266 The Mathematical Electricians of the 



metals, A and B, and let one junction be maintained at a 

 slightly higher temperature (T + $T) 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 converts 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, each divided by the absolute temperature at 

 which it is absorbed, must vanish. Thus we have 





T+ST 



so the Peltier effect H^(T) must be directly proportional to 

 the absolute temperature T. This result, however, as Thomson 

 well knew, was contradicted by the observations of Gumming, 

 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 + $T) in a metal A is denoted by S A (T).ST. 

 The thermodynamical equation now takes the corrected form 



~ SA(T)} 



