274 Mr Parker, On Contact- and Titer mo- Electricity. [Nov. 23, 

 which corresponds to P BA of equation (5), 



€ (V'-v) + ^dd=td0=e~de. 



do do 



Hence t " e W"fe- | (7). 



and therefore V — V = J 



The result F' — V = 0, which asserts that there is wo electro- 

 motive force of contact between two pieces of the same metal at 

 different temperatures, is of the utmost importance. At first 

 sight it may seem to be in contradiction to experiment ; but on 

 closer examination, as we shall shew later on, this is found not to 

 be the case. 



Equations (5), (6), and (7) contain the whole theory of the 

 Peltier and Thomson effects. They enable us to discuss the 

 properties of themoelectric circuits, and the results thus obtained 

 include all those of Thomson and others which have been tested by 

 experiment. After shewing this, we will point out the close 

 analogy between our theory of thermoelectric circuits and Helm- 

 holtz' theory of the galvanic battery. Then we will consider some 

 experiments bearing on our theory. 



In the first place, we obtain, from equations (6) and (7), 

 Thomson's result 



d fJr Bi \ 2< B — z< A /gv. 



d6 



Next, let two pieces A, A', of the same kind of metal, be con- 

 nected by a piece B of a different kind of metal, and let the free 

 ends of A and A' be at the same temperature 6, while the junctions 



a, 



A B A' 



of B with A and A' are at the different temperatures 6 X , 2 , re- 

 spectively. Then since there is no electromotive force of contact 

 between two pieces of the same metal at different temperatures, it 

 follows that, in the state of equilibrium, the potential of the free 

 end of A' will exceed that of the free end of A by 



This will not generally be zero, and therefore, as experiment also 

 shews, if a circuit be formed by joining the free ends of A and A', 

 equilibrium will be impossible and there will be a current, called 

 a thermoelectric current. 



