the resistances so that there is no deflexion on charge or discharge (Fig. 219). Then K1: K2::r2:r1, the larger capacity acting as a smaller resistance.

(d) Potential-divider nul Method. - Two resistances r and r2 are joined in series to the + and - poles of a battery. The middle point between r, and r2 is connected to one of the terminals of K, and also of Kg.

K,

The free

K2

Fig. 219.

terminals of K, and K, are momentarily joined to the + and poles of the battery respectively and receive charges of opposite sign. They are then connected; and if of equal amount the charges will neutralize each other. The resistances Τι and r2 are adjusted until this condition is satisfied, as shown by nul deflexion when the key of a galvanometer circuit across their terminals is depressed. Then K, Krip

(e) Tuning-fork Method. - A tuning-fork acting as a vibrating two-way switch charges and discharges the condenser n times per second, allowing to pass VKn coulombs per second or VKn amperes. The apparent resistance r of this combination is 1/Kn, and can be measured by a Wheatstone bridge, whence K = 1/nr.

(f) Loss of Charge Method. This is the same as the last method in Art. 411e, a known high resistance being used.

CHAPTER VII

THERMO-ELECTRICITY

LESSON XXXV. - Thermo-Electric Currents

419. Seebeck Effect. In 1822 Seebeck discovered that a current may be produced in a closed circuit by heating a point of contact of two dissimilar metals. If a piece of bismuth and a piece of antimony be soldered together, and their free ends connected with a short-coil galvanometer, it is found that if the junction be warmed to a temperature higher than that of the rest of the circuit, a current flows in the direction from bismuth to antimony across the heated point; the current being proportional to the excess of temperature. If the junction is cooled below the temperature of the rest of the circuit a current in the opposite direction is observed. The electromotive-force thus set up will maintain the current so long as the excess of temperature of the heated point is kept up; heat being all the while absorbed in order to maintain the energy of the current. Such currents are called Thermo-electric currents, and the electromotiveforce producing them is known as Thermo-electromotiveforce.

420. Peltier Effect. In 1834 Peltier discovered a phenomenon which is the converse of that discovered by Seebeck. He found that if a current of electricity from a battery be passed through a junction of dissimilar

metals the junction is either heated or cooled, according to the direction of the current. Thus a current which passes through a bismuth-antimony pair in the direction from bismuth to antimony absorbs heat in passing the junction of these metals, and cools it; whereas, if the current flow from antimony to bismuth across the junction it evolves heat, and the junction rises in temperature. It is clear that if bismuth is positive with respect to antimony, any current that may be caused to flow from bismuth to antimony is aided by the electromotiveforce at that junction; whilst any current flowing from antimony to bismuth will meet with an opposing electromotive-force. In the latter case the current will do work

and heat the junction; in the former the current will receive energy at the expense of the junction, which will give up heat. In Fig. 220, the feathered arrows at the junctions represent the Peltier electromotive-forces, and the plain arrows the direction of the current.

This phenomenon of heating (or cooling) by a current, where it crosses the junction of two dissimilar metals (known as the "Peltier effect," to distinguish it from the ordinary heating of a circuit where it offers a resistance to the current, which is sometimes called the "Joule effect"), is utterly different from the evolution of heat in a conductor of high resistance, for (a) the Peltier effect is reversible; the current heating or cooling the junction according to its direction, whereas a current meeting with resistance in a thin wire heats it in whichever direction it flows; and (b) the amount of heat evolved or absorbed in the Peltier effect is proportional simply to the current, not to the square of the current as the heat of resistance is.

The complete law of the heat developed in a circuit will therefore require to take into account any Peltier effects which may exist at metal junctions in the circuit. If the letter P stand for the difference of potential due to the heating of the junction, expressed as a fraction of a volt, then the complete law of heat is

U=0·24 × (C2Rt + PCt),

which the student should compare with Joule's law in Art. 427. The quantity called P is also known as the coefficient of the Peltier effect; it has different values for different pairs of metals, and is numerically equal to the number of ergs of work which are evolved as heat at a junction of the particular metals by the passage of one absolute unit (10 coulombs) of electricity through the junction.

421. Thermo-electric Laws. The thermo-electric properties of a circuit are best studied by reference to the simple circuit of Fig. 221, which represents a bismuth - antimony pair united by a copper wire. If all parts of the circuit are at one temperature, even though there may be at the junctions electromo

Fig. 221.

B

tive-forces as suggested above, there will be no current, since the electromotive-forces are in equilibrium. But when a junction is heated this equilibrium no longer exists, and there will be a resultant electromotive-force. It is found to obey the following laws:

(i.) The thermo-electromotive-force is, for the same pair of metals, proportional (through limited ranges of temperature) to the excess of temperature of the junction over the rest of the circuit.

(ii.) The total thermo-electromotive-force in a circuit is the algebraic sum of all the separate thermo-electromotiveforces in the various parts.

It follows from this law that the various metals can be arranged, as Seebeck found, in a series, according to their thermo-electric power, each one in the series being thermoelectrically positive (as bismuth is to antimony) toward one lower down.

422. Thermo-electric Power. In the following table is shown the thermo-electric series of metals, together with the thermo-electric power of each when cold. The term thermo-electric power of a metal means the electromotiveforce per degree (centig.) for a pair made of that metal with the standard metal (lead). In the table the numbers are microvolts per degree.

A very small amount of impurity may make a great difference in the thermo-electric power of a metal, and some alloys, and some of the metallic sulphides, as galena, exhibit extreme thermo-electric power.

The electromotive-forces due to heating single pairs of metals are very small indeed. If the junction of a copper-iron pair be raised 1° C. above the rest of the circuit its electromotive-force is only 16.14 microvolts.