Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/344

current and the amount of heat produced or absorbed, we can determine the electromotive force required to urge the current through that portion of the conductor, and this measurement is entirely independent of the effect of contact forces in other parts of the circuit.

The electromotive force at the junction of two metals, as determined by this method, does not account for Volta's electromotive force as described in Art. 246. The latter is in general far greater than that of this Article, and is sometimes of opposite sign. Hence the assumption that the potential of a metal is to be measured by that of the air in contact with it must be erroneous, and the greater part of Volta's electromotive force must be sought for, not at the junction of the two metals, but at one or both of the surfaces which separate the metals from the air or other medium which forms the third element of the circuit.

250.] The discovery by Seebeck of thermoelectric currents in circuits of different metals with their junctions at different temperatures, shews that these contact forces do not always balance each other in a complete circuit. It is manifest, however, that in a complete circuit of different metals at uniform temperature the contact forces must balance each other. For if this were not the case there would be a current formed in the circuit, and this current might be employed to work a machine or to generate heat in the circuit, that is, to do work, while at the same time there is no expenditure of energy, as the circuit is all at the same temperature, and no chemical or other change takes place. Hence, if the Peltier effect at the junction of two metals $a$ and $b$ be represented by $\Pi _{ab}$ when the current flows from $a$ to $b$, then for a circuit of two metals at the same temperature we must have

$\Pi _{ab}+\Pi _{ba}=0,$

and for a circuit of three metals $a,b,c,$ we must have

$\Pi _{bc}+\Pi _{ca}+\Pi _{ab}=0.$

It follows from this equation that the three Peltier effects are not independent, but that one of them can be deduced from the other two. For instance, if we suppose $c$ to be a standard metal, and if we write $P_{a}=J\Pi _{ac}$ and $P_{b}=J\Pi _{bc}$, then

$J\Pi _{ab}=P_{a}-P_{b}.$

The quantity $P_{a}$ is a function of the temperature, and depends on the nature of the metal $a$.

251.] It has also been shewn by Magnus that if a circuit is