338 Dr. J. Hopkinson on the Seat of the 



Thomson proved that this follows from the fact of thermo- 

 electric inversions and the second law of thermodynamics, 

 and verified the inference by experiment, his reasoning being 

 quite independent of any hypothesis. 



Suppose wires of metals X and Y are joined at their extre- 

 mities, and the junctions are kept at temperatures t 2 , t\. The 

 observed electromotive force around the circuit is/(£ 2 )-~/(£i) 

 or within limits according to Tait, B(£ 2 — ^)— ^C(t 2 2 — t x 2 ). 

 The work done or dissipated by the current when unit of 

 electricity has passed isf(t 2 ) — f{h)> and this is obtained by 

 abstraction of heat from certain parts of the circuit and 

 liberation of heat at other parts by a perfectly reversible 

 process. Let F(£ 2 ) be the amount of heat which disappears 

 from the region surrounding the junction t 2 when unit of 

 electricity has passed from X to Y. Let an element of the 

 wire X have its ends at temperatures t and t + dt, and let the 

 quantity of heat abstracted from this element when unit of 

 electricity passes from t to t + dt be represented by <j>(t)dt, 

 and let the same for Y be represented by ty(t)dt. By the 

 first law of thermodynamics we have 



F('*) + f V(*)*-F(*0 + f %(t)dt=f(t 2 ) -/ft), 



and by the second law, since the transference of heat from 

 part to part is reversible, 



F(* 2 ) A 2 -F(OAi+ f%(0/* • dt-\%(t)/t . dt=0. 

 Differentiating we have 



F(«) + *(*)-*(*) =/(*),' 



whence 



fF(«) -«/(*) = Bt-W, 



\ct>(t)-ir(t)=tf>(t) = Ct. 



This really contains the whole of thermoelectric theory 

 without any reference to local differences of potential, but 

 only to electromotive force round a complete circuit. But 

 when we come to the question of difference of potential 

 within the substance at different parts of the circuit, we find 

 that according as we treat it in one or the other of the 

 following ways we may leave the difference of potential at the 

 junctions indeterminate and free to be settled in accordance 

 with hypotheses which may be found convenient in electro- 

 statics, or we find it determined for us, and must make our 

 electrostatic hypotheses accord therewith. 



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