296 Prof. Thomson on the Dynamical Theory of Heat. 



combination of solid conductors must he zero, if all the localities 

 in which they are produced are kept at the same temperatwe. 



Cor. 1. If in any circuit of solid conductors the temperature 

 be uniform from a point P through all the conducting matter to 

 a point Q, both the aggregate thermal actions and the electro- 

 motive force are totally independent of this intermediate matter, 

 whether it be homogeneous or heterogeneous, crystalline or non- 

 crystalline, linear or solid, and is the same as if P and Q were 

 put in contact. [The importance of this simple and elementary 

 truth in thermo-electric experiments of various kinds is very 

 obvious. It appears to have been overlooked by many experi- 

 menters, who have scrupulously avoided introducing extraneous 

 matter (as solder) in making thermo-electric junctions, and who 

 have attempted to explain away Cumming's and Becquerel's 

 remarkable discovery of thermo-electric inversions, by referring 

 the phsenomena observed to coatings of oxide formed on the 

 metals at their sui'faces of contact.] 



Cor. 2. If n(A, B), n(B, C), n(C, D), n(Z, A) denote 



the amounts of the Peltier absorption of heat per unit of strength 

 of current per unit of time, at the successive junctions of a cir- 

 cuit of metals A, B, C, . . . . Z, A, we must have 



n(A, B)4-n(B,C)-f — +n(z, A)=o. 



Thus if the circuit consist of three metals, 



n(A, B)+n(B, C)4-n(C,A)=0; 



from which, since 11 (C, A) = — n(A, C), we derive 



n(B,C)=n(A, c)-n(A, B). 



139. Now, by (19) above, the electromotive force in an ele- 

 ment of the two metals (A, B), tending from B to A through 

 the hot junction, for an infinitely small diiference of temperature 



T, and a mean absolute temperature t, is -^ — t, and so for 



every other pair of metals. Hence, if <j!>(A, B), 0(B, C), &c. de- 

 note the quantities by which the infinitely small range r must 

 be multiplied to get the electromotive forces of elements com- 

 posed of successive pairs of the metals in the same thei'mal cir- 

 cumstances, we have 



«^(A, B)-f <^(B,C)+ +0(Z,A)=O; 



and for the case of three metals, 



_</>(B,C) = <^(A,C)-</,(A,B). 

 Since the thermo-electric force for any range of temperature is 

 the sum of the thermo-electric forces for all the infinitely small 

 ranges into which we may divide the whole range (being, as 



