284 Prof. Thomson on the Dynamical Theory of Heat. 

 have 



n(T)=n(T'), 



if the temperatiires were equal, since the Peltier phsenomenon 

 consists, as we have seen, of equal quantities of heat evolved or 

 absorbed, according to the direction of a current crossing the 

 junction of two diflferent metals ; and if these quantities be not 

 actually equal, we may consider them as particular values of a 

 function II of the temperature, which depends on the particular 

 relative thermo-electric quality of the two metals. Accordingly, 

 the preceding notation is reduced to n = 2, Ti = T, T2 = T', 

 n, = n(T), n2= -n(T') ; and we have 



fTo TTi CTi rv 



Jt, Jt, JTo ^'T 



and similarly for the integral involving -. Hence the general 

 equations become 



F=j|n(T)-n(T') + ^'^(o-,-o-2y^J- . . (13) 



j]^)_iim+j;^».,=o .... (14). 



If in the latter equation we substitute / for T, and differentiate 

 with reference to this variable, we have as an equivalent equation, 



ii) 



\ t / a■■^— a. 



This last equation leads to a remarkably simple expression for 

 the electromotive force of a thermo-electric pair, solely in the 

 terms of the Peltier evolution of heat at any temperature inter- 

 mediate between the temperatures of its junctions ; for we have 

 only to eliminate by means of it [cTi — a^ from (13), to find 



fT n 



dt (17). 



116. Let us first apply these equations to the case of a thermo- 

 electric pair, with the two junctions kept at temperatures differing 

 by an infinitely small amount t. In this case we have 



