galena battery of 120 pairs affording a strong current; but it is extremely difficult to maintain them in effective action for long, as they fail after continued use, probably owing to a permanent molecular change at the junctions. In the hands of Melloni the thermo-electric pile or thermopile, constructed of many small pairs of antimony and bismuth united in a compact form, proved an excellent electrical thermometer when used in conjunction with a sensitive short-coil astatic galvanometer. For the

detection of excessively small differences of temperature the thermopile is an invaluable instrument, the currents being proportional to the difference of temperature between the hotter set of junctions on one face of the thermopile and the cooler set on the other face. The arrangement of a thermopile with the old astatic galvanometer is shown in Fig. 225.

A still more sensitive arrangement for detecting minute heating due to radiation consists in suspending between the poles of a powerful magnet a closed circuit having a bismuth-antimony junction in it. Sturgeon

proposed a thermo- galvanometer on this plan in

1835.

In the radio-micrometer of Vernon Boys (1889) a loop of wire, suspended by a delicate quartz fibre between the

poles of a magnet (like the coil in Fig. 126) has its circuit closed at its lower end by a piece of antimony and a piece of bismuth (or alloys of these metals) soldered to a minute disk of copper foil. A rise of temperature of the copper foil even so small as one millionth of a degree will generate a current in the loop and give a deflexion over one division of the scale. With an instrument of this kind the radiant heat of a candle can be detected at a distance of two miles.

CHAPTER VIII

HEAT, POWER, and LIGHT, FROM ELECTRIC CURRENTS

LESSON XXXVI. — Heating Effects of Currents

A current may do

426. Heat and Resistance. work of various kinds, chemical, magnetic, mechanical, and thermal. In every case where a current does work that work is done by the expenditure of part of the energy of the current. We have seen that, by the law of Ohm, the current produced by a given battery is diminished in strength by anything that increases the external resistance. But the current may be diminished, in certain cases, by another cause, namely, the setting up of an opposing electromotive-force at some point of the circuit. Thus, in passing a current through an electrolytic cell (Art. 237) there is a diminution due to the opposing electromotive-force ("polarization") which is generated while the chemical work is being done. So, again, when a current is used to drive an electric motor (Art. 443), the rotation of the motor will itself generate a back E.M.F., which will diminish the current. Whatever current is, however, not expended in this way in external work is frittered down into heat, either in the battery or in some part of the circuit, or in both. Suppose a quantity of electricity to be set flowing round a closed circuit. If there were no resistance to stop it it would circulate for ever; just as a waggon set rolling along a

circular railway should go round for ever if it were not stopped by friction. When matter in motion is stopped by friction the energy of its motion is frittered down by the friction into heat. When electricity in motion is stopped by resistance the energy of its flow is frittered down by the resistance into heat. Heat, in fact, appears wherever the circuit offers a resistance to the current. If the terminals of a battery be joined by a short thick wire of small resistance, most of the heat will be developed in the battery and so wasted; whereas, if a thin wire of relatively considerable resistance be interposed in the outer circuit, it will grow hot, while the battery itself will remain comparatively cool.

427. Laws of Development of Heat: Joule's Law. To investigate the development of heat by a current,

Fig. 226.

Joule and Lenz used instruments on the principle shown in Fig. 226. A thin wire joined to two stout conductors is enclosed within a glass vessel containing alcohol, into which also a thermometer + dips. dips. The resistance of the wire being known, its relation to the other resistances can be calculated. Joule found that the number of units of heat developed

(ii.) to the square of the strength of the current;

and

(iii.) to the time that the current lasts.

The equation expressing these relations is known as Joule's Law, and is

UC2Rt x 0.24,

where C is the current in amperes, R the resistance in ohms, t the time in seconds, and U the heat in calories; one calorie being the amount of heat that will raise 1 gramme of water through 1o C. of temperature (Art. 281).

This equation is equivalent to the statement that a current of one ampere flowing through a resistance of one ohm developes therein 0·24 calories per second. The proof of this rule is given in Art. 439. The heat produced thus by the degradation of energy in a resistance is sometimes called the "ohmic" heat to distinguish it from the reversible Peltier effect (Art. 420).

The electric unit of heat, the joule, is only 0·24 of an ordinary heat-unit or calorie, and 1 calorie will be equal to 4.2 joules.

The second of the above laws, that the heat is, cæteris paribus, proportional to the square of the strength of the current, often puzzles young students, who expect the heat to be proportional to the current simply. Such may remember that the consumption of zinc is, cæteris paribus, also proportional to the square of the current; for, suppose that in working through a high resistance (so as to get all the heat developed outside the battery) we double the current by doubling the number of battery cells, there will be twice as much zinc consumed as before in each cell, and as there are twice as many cells as at first the consumption of zinc is four times as great as before.

428. Favre's Experiments. -Favre made a series of most important experiments on the relation of the energy of a current to the heat it developes. He ascertained that the number of calories evolved when 33 grammes (1 equivalent) of zinc are dissolved in dilute sulphuric acid (from which it causes hydrogen to be given off) is 18,682. This figure was arrived at by conducting the operation in a vessel placed in a cavity of his calorimeter, an instrument resembling a gigantic thermometer filled with mercury, the expansion of which was proportional to the heat imparted to it. When a Smee's cell was introduced into