Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/286

 metals, A and B, and let one junction be maintained at a slightly higher temperature (T + δT) than the temperature T of the other junction. As Seebeck had shown, a thermo-electric current will be set up in the circuit. Thomson saw that such a system might be regarded as a heat-engine, which absorbs a certain quantity of heat at the hot junction, and convorts part of this into electrical energy, liberating the rest in the form of heat at the cold junction. If the Joulian evolution of heat be neglected, the process is reversible, and must obey the second law of thermodynamics; that is, the sum of the quantities of heat absorbed, cach divided by the absolute temperature et which it is absorbed, must vanish. Thus we have

so the Peltier effect $$\textstyle \prod_B^A(T)$$ must be directly proportional to the absolute temperature T. This result, however, as Thomson well knew, was contradicted by the observations of Cumming, who had shown that when the temperature of the hot junction is gradually increased, the electromotive force rises to a maximum value and then decreases. The contradiction led Thomson to predict the existence of a hitherto unrecognized thermo-electric phenomenon-namely, a reversible absorption of heat at places in the circuit other than the junctions. Suppose that a current flows along a wire which is of the same metal throughout, but varies in temperature from point to point. Thomson showed that heat must be liberated at some points and absorbed at others, so as either to accentuate or to diminish the differences of temperature at the different points of the wire. Suppose that the heat absorbed from external sources when unit electric charge passes from the absolute temperature T to the temperature (T + δT) in a metal A is denoted by SA(T).δT. The thermodynamical equation now takes the corrected form