95 



thermo-electric pair, with the two junctions at temperatures S and T 

 differing by any finite amount, are then estabhshed in terms of the 

 preceding notations, with the addition of suffixes to denote the par- 

 ticular values of for the temperatures of the junctions. 



'S 



= j[0jl-e"'T )+7^(i-e Jt )dt] 



(9) 



6. It has been shewn by Magnus, that no sensible electromotive 

 force is produced by keeping the different parts of a circuit of one 

 homogeneous metal at different temperatures, however different their 

 sections may be. It is concluded that for this case ^==0; and 

 therefore that, for a thermo-electric element of two metals, we must 

 have, — 



where T^ and Y^ denote functions depending solely on the qualities 

 of the two metals, and expressing the thermal effects of a current 

 passing through a conductor of either metal, kept at different uniform 

 temperatures in different parts. Thus, with reference to the metal 

 to which T^ corresponds, if a current of strength y pass through a 

 conductor consisting of it, the quantity of heat absorbed in any 

 infinitely small part PP' is T^ (t) {^—t) 7, if t and t' be the tem- 

 peratures at P and P' respectively, and if the current be in the 

 direction from P to P'. An application to the case of copper and 

 iron is made, in which it is shewn that, if Y^, and Tg refer to 

 these metals respectively, if S be a certain temperature defined below 

 (which, according to Regnault's observations, cannot differ much 

 from 240° cent.), and if T be any lower temperature ; we have 



r^ 1 



J {'¥,{t)-Y,{t)}dt=ze^ +jF, 



T 

 since the experiments made by Becquerel lead to the conclusion, 

 that at a certain high temperature iron and copper change their 

 places in the thermo-electric series (a conclusion which the author 

 has experimentally verified), and if this temperature be denoted 

 by S, we must consequently have 0*^ = 0. 



