CHAPTER XXXV. ELECTRIC LIGHTING. 425. Incandescent Lighting.-Electric energy is used for lighting purposes chiefly in two ways, namely, in incandescent lamps and in arc lights. The former method consists in raising a conducting thread to so high a temperature that it becomes luminous. Platinum was first tried for this purpose, but it rapidly disintegrates. The best substance is a thin filament of carbon placed in a vacuum so as to prevent its being burnt. In Edison's lamp, for instance (Fig. 355), the carbon is a filament of bamboo calcined at a high temperature, and contained in a glass bulb which is exhausted by means of a mercury pump; it is fixed at the ends to two platinum wires fused into the glass, which are the electrodes. Before the bulb is finally sealed the filament is kept incandescent for some time in an atmosphere of a hydrocarbon. Carbon resulting from the decomposition of the hydrocarbon by the great heat is deposited on the filament, which thereby becomes more compact and regular. The rarefaction is pushed to one or two hundredths of a millimetre of FIG. 355. L.P. mercury. At a lower pressure the filament rapidly disintegrates, and the bulb becomes covered with a layer of carbon; at a greater pressure, 2 or 3 millimetres, for example, the bulb becomes heated. The illumination* rapidly increases with the strength of the current; but the life of the lamp is thereby shortened. The conditions of maximum economy are those in which the gain in luminosity and the loss in the life of the lamp, each estimated by its money value, exactly compensate each other. Equilibrium of temperature is attained when the rate at which heat is lost by radiation is equal to the rate at which it is generated in the carbon filament, the conditions of this generation being expressed by Joule's law. The ratio of the light emitted to the energy expended is a function of the temperature only, and does not depend on the shape of the carbon filaments, provided they have the same emissive power. By measuring the quantity of heat imparted by the lamp to a calorimeter with opaque sides, which absorbs the whole of the radiation, and then to one which transmits the light, it is found that the light is about 5 per cent. of the total energy; in the case of an ordinary candle the ratio is scarcely 3 in 1000. Such a An Edison lamp of 15 candle-power works with a current of 0.8 ampere, and a difference of potential of 100 volts. lamp usually lasts about 1000 hours. - 80 The energy consumed in this case per second is 100 x 0.8 joules. But 80 joules per second, or 80 watts, is nearly one-ninth of a horse-power; hence I horse-power radiated from such lamps would amount to about 140 candle-power. The resistance of the lamp when hot is = 125 ohms. 100 The lamps are generally arranged in parallel circuit. Suppose there are n lamps of the same kind : let be the resistance of one lamp, and c the current through each. On the other hand, let E be the electromotive force of the generator and R the resistance of the circuit, exclusive of the lamps; the resistance p of the whole of the ʼn lamps in parallel is and we have r E = (R+p) nc = (nR + r) c ; the useful work is nrc, and the efficiency r nR + r • The English official standard of illumination is a spermaceti candle, J-inch in diameter, six to the pound, burning 120 grains per hour. The French standard is the Carcel lamp, burning 42 grammes of oil in an hour: this is equivalent to about 8.9 English candles. $ 426.] Incandescent Lighting. 501 Suppose it is desired to work lamps of the preceding type by means of a battery. Let us assume that the only appreciable external resistance is that of the battery; in order to obtain the maximum rate of doing work (§ 131), we must take nR = r = 125 ohms. For Bunsen's elements the preceding formula gives ✰ being the number of elements. From this we deduce x = III.I. Hence there must be 11 elements in series, whatever be the number of lamps to be maintained. The resistance alone must vary with the number of lamps, and will be equal to Lamps of the Edison type require a high electromotive force and a weak current. As an example of a different type, the Bernstein lamp may be mentioned. This is formed of a straight rod of carbon, and requires a current of 10 amperes at a potential difference of 7 volts, which gives 0.7 ohm for the resistance of a single lamp when hot. The lamps are arranged in series. A calculation similar to the foregoing shows that to work them with Bunsen's elements, arranged to give the maximum of external energy, eight elements must be taken per lamp, each having oneeighth the resistance of a single lamp. The use of Bunsen's elements is only mentioned by way of example. In practice the lamps are always fed by dynamos or accumulators. Take the case of an installation of 1000 lamps. With high-resistance Edison lamps arranged in parallel circuit, the dynamo must give 800 amperes with an electromotive force of 100 volts. With Bernstein lamps in series, 10 amperes would be required with 7000 volts. As no machine could in practice work under these latter conditions, the lamps might be arranged in five parallel series with 200 lamps in each. A current of 50 amperes at 1400 volts would in that case be sufficient. In this calculation no allowance is made for the resistance of the conductors. 426. Voltaic Arc.-Davy having attached two rods of carbon to the poles of a battery of 2000 elements, found that, on gently drawing them apart after being in contact, a flame formed between the two points, to which he gave the name of the voltaic arc. The phenomenon is so brilliant that it can only be looked at through a dark glass; a still more convenient way of observing it is to project the image of the arc and the two carbons on a screen by means of a lens. It is then seen that the arc has far less brilliance than the points of the carbons themselves (Fig. 356); that it consists of two distinct parts-one the arc, properly so called, which is blue, and the other, which has the ordinary appearance of a flame, and is reddish; that the positive carbon is brighter than the negative, and that a greater length of it is luminous, indicating that its temperature is higher; that the positive carbon is hollowed out in the form of a crater, while the negative one is sharpened to a point; finally, that the positive wears away more rapidly than the negative carbon. In a vacuum the effects are the same, apart from the action of air on the carbons, and it is clearly seen that matter is carried from the positive to the negative carbon. The temperature of the arc is very high, and difficultly fusible substances, such as platinum, melt easily in it. Hence a permanent arc can only be produced with rods of carbon. For illuminating purposes it is best to have the positive carbon, which is the FIG. 356. brightest, above, as the light is thereby better diffused. If the heat is to be used for melting or volatilising a substance, the lower carbon is made the positive one, and its extremity is hollowed out. The light emitted is very rich in highly refrangible rays, and appears bluish as compared with sunlight. In the spectroscope the carbons give a continuous spectrum extending far towards the violet; the arc itself, like all incandescent gases, gives a fluted spectrum showing the rays of carbon, and those of any metals which may be present in the carbons. Calorimetrical experiments made in a transparent and in an opaque vessel show that the fraction of energy converted into iuminous rays is about one-tenth of the total energy expended in the arc. The arc is acted upon by a magnet like ordinary movable conductors (§ 266). In air the arc produces ozone, and in an atmosphere of hydrogen it gives acetylene. $428.] Electromotive Force of the Arc. 503 427. Electromotive Force of the Arc.-Measured either by an electrometer or by a high-resistance galvanometer, the difference of potential between the two carbons is found to be never lower than 30 volts. It varies from 30 to 70 volts. Experiment shows that this difference or fall of potential, which of course takes place in the direction of the current, consists of two parts. One of these is fixed, and is independent of the strength of the current and of the distance of the carbons, acting therefore like a true electromotive force; the other varies with the strength of the current and the distance of the carbons. According to recent experiments by Mrs. Ayrton, the connection between the observed difference of potentials, E, the length of the arc, L, and the strength of the current may be expressed by an equation of the form Ec=p+qL, when the strength of the current is constant; and by an equation of the form when the length of the arc is constant; p, q, s, and t being numerical quantities determined by experiment. These expressions are included in the following more general equation When the length of the arc was measured in millimetres, the current in amperes, and difference of potentials in volts, the values obtained with solid carbons agreed with the formula This formula indicates an electromotive force at the carbons of about 52.6 volts as being required to maintain an arc of 4 mm. with a current of 10 amperes. 428. Work Expended in the Arc.—The difference of potentials multiplied by the strength of the current gives the rate of expenditure of energy in the arc. For the rate of expenditure in watts, Mrs. Ayrton's experiments give W = 11.7 + 10.5 L + (38.9 + 2.07 L) C, or 526 watts for an arc such as that referred to in § 427. |