40 PROCEEDINGS OF THE AMERICAN ACADEMY 



effects, if any, which vary as the first power of the cuiTent strength, 

 taken by themselves, are subject to the second law of thermodyna- 

 mics." 



This law gives : — 



ttI tt'I ^ 



6 and 6^ being the absolute temperatures of the hot and cold junctions. 



•••:-=^ . (3) 



C being a constant, depending only on the nature of the metals. 



In accordance with this, the electromotive force in the circuit 

 =. G {6 — ^j) .*. it would be proportional to the difference between 

 the temperatures of the junctions. 



" Now, this conclusion is wholly inconsistent with the existence of 

 thermo-electric inversion. We must, therefore, either deny the appli- 

 cability of the second law, or else seek for reversible heat effects other 

 than those of Peltier." This was essentially the reasoning that led 

 Thomson to the discovery of the Thomson effect. Before questioning 

 Thomson's conclusion, it is best to consider the formulge which are 

 deduced from his hypothesis. 



Suppose we have a circuit of two metals. Let the heat absorbed by 

 the Thomson effect in passing from a point at temperature ^ to a point 

 at temperature -\- d9 in one metal be cr-^dO per unit current per unit 

 time. Let <j^d6 be the corresponding expression for the other metal. 

 cTj and o-j are functions of the temperature. They depend on the nature 

 of the metals, but are independent of the form or magnitude of the 

 section of the conductors. These effects are proportional to the first 

 power of the current strength. 



By the first law of thermodynamics : — 



El + Tt/— 7r'/+ / / (o-i — (To) dQ = RP («) 



J a' 



7 = 



i? + ^ _ ,,' -^fy^ - a-,) d6 ^^ 



R 



If ^ = we have as the electromotive force of the thermo-electric 

 current, by the same reasoning as before : — 



= ^ _ ^/ _|_ r(^j _ ^,) dO (y) 



J a' 



