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



operation similar to that just described. Then since dU , d<f> , dW, 



00' 

 and edZ -^- are the same as before, we obtain 

 r 



dU-d A d<f>-dW+ edZ^ - Q A dF A - ... 



+ Q A A dH A +Q B A dH B + ., : =O. 



These two relations being true for all values of Q A , Q B , ..., it 

 follows that 



dF\ 

 d6 A 



dJL 



dd. ' 



.(3). 



To obtain the theory of the Peltier effect and the correspond- 

 ing change of potential, let two long wires A, B, of different metals, 

 be joined together at J, and also connected, as in the figure, with 



Iron 



B 3 & 



Iron 



two plates A, B, which are respectively of the same metals as the 

 two wires. Parallel and opposite to these two plates place equal 

 plates of any the same metal, as iron, and connect the iron plates 

 by long iron wires with each other, or with a large distant mass of 

 iron in the neutral state, so that the two iron plates are always at 

 potential zero. Also, to make the calculations simple, let us 

 suppose the air exhausted about the plates ; but, to make the 

 results general, the junction J must be surrounded by air, and to 

 prevent the air coming near the plates, it must be enclosed in a 

 bag and the junction J and the bag kept at a great distance from 

 the plates. Then when the system is at a uniform temperature 0, 

 if Q B , Q A be the charges of the plates ; V B , V A the potentials ; U 

 and <fi the energy and entropy of the system, we have 



•(4), 



U=U + e [IQ B V B + iQ A V A ] + Q B F B (6) + Q A F A {6) 

 ^ = <f> o + Q B H B (0) + Q A H A (e) 

 where U and </> will remain constant in what follows. 



If now by slowly moving the plates B nearer together and slowly 

 separating the plates A, any quantity of electricity q be made to 

 pass slowly from A to B against the abrupt rise of potential V B — V A 

 at J, and the temperature of the system be kept constantly equal 



