HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 91 



the last term, 

 from (29) 



If i?i = R 2 , this last term disappears and we have as 



F 2 — Fi 



RTlog-. 



J n 2 



The difference of virtual potential expressed by equation (29) 

 applies to the (A) electrons as well as to the (B) electrons; for it is to 

 be remembered that, even when we have been dealing with a tem- 

 perature gradient, the rate of change of F has depended not at all upon 

 x, though the Thomson effect was found to be a function of x, as the 

 Peltier effect doubtless will prove to be. 



The Peltier Effect: — Referring to equation (17) we see that, when 



e 



electrons pass reversibly at temperature T from A/\ to Mo, the gain 

 of total energy of these electrons, which must be equal to the amount 

 of heat energy absorbed by the electrons from the metals at the junc- 

 tion, is 



2e e e 



3 + 2.n 



2e 



e 



(1— a*)*i 



(30) 



Substituting for (F 2 -F x ) from equation (29), we get 

 T 



Q = 



1 



>h 



. T R 2 ni — Ritio, 



H • - - log - 



e ni — n* n» 



+ 



(1— .r 2 )*2 — (1— .n)$i 



(31) 



This is the Peltier effect heat at the junction of temperature T. 



With thermal effusion equation (30) would hold unchanged, but 

 (31) would become 



Q= T (.r, R 2 - xi R,) + - 

 e e 



+ 



1 



(l-a- 2 )$ 2 -(l 



i?2 »i — Ri no 

 ni — ?i 2 



- Xi) <f>i 



(31') 



The Volta Effect: — It is evident that the equilibrium which we are 

 discussing between two metals at their junction is of the mobile type, 

 the superior gas-pressure of the electrons in one metal maintaining a 

 movement of individual electrons from this metal to the other, while 

 the superior "virtual potential" of the second metal has become great 

 enough to maintain an equal movement of other individual electrons 



