HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 83 



if equation (6) is followed, and 



dF= -(& + q')RdT = -(±(1 + p) + v)RdT, (16') 



if equation (6') is followed. 



Integrating from T' to T we get from (16) 



(F - F 1 ) = - (l + j^-^ (RT - R'T') (16 ) 



and from (16') 



(F ~n=-(^+ Y ^p) (RT-R' D (16.') 



The difference of potential which might, conceivably, be detected 

 by a sufficiently sensitive electroscope applied to the two ends of the 

 wire in succession would not, probably, be equal to our (F-F'); for, 

 according to our assumptions, the value of F is dependent upon the 

 attraction of the atoms for the electrons as well as upon electric 

 charge, and this action of the atoms would perhaps not be effective at 

 any distance from the metal greater than the range of ordinary 

 molecular attraction. 



Equilibrium in a Single Unequally Heated Wire 

 (with regard to both (A) and (B) electrons). 



The part played by the (A) electrons in electric conduction has been 

 considered in connection with equation (2). We must now ask what 

 they have to do with thermo-electric / 



action or thermo-electric equilibrium. 



It is to be observed that, if we 

 take our single wire as part of a 

 thermo-electric circuit like that indi- 

 cated in Fig. 2, with a very large 

 resistance, R, introduced at one 

 junction, we shall have a current 

 flowing around the circuit, though 

 conditions as near as we please to those of equilibrium exist in each 

 of the metals Mi and M». That is, we mav assume thermo-electric 

 action, bringing into play the conductive function of the (A) electrons, 

 while keeping all our equations, from (5) to (10) inclusive, just as we 

 have derived and used them with respect to the (B) electrons alone. 



