is a finite change of temperature within a distance so small that it may be considered to be within the limits of molecular action. In such a case there is a ▲ V occurring abruptly, as in (II.).

(IV.) Two metals; the junctions at different temperatures; the E.M.Fs all round the circuit being considered; compare with (11.).

If there be two metals A and B with junctions at different temperatures, the total E.M.F. in the circuit will be the algebraic sum of (the E.M.F.s at the junctions) + (the E. M.F.s in the metals A and B). The former were considered in (II.). As regards the latter, these would have a zero sum were the metals the same, as stated in (III.). But in general a metal A with its ends at t, and t1 does not give the same E.M.F. as another metal B with its ends at t, and 1 ; and so in general the sum of these 'gradual E.M.F.s' (as we may call them to distinguish them from the abrupt junction-E.M.F.s) is not zero. In the case of lead there is no E.M.F. due to its unequal heating. Hence, in a cell of which one metal is lead we have a somewhat simpler sum of E.M.F.s in the circuit.

(V.) Thus when the current is running in a thermo-cell of junctions at and t, respectively, the distribution of potential in the circuit is a resultant distribution comprising three components.

(i.) The abrupt changes of potential at the junctions. These measure what we may call the junction-E.M.F.s or PeltierE.M.F.S.

(ii.) The rises and fails of potential occurring gradually along the conductors, due to the unequal heating of these conductors. These measure what we may call the Thomson-E.M.F.s.

(iii.) The regular fall of potential that follows Ohm's law, discussed in Chapter XIII.

The total E.M.F. in the circuit could be measured by breaking the circuit at some place where it is homogeneous (¿.e. not at a junction) and measuring the AV between the broken ends.

(VI.) Experiment tends to show that at the neutral point T° C. of two metals A and B there is no junction E.M.F. between them, though this is hardly certain; and most certainly shows that in a cell where the junctions have T° C. as their mean temperature, the total E.M.F. in the circuit is zero.

The above statements represent, in a neccssarily very imperfect form, the present views as to the sources of the E.M.F. in a thermo-cell.

For practical purposes it is simpler to depend upon the diagram and formula of §7; since these (when fully given) embody all the known results of experiment.

§ 11. Theory of the Peltier and Thomson Effects.

(I.) Let there be a cell of two metals A and B whose junctions are at t° C. and t° C. respectively. We will suppose, for the sake of more clearly defining the particular case that we at first consider, that t is higher than t1, and that both temperatures are above T; further we will suppose that, for temperatures above T, the metal B is of higher thermo-electric power than A. This is the case in which the total E.M.F. in the circuit is represented by the area B3 B4 A4 A3 in the diagram, fig. i., of § 7.

(II.) When a current is running we have manifested electrical energy. If this energy be not converted (in part) into chemicalpotential-energy or into inechanical or other enrgy, it will all be converted finally into heat energy.

Now this electrical energy must have been derived from some original form of energy of which an equivalent amount must have disappeared.

In the voltaic-cell it was chemical-potential-energy that was so used up.

But in the thermo-cell the only available source of energy is the heat energy supplied to the cell by a flame or other source of beat.

(III.) When, therefore, the current does no other work it must be that (i.) heat energy is absorbed, and disappears, somewhere in the circuit; (ii.) this is transformed into an equivalent amount of electrical energy; (iii.) and this again is finally transformed into an equivalent of heat energy, distributed over the circuit according to the resistances of the several portions of the circuit. The question arises, from what part of the circuit is the original heat energy derived?

(IV.) In attempting to answer this question theoretically, we must be guided mainly by two considerations. Firstly, we may feel sure that the well-established law of 'Degradation of energy' will hold here as in all the phenomena of inanimate nature. That

is, the source of heat must be on the whole the hotter part of the cell; and the general result of the action must be that the temperatures of the cell tend to become equalised. Secondly, we must remember that when a current runs against an E. M. F. work is done; and, if the work takes no other form, it will appear as heat evolved. Further, it seems almost certain that this heat will be evolved in that portion of the conductor in which the work is done, i.e. in which the E. M.F. lies. Conversely, when a current runs with an E.M.F., this E. M. F. does work on the current; and, when no heat is supplied, this work will be done at the expense of heat absorbed from the conductor; further, it seems almost certain that this heat will be absorbed from that portion of the conductor in which the E.M.F. lies.

(V.) The consideration of (IV.) will lead us to predict that, on the whole, the hotter portion of the cell will be cooled and the cooler portion will be heated; while some of the heat derived from the hotter portion of the cell will, after passing through the intermediate form of electrical energy, reappear as heat distributed round the circuit in accordance with Joule's law.

(VI.) Where the current crosses a section (e.g. a junction of two different metals) at which occurs an abrupt E.M.F., or [see § 10 (V.)] a 'Peltier E.M.F.,' there we should expect to have heat absorbed or given out according as the current flows with the E.M.F. or against it respectively.

Such an absorption or disengagement of heat, occurring at a mere section and not over any finite length of the conductor, is the true Peltier effect referred to in § 8.

There is probably no Peltier effect when the junction of the two metals is at their neutral temperature T; for it seems probable that at that temperature the two metals are as one.

(VII.) Where the current flows through an unequally heated metal, it flows (in all metals excepting lead) with or against the Thomson E.M.F. spoken of in (III.) and (V.) of § 10.

We should then expect heat to be absorbed or given out respectively, over a finite length of the conductor in question. This is, in fact, observed in the Thomson effect of § 9.

Since the unequally heated ends of each metal are at the two junctions, the result of the Thomson effect will be to alter the temperatures of the two junctions. Unless, therefore, special ex

periments are performed from which we can calculate each effect separately, we shall in general observe the sum of these two effects (i.e. of the Peltier and Thomson effects) at the junctions, and shall not be able to ascribe the heating or cooling of the junctions to the Peltier effect only.

(VIII.) We may then say that the transformations of energy referred to in (IV.) and (V.) take place through the intermediency of the Peltier and Thomson effects together.

When the hotter junction is at the neutral temperature T, then if the Peltier effect be zero, heat energy must be supplied through the intermediency of the Thomson effect only.

(IX.) Now let us suppose that we cease to supply heat from external sources. The junctions will arrive at the same temperature, by the cooling of the hotter and the heating of the cooler junction.

If now the current be continued from some external source in the same direction as before, there is no reason for supposing that the above Peltier effects would cease, though there would now be no Thomson effects, since the metals are at one temperature. We should predict then that the junction which was the hotter would now become the cooler, and conversely.

This would raise up an E.M.F. opposed to the former E.M.F., and therefore opposed to the current that is flowing.

Some such reasoning as the foregoing would therefore lead us to predict the ordinary case of the Peltier effect; the case, namely, where a current is sent across a junction of two metals A and B, and where it is found that the junction is so heated or cooled as always to raise up an E M.F. opposing the current, provided that the junction is not at the neutral temperature. In other words, there will be heating or cooling according as the current flows from the metal of lower, to the metal of higher, thermo-electric power, or vice versa.

The whole of the above reasoning is necessarily rather of the nature of guessing at probable results than of strict argument. The fact is that the theory of thermo-cells is beyond the scope of an elementary book.

CHAPTER XVII.

GALVANOMETERS; WITH A PRELIMINARY ACCOUNT OF THE MAGNETIC ACTIONS OF CURRENTS.

§ 1. Magnetic Field about a Simple Rectilinear Current.—We will now turn our attention to the very important class of phenomena coming under the head of the magnetic actions of currents.'

On these magnetic phenomena depend the construction and use of that important class of instruments called galvanometers, whose use, as current detectors and current measurers, is so essential in the modern science of electricity.

In the present Chapter we propose describing various forms of galvanometers. But, in order the better to understand their theory, we shall give some preliminary account of the magnetic fields due to electric currents; leaving, however, the main part of this important subject to be pursued further in Chapters XVIII.-XX.

When a conductor is charged statically with electricity, we have about it what we call an electrostatic field. This field acts on a unit of electricity in lines of force that run to or from the conductor, as explained in Chapter X. The case of a conductor carrying a current is very different It is true that still a + unit of electricity would in general find a field of force about the conductor, for this conductor will be in general at potentials different from that of the earth, and different from point to point of the conductor.

But this electrostatic field is quite unimportant and negligible compared with the new field of force that springs into existence directly the 'electricity' moves, or directly there is a current. This new field is a magnetic field; and we shall therefore consider its action, not on a unit of electricity, but on a + unit magnetic pole.