214 PROCEEDINGS OF THE AMERICAN ACADEMY 



Investioations ojc Ligiit and Heat, published with Appbopbutioi* feom tm 



KuMFORD Fund. 



XIV. 



CONTRIBUTIONS FROM THE PHYSICAL LABORATORY OF 

 HARVARD UNIVERSITY. 



PAPERS ON THERMO-ELECTRICITY.— No. I. 



By John Trowbridge and Charles Bingham Penrose. 



Presented May 29th, 1883. 



In general we have, if cr denote the Thomson effect and T the tem- 

 perature, 



There are, however, certain cases in which it appears that this integral 

 is not zero. These cases occur when an abrupt variation of tempera- 

 ture takes place across any plane cutting the conductor. It is well to 

 consider the problem from several points of view. Suppose a homo- 

 geneous circuit so heated that one part is maintained at the constant 

 temperature 7', and the rest at the temperature T^, the change of 

 temperature taking place at two planes which cut the conductor. 

 The Thomson effect can only take place at these planes, and it is of 

 opposite sign at each. The only heat effect, as far as we know, in 

 this circuit, is the Thomson effect ; if there is any electromotive force, 

 we must have 



E =^ (T^ — o"b> 



a^ and o-^ being the effects at the planes. 



From thermodynamic principles, it is obvious that the absorption 

 must take place at the higher temperature T, and the evolution at T^. 

 The second law of thermodynamics gives 



This equation shows that o-^ cannot equal o-^, and in this special case 

 of a homo<^eneous circuit there must be an electromotive force. "We 



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