276 Mr Parker, On Contact- and Thermo-Electricity. [Nov. 23, 



which is exactly equal to the heat evolved in the rest of the 

 circuit. 



We can now give the principal results obtained by Sir W. 

 Thomson, who avoids entirely the question of the electromotive 

 forces of contact at the various junctions, either of two different 

 metals, or of two portions of the same metal at different tempera- 

 tures. 



Combining equation (9) with the results 



P = 0^ and 



dd\ e )~ 



de dd\ e j e 



we get Thomson's formulae 



E=\ e ^de=\\H B -H A )de^ 



F =C ■ \ do). 



dE _ dP BA ,~ ^ . 

 dd~~aW ^-^ 



From the second of these equations, we see that if the cur- 

 rent tends to cool any junction of two metals in passing through 

 it, the electromotive force will be increased by raising the tem- 

 perature of that junction. The electromotive force, as far as it 

 depends on that junction, will be a maximum when P vanishes. 

 As further increases, P will become negative and the electro- 

 motive force will diminish. The temperature T at which P 

 vanishes is called the ' neutral point ' of the two corresponding 

 metals, or of the circuit when it is composed of these two metals 

 only. 



Again, when and O are so nearly equal that we may put 

 6 Q = — t, where t is small, we have 



dD r 2 d 2 D 

 T dd + 2d6» '"' 



and therefore for a circuit of two metals 



P r 2 d fP\ 



„ P t" d /P\ 



E = T J-Jdd[w) + 



When the 6 junction is at the neutral point T, this gives Thom- 

 son's formula 



* = "!?§ ("> 



