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of temperature, which is the same in all parts of the conductor where the cross-section is the same; but he did not succeed in connecting the thermal phenomena quantitatively with the strength of the current—a failure which was due chiefly to the circumstance that his attention was fixed on the rise of temperature rather than on the amount of the heat evolved. But incidentally the investigation led to an important discovery—namely, that when a current was passed in succession through two conductors made of dissimilar metals, there was an evolution of heat at the junction; and that this depended on the direction of the current; for if the junction was heated when the current flowed in one sense, it was cooled when the current flowed in the opposite sense. This Peltier effect, as it is called, is quite distinct from the ordinary Joulian liberation of heat, in which the amount of energy set free in the thermal form is unaffected by a reversal of the current; the Joulian effect is, in fact, proportional to the square of the current-strength, while the Peltier effect is proportional to the current-strength directly. The Peltier heat which is absorbed from external sources when a current i flows for unit time through a junction from one metal B to another metal A may therefore be denoted by

$\textstyle \prod _{B}^{A}(T)\mathbf {.} i$,

where T denotes the absolute temperature of the junction. The function $\textstyle \prod _{B}^{A}(T)$ is found to be expressible as the difference of two parts, of which one depends on the metal A only, and the other on the metal B only; thus we can write

$\textstyle \prod _{B}^{A}(T)=\textstyle \prod _{A}(T)-\textstyle \prod _{B}(T)$.

In 1851 a general theory of thermo-electric phenomena was constructed on the foundation of Seebeck's^[1] and Peltier's discoveries by W. Thomson.^[2] Consider a circuit formed of two

1. Cf. pp. 92, 93.
2. Proc. B, S. Edinb. iii (1851), p. 91; Phil. Mag. iü (1852), p. 529: Kelvin's Math. and Phys. Papers, i, p. 316. Cf. also Trans. R. S. Edinb. xxi (1854), p. 123, reprinted in Papers, i, p. 232: and Phil. Trans., 1836, reprinted in Papers, i, p. 189.