274 THERMOELECTRIC CURRENTS. 



Let T 2 and Tj be the absolute temperatures between which the 

 couple works, and T the absolute temperature of any given point 

 of the conductor. At the hot junction the calorific work is H 2 I ; at 

 the cold junction H-J ; on an element of the conductor taken between 

 the temperatures T and T + ^T, this work is IvdT. Hence, sup- 

 pressing the common factor, we shall have 



a.a + r* 



T 2 T, J Tl T 



If the difference T 2 - T x is infinitely small and equal to *?T, we may 

 write 



d 



or 



i </H H o-'-o- 

 ---- + - = 0, 



T *rr T 2 T 



and, lastly, 



H </H , 



= -- \-<r or. 



T </T 



From equation (5), the second member of this equation is 

 nothing but the thermoelectrical power < (/) of the two metals ; 

 we have then 



(8) H = T*(/). 



Thus, the electromotive force of contact of two metals, and 

 therefore the Peltier effect at any given temperature, is equal to the 

 product of the absolute temperature by their thermoelectrical power 

 at the same temperature. 



We deduce from this same equation 



and, therefore, 



(9) E- TV/- p ?- 



JT, JT, T 



