CONSEQUENCES OF INVERSION. 265 



275. CONSEQUENCES OF INVERSION. The principle of Volta, 

 restricted to the contact of bodies of different kinds, is not sufficient 

 to explain the phenomena of inversion. 



Let us consider, in fact, a circuit consisting of two metals A and 

 B. In order to account for inversion as a mere effect of contact, 

 we must assume that the difference of potential of the junction at 

 first increases with the temperature, passes through a maximum, then 

 diminishes, and, at the temperature of inversion, becomes equal to 

 the difference of potential at the cold junction. The value of H 2 

 would then continue to decrease; and next, the current having 

 changed its sign, the play of the electrical forces would produce a 

 disengagement of heat at the hot junction, and an absorption at the 

 cold one, besides the heating of the circuit in virtue of Joule's law. 

 We may imagine that the causes of the cooling of the circuit are so 

 diminished that it is possible to dispense with the source of heat, and 

 that the mere passage of the current would be sufficient not merely 

 to keep up the temperature of the hot junction, but even to increase 

 it, and to diminish that of the cold one, the effect of which would 

 be to intensify the current. In this way we should have realised a 

 metallic circuit possessing the remarkable property of transferring 

 heat from the colder to the hotter parts without any expenditure 

 of energy. And although such a result is not so obviously im- 

 possible as that of the impossibility of perpetual motion, it is 

 incompatible with the general course of thermal phenomena ; it is, 

 moreover, in direct contradiction with Carnot's principle. 



If, on the other hand, thermoelectrical currents were merely 

 due to the electromotive forces at the junctions, Carnot's principle 

 would necessitate that all couples had a uniform course. 



Let us imagine, for example, that a thermoelectrical couple 

 working between the temperatures / x and / 2 is connected with an 

 electrolyte whose electromotive force of decomposition is E; we 

 shall have the ratio 



or 



If the current I is very small, and the resistance R moderate, 

 the term I 2 R may be neglected, the opposing electromotive force E 

 is very little less than H 2 - Hj , and the excess of heat furnished 

 by the hot source is employed in performing the external work IE. 

 Let us suppose that, by any means, E is made to increase to the 



