632 



Mr. H. E. Schmitz on th 



Various formulae have been proposed as the expression of 

 the electromotive force of a circuit of two metals in terms of 

 the temperatures of the junctions. The simplest of these is 

 the parabolic formula, in accordance with which we may 

 write : — 



(V,A)l = a 2 t + ib 2 t 2 , (4) 



(A,B)* = a 3 * + i^ 2 . , 

 Using these relations, equation (1) assumes the form 



E = atf! + a 2 t 2 + a 3 t d + § Mi 2 + 1 b 2 tj + £ bfy*. . (5) 

 To satisfy equation (2) we must have 

 ai + <2 2 + «s = 

 and b 1 + b 2 -\-b s = 0. 



Using these relations to eliminate a 2 and b 2 , equation (5) 

 assumes the form corresponding with equation (3), namely : 



E = a^h-t,) + a 3 (t 3 -t 2 )+ib 1 (tf-t 2 *)+ib 3 (tf--t 2 *). (6) 



Fig. 1. 



Equations (4) imply that the lines of the thermoelectric 

 diagram for the metals A and C are straight if the line for 

 the metal B is straight. The diagram is given in fig. 1 for 

 the case where a 1? « 3 , b 1P b B are all positive and t s >t l >t 2 . 



