532 Royal Society of Edinburgh. 



if Mayer's hypothesis, which leads to the expression ^ ^ for fx, 



were true, the electromotive force of the same pair of metals would 

 be the same, for the same difference of temperatures, whatever be 

 the absolute temperatures. Whether the values of /x previously 

 found were correct or not, it would follow, from the preceding expres- 

 sion for 0, that the electromotive force of a thermo-electric pair is 

 subject to the same law of variation, with the temperatures of the 

 two junctions, whatever be the metals of which it is composed. This 

 result being at variance with known facts, the hypothesis on which 

 it is founded must be false ; and the author arrives at the remark- 

 able conclusion, that an electric current produces different thermal 

 effects, according as it passes from hot to cold, or from cold to hot, in 

 the same metal. 



4. If S(t'—t) be taken to denote the value of the part of 2a, 

 which depends on this circumstance, and which corresponds to all 

 parts of the circuit of which the temperatures lie within an infinitely 

 small range t to t' ; the equations to be substituted for the preceding 

 are, 



<t,=At'-t) + J$(t>-t), (e) 



at 



and therefore, by (d), 



dQ „ 1 



^+$=^9/. (/) 



5. The following expressions for F, the electromotive force in a 

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

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

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

 ticular values of 6 for the temperatures of the junctions. 



F=/ T >^=.i{e s -e T +/ T s ^} 1 



i /"S i rt i iff) 



= J{0 S (l-e-j/r ^')+/ T S 9(l-e"jA **)&} J 



6. It has been shown 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 there- 

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

 have 



where ~9 X and ¥ 2 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 uni- 

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

 metal to which ^, 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)y, if t and t' be the 



