HALL. — ELECTRIC CONDUCTION AND THERMOELECTRIC ACTION. 81 



whence, by use of equations (1) and (6), we get 



1 



a = £ (1 + p) R 



n + q )R 



1 (I (1 + '> 



v V. (15) 



If, on the other hand, we go through the argument regarding a 

 from the point of view of thermal effusion, as expressed in (6'), where 

 (/ + 13) = -RQ + <?'), and q' = v + \p, we get 



1 



a = - 2 (1 + p) - v R = ~ 2 (1 + p) 



h 



TP 



(15') 



Now on the thermo-electric diagram, as it is usually made, we find 

 three types of lines representing the 

 various metals, all these lines being 

 straight. The character of these 

 representative lines and their inclina- 

 tions toward each other remain un- 

 changed when we make the diagram F/&. / 

 in the form shown by Fig. 1, with 

 the temperature axis vertical and 

 the entropy axis horizontal. If we 

 mark the temperature interval dT 

 on line (l)-(l) of this diagram, the 

 area under this portion of the line, 



between the two verticals extending to the S axis, will represent the. 

 amount of heat energy absorbed by the unit quantity of electricity, 



- electrons, in passing along the metal (1) through a rise of tempera- 



ture dT. This amount of heat is TdS and is a positive quantity for 

 the line (l)-(l). Evidently we have adT = TdS, and, if the (l)-(l) 

 is really a straight line, dT<* dS, and so o&T. That is, in this case, 

 the p of (15) or (15') must equal 1, and this must be true for every 

 metal which can properly be represented on our diagram by a 

 straight line. 



For the line (2)-(2) dS is zero and a also is zero. For the line (3)-(3) 



1 

 the area under dT represents the heat taken from the metal by 



electrons in going along metal (3) through a fall of temperature dT, 

 and we have a (-dT) = TdS, so that a is negative, though it is still 

 cc T, if (3)-(3) is a straight line. 

 Dealing, then, with metals represented by such lines 18 as (l)-(l) 



18 If a line is convex upward, as from my own observations I believe the line 

 for iron to be, the indication is that p is numerically > 1. 



