387 calories, and is called a joule.

The law that the heat developed in a conductor is proportional to the square of the current and to the resistance was discovered experimentally by Joule in 1841, and hence is known as Joule's law.

The quantity of energy which becomes converted into heat when a given current flows through a given conductor is independent of the direc

tion in which the current flows, for, as the current always flows from the point at the higher potential to the point at the lower potential, if we reverse the direction in which the current is flowing, this means that we have reversed the direction in which the E.M.F. is acting; and since the resistance of a conductor is independent of the direction in which the current is flowing, the conditions, as far as the work done by the current and hence the heat developed, are exactly the same when the current is reversed as they were before. Thus the passage of a current through a conductor of finite resistance is always accompanied by the conversion of a definite quantity of electrical energy into the form of heat. Since when the current is reversed the conversion into heat continues at the same rate as before this conversion of electrical energy into heat, when a current passes through a conductor, is an irreversible process. As we shall see later, there are conditions under which heat developed at a given point due to the passage of a current is a reversible process, so that on reversing the current heat is now absorbed at the point; in the case of heat developed according to Joule's law, however, this is never the case. Since in many cases the heat produced according to Joule's law is simply a waste of energy, it is important to reduce it to a minimum. This can be done, if we suppose that a given current has to be transmitted, by reducing the resistance of the conducting wires. Since, as we have seen, the resistance of a pure metal at the absolute zero appears to be zero, a current could be passed through such a conductor at the absolute zero without the production of any heat and the consequent loss. of electrical energy.

494. The Mechanical Equivalent of Heat derived from Electrical Experiments. Since the heat developed by a current of A amperes in a wire of resistance 0 ohms, in a time t seconds, is equal to OA3× 10 ergs or OA't x 107 calories, where is the value of Joule's equivalent, if we measure the heat developed by means of a calorimeter, and also the current and the resistance O of the wire, or, what comes to the same thing, the E.M.F. between the ends of the wire, we can at once calculate the value of J. A most careful determination of the value of / by this method has been carried out by Griffiths. His apparatus consisted of a coil of platinum wire through which the current could be passed, and which had two wires attached, so that the difference of potential between the ends of the coil could be compared with the E.M.F. of a standard Clark cell ($ 554), by the method given in § 490. This coil was contained inside a closed calorimeter, which was itself placed inside a large steel chamber, the space between the outside of the calorimeter and the walls of this vessel being exhausted of air so as to reduce the loss of heat due to convection. The calorimeter contained, in addition to the coil, a stirrer, which was rotated at a high speed, so as to insure the water inside being thoroughly well mixed. The temperature of the water in the calorimeter was measured with a platinum thermometer, and the resistance of the

coil at different temperatures was determined, so that, knowing the E.M.F. between the terminals and the temperature, the resistance of the col and the rate at which heat was being developed by the current could be calculated. A certain amount of heat was also developed by the friction of the stirrer against the water. The amount of heat thus developed at different rates of stirring was determined by making observations of the rise in temperature of the calorimeter, due to the stirring alone, when no current was passing through the coil. The water value of the calorimeter and of the stirrer and coil was determined by making experiments with various quantities of water in the calorimeter.

As has been given already, the value obtained for the mechanical equivalent of heat was 4.1940 × 107 ergs per calorie. The accuracy of this value depends, of course, on the accuracy with which the values of the electrical quantities are known in terms of the fundamental units.

495. The Incandescent Electric Lamp.-The heat developed in a conductor by the passage of an electric current is made use of in the electric incandescent lamp. The modern form of lamp consists of a fine carbon filament enclosed in a glass globe from which the air has been exhausted. The resistance of a carbon filament being fairly great, the heat developed is sufficient to raise the temperature to such a point that the filament glows with a bright white light.

The energy which becomes converted from the electrical form in the filament is partly given out from the lamp in the form of light and partly as heat. The object of the lamp-maker is to produce a lamp in which the proportion of the energy used up to produce heat, and which as far as the production of light is concerned is completely wasted, is reduced to a minimum. It is found that the energy which has to be supplied to a lamp in order to produce a light of one candle-power decreases as the temperature of the filament is increased, so that from this point of view it is an advantage to run the lamps as bright as possible. It is, however, found that when the temperature is raised above a certain point the filament soon gives way, so that the life of the lamp is short. The resistance of the filaments of the lamps are adjusted so that when the E.M.F. between the ends of the filament has certain definite values, such as 100 volts or 200 volts, the current which passes, according to Ohm's law, will raise the temperature of the filament to the greatest value which will not endanger its life. With most of the incandescent lamps of good make the energy consumed to produce a light of one candle-power is about four watts, or, since one watt is equal to 107 ergs per second, is about 4× 107 ergs per second.

The number of watts required per candle-power increases very rapidly as the E.M.F. between the ends of the filament is reduced below the value for which the lamp is intended, so that it is very wasteful to run the lamps at a low voltage, although by this means the life of the filament may be increased.

496. The Arc Lamp.-Another source of light which depends on he conversion of electric energy into light is the arc lamp. When two ods, composed of the carbon which is deposited inside the retorts used n the manufacture of illuminating gas, connected to two conductors which are at a difference of potential of about 60 volts, are first brought into contact and are then gradually separated for a short distance the current continues to pass, and where it crosses the air space between the carbon rods an intense light is emitted. This arrangement constitutes an electric arc, and it is found that the carbon rod which is at the higher potential, that is, from which the current goes, is eaten away more rapidly than the other carbon. If an image of the arc is projected on a screen, it is seen that the carbon which is at the higher potential, the positive carbon as it is usually called, is worn slightly hollow, and that the greater proportion of the light is emitted from this hollow, which is called the crater of the arc. The end of the negative carbon, i.e. that at the lower potential, becomes worn to somewhat of a point. In order to allow for the wearing away of the carbon rods, they are held in an arrangement by which they are automatically brought nearer together as the ends wear away, so that the length of the arc is maintained constant. If by chance the distance between the carbons becomes too great the current will cease to pass, and the arc cannot again be started till the carbons are brought into contact and then separated. Hence the lamp is fitted with an electrical arrangement by which, directly the current ceases, the rods are first brought together, and then, when the current passes, are again separated to the correct distance.

An ordinary arc requires about one watt for each candle-power produced, so that the energy consumed in order to produce a given quantity of light by means of an arc is much less than is required when incandescent lamps are used.

497. The Electric Furnace. The temperature of the arc is extremely high, it having been estimated to be about 8000° C., and this high temperature has been utilised for melting refractory substances and for conducting chemical processes which require a very high temperature.

The form of electric furnace used by Moisson on his important researches at high temperatures consists of a block of lime or fireclay through which pass two thick rods of carbon, which act as electrodes for the supply of the current. The arc is formed between the ends of these rods just above the substance which is to be heated, which is contained in a small crucible placed in a cavity cut in the block of lime.