1891.] Mr Parker, On Contact- and Thermo- Electricity. 275 



If A be a piece of metal in the same molecular state through- 

 out whose temperature varies in any gradual way we please from 

 end to end but has the same value at both ends, the ends will be at 

 the same potential, and therefore if they be joined so as to form a 

 circuit, there will be no current produced. This is the result 

 obtained experimentally by Magnus, who found it impossible to 

 obtain a current by unequal heating in a homogeneous circuit. If, 

 however, we take a homogeneous circuit, and by filing make a 

 junction of a very thick piece and a very thin piece, it was found 

 by Maxwell that on applying a flame to this junction, a current 

 is produced. 



Now let a thermoelectric circuit be formed of two different 

 metals A, B, as in the figure, and let the temperature of every 



e^> >- B 



A 



part of the circuit be kept constant ; and O being the tempera- 

 tures of the junctions. Then the 'electromotive force of the 

 circuit' is defined to be e times the sum of the abrupt rises of 

 potential as we travel round the circuit in the direction of the 

 current. Hence since the electromotive force of contact of two 

 pieces of the same metal at different temperatures is zero, if the 

 current be supposed to flow from A to B through the junction of 

 temperature 6, the electromotive force E will be given by 



E = D-D, (9). 



For a circuit formed of several metals, we shall have 



E = XD (9)'. 



This result, which has not been tested directly by experiment, 

 has been given by Duhem and assumed by Clausius. 



When the current is steady, let I be its strength and R the 

 resistance of the circuit. Then 



E = RI, 



since the sum of the abrupt rises of potential at the various 

 junctions must be exactly balanced by the gradual fall of potential 

 in the other parts of the circuit. 



Confining ourselves, for the sake of simplicity, to the case of 

 a circuit formed of only two metals, as in the preceding figure, 

 the heat absorbed in a second at the junctions 0, O , will be 



(P - P ) /h I [{D + F B (0) - F A (0)} - [D + F B {0 O ) - F A (0 O )}] 



= 1{E+ {F B (0) - F B (0 O )} - [F A (0) - F A (0 O )}], 



