carbons two inches in diameter are mounted horizontally and embedded in the materials that are to be heated, the whole is surrounded by walls of brick or fire clay, and the electric arc is established between the carbons. Under the combined influence of the enormous heat and the electrolytic action of the current the desired transformations are wrought.

Problems.

1. A current of 14 ampères divides between two branches, one of 2 ohms and one of 5 ohms resistance. Find the current in each branch, and the watts spent in each. In which resistance is the greatest amount of heat developed per second?

2. The terminals of a gravity cell of 2 ohms resistance and 1 volt E. M. F. are connected with a coil of resistance 3 ohms. Find the watts spent in heat in the coil and also in the cell, also the total watts supplied by the cell.

3. What must be the resistance of a coil of wire in order that a current of 2 ampères flowing through the coil may give out 1200 gram-calories of heat per minute?

4. If the difference in potential of the ends of a coil is 50 volts, what must be its resistance that 500 gram-calories of heat may be developed in it per second?

5. Find the gram-calories per second developed in each of two coils; one having resistance 3 ohms and current 6 ampères, the other a resistance of 4 ohms and a difference of potential of 20 volts between its ends.

6. How many horse-power must be expended to maintain 200 100volt lamps in operation, each lamp taking ampère of current and having a potential difference of 100 volts between its terminals? 7. How many horse-power are required to operate a series of 60 incandescent street lamps in series, the current in each lamp being 3 ampères and the resistance per lamp being 7 ohms?

8. In an electric railway having a total line resistance of 0.4 ohm per mile, what is the loss in horse-power in two miles of line when 50 ampères of current is being supplied to a distant car?

THERMOELECTRICITY.

664. Seebeck's Discovery. In 1821, Seebeck, of Berlin, discovered that in a circuit made of two different metals if one junction is hotter than the other there is an electromotive force which causes an electric current. This electromotive force is

generally very small compared with ordinary battery cells, and consequently to obtain much current the circuit must have very low resistance. For example, in the copper-iron circuit shown in figure 375 when one junction is at 100° and the other at 0°, the electromotive force is about 0.001 of a volt and causes an electric current from copper to ok iron at the hot junction and from iron to copper at the cold one. The introduction of another metal does

Iron

100°

Nickel

100°

Copper

FIG. 375.

not make any difference provided the two junctions of the new metal are at the same temperature.

For example, the electromotive force is the same in the three circuits shown in figures 375 and 376.

665. Thermopile.-In order to obtain larger electromotive forces pairs of metals are combined in series to form thermopiles. The form devised by Nobili and used by Melloni in his researches

WIRES TO
GALVANOMETER,

FIG. 377.-Thermopile diagram.

H

on heat radiation consists of alternate strips of antimony and bismuth connected as shown in the figure, and carefully insulated from each other except at the junctions, where they are soldered together. These metals were chosen because they give a large electromotive force which acts from bismuth to antimony at the hot junctions and from antimony to bismuth at the cold.

Rubens has improved the thermopile by using fine wires of iron and constantan (a nickel alloy) in place of antimony and bismuth. The mass to be heated in this case is very small so that it warms quickly when exposed to radiation.

The thermopile is usually mounted in a metal case so that only one set of ends is exposed to the source of heat to be investigated. If its terminals are connected to a sensitive galvanometer of low resistance, it becomes an exceedingly delicate means of measuring heat radiation.

E. M. F.

B

666. Change of Thermoelectric Force with Temperature.If one junction of a copper-iron circuit is kept at 0° C. while the other is steadily raised in temperature, the electromotive force is found to increase rapidly at first, then more gradually, reaching a maximum when the hot junction is at 260° C., after which the electromotive force falls off, becoming zero at 520° C. If the junction is heated still hotter the electromotive force reverses and the current flows from iron to copIf the per at the hot junction. observations are plotted with the

0° 100°

260° Temperatures

FIG. 378.-Thermoelectric curve of e. m. f. of copper and iron.

temperatures of the hot junction as abscissas and electromotive forces as ordinates a curve such as shown in figure 378 is obtained. It is a parabola and is perfectly symmetrical about the vertical line through its vertex, which corresponds to the temperature of maximum electromotive force.

This reversal of the thermoelectric current was discovered by Cumming in 1823.

If the cold junction is kept at 100° instead of zero the curve will be exactly the same except that the origin of coordinates will be moved from 0 to A, and electromotive forces will now be measured from the base line AB.

667. Thermoelectric Powers.-It is clear from the foregoing that the inclination of the curve at any point, or the rate of change of electromotive force per degree change in temperature, depends only on the temperature of the junction which is being warmed or cooled and not at all on the temperature of the other junction, provided it is constant.

This change of electromotive force per degree change of temperature of a junction is known as the relative thermoelectric power of the substances involved.

If the thermoelectric powers of iron and copper are plotted as ordinates along a scale of temperatures we shall obtain the diagram shown in figure 379. The curve is a straight line intersecting the axes at 260° C; for at that temperature the relative

260

0 100 200 300 400 500

thermoelectric power is zero, as is seen also from the curve in figure 378, where the maximum point is at 260°, showing that a small change in temperature produces no change in electromotive force. FIG. 379.-Thermoelectric powers of This is called the neutral temperature for these two metals.

iron and copper.

668. Thermoelectric Diagram. In the thermoelectric diagram devised by Tait, the thermoelectric powers of the metals referred to lead are plotted as ordinates along a scale of temperatures; lead being taken as standard because in it the Thomson effect (§671) is zero. Such a diagram is shown in figure 380. It will be observed that within the limits of the diagram the variations with temperature of the thermoelectric powers of the metals are represented by straight lines.

FIG. 380.-Thermoelectric Diagram.

Thermoelectric powers are given in micro-volts per degree.

The electromotive force of a couple made of any two metals is expressed by the area included between the lines of the two metals and the ordinates of the temperatures of the junctions.

The diagram is so constructed that the direction of the resultant electromotive force is clockwise; that is, in case of iron and copper between 0° and 100°, the current will be from copper to iron at the hot junction.

669. Peltier Effect. It was discovered by Peltier in 1834, that if a current of electricity flows around a circuit made up of two metals heat will be given out at one junction and absorbed at the other.

A beautiful demonstration of the Peltier effect was given by Tyndall by means of an ordinary thermopile. A thermopile is taken in which all parts are at the same temperature, so that it gives no current. On connecting it for a few seconds to a battery and then disconnecting it and joining it to a galvanometer a decided current is observed, showing that one set of junctions must have been more, heated by the current than the other set. The current obtained is opposite to the first and tends to restore the equality of temperature disturbed by the first, for one stored up heat energy in the thermopile and the other transforms that energy back again into energy of current.

By a thermopile there is a direct transformation of heat energy into electrical energy, but it is not efficient because there is a serious loss of heat by conduction from the hot junctions to the cold.

670. The Conservation of Energy in Thermoelectricity.The Peltier effect affords a beautiful illustration of the principle that energy is absorbed at those points in a circuit where there is an electromotive force acting with the current and is given out at those points where there is an electromotive force acting against the current (§655).

In a circuit of two metals all at one temperature there may be electromotive forces at the two junctions, but since the temperature is the same at both, these electromotive forces are equal and opposite and consequently there is no current. current is now caused to flow by means of a battery, energy is given out at the junction where the electromotive force is against the current and it is heated, while the other is cooled. The two junctions no longer balance each other, and it is clear that the resultant electromotive force which arises from the change in temperature must be against the current which brought it about.