HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 95 



is strictly analogous to measurement of the e. m. f. of a galvanic cell 

 in open circuit. 



Our preceding discussion suggests two expressions for this net 

 e.m.f. of the circuit. On the one hand, since we begin and end with 

 the same metal, Mi, at the same temperature, 7", the difference of F 

 between these two terminals must be independent of the specific 

 attraction of Mi for the electrons, and must therefore represent the 

 charge-difference of potential, the difference of potential in the ordi- 

 nary sense, between the terminals. Accordingly we have for the 

 open circuit of Fig. 8, 



B 



T 

 E 



-if*- 



e 



'' Bmi ~ R ^log r ± + 2{Ri-B*) 



7li — Tin, W2 



> + 1 -f>-( 1 + rf-J 



(34) 



r 



e 



R' 2 n'i — R'm'i , n\ , , , . 

 7 log — 4- 2 (R i - R 2 ) 



n\ — n'2 " n-2 



-( 1 + r ^KK 1 + if> 



Equation (34'), from (16') and (29'), for the case of thermal effusion, 

 would differ from (34) only in having, as the first term within the 

 brackets containing v, | instead of 1, and in having f instead of 2 as 

 the coefficient of the (R\-Ro) and (Ri'-R/). 



The other way of getting an expression for E is to integrate dQ from 

 A to B in Figure 8, assuming now that a current, due to the thermo- 

 electromotive-force, is flowing in the circuit, with sufficient resistance 

 between A and B, at the low temperature part of the cycle, to absorb 

 there practically all the work done by this current, the resistance of 

 the rest of the circuit being negligible in comparison. But, if we 

 perform this integration, we find that the expression obtained for E 

 reduces to precisely what we already have in (34) or in (34'), as of 

 course it should. 



If R were a constant and the same for both metals, and if vi were 

 equal to v 2 , we should get from each of these equations 



E= [ (T- T) Rlog-. (35) 



That is, E would be simply proportional to (T-T'); but in order that 

 this relation may hold we must have the representative lines of the 

 two metals, on the temperatuVe-entropy diagram, the same distance 



