470 Prof. 0. Lodge on the Controversy 



the circuit by the equations 



or b dE n 



«JL== 



J T dT~T' 



therefore 



n„ 



n = ReTloff' 



Now n represents the number of active corpuscles in unit 

 volume, and this number is a function of the temperature; 

 and its rate of change probably depends on the number 

 already there and on a coefficient characteristic of the metal; 



— —aoT^, say: therefore let n a = ae aT , n b = be^ T . 



In substances whose conductivity increases with tempe- 

 rature a, will be positive, but in metals it is usually negative, 

 and at absolute zero the conductivity would rise to a maximum 

 value corresponding to the maximum corpuscular concen- 

 tration a or b. 



n = EeTlog|-f(«-/3)ReT 2 ; 



whence the neutral point is 



_ log h -log a 



and 



<r a = aReT = # a T, 

 and 



and 



E=( a -/3)Re(T 1 -T 3 )(T -KT 1 +T 2 )), 



or 



P s =*IU(T -f). 



So that hypothesis does fairly well to express thermoelectric 

 facts; but, unless the opposite sign of corpuscles is attended 

 to, it does not account for the fact that the coefficient a is 

 positive in some metals and negative in others; though it 

 suggests an opposite sign for a in metals and electrolytes, 

 because a. changes sign along with the temperature-coeffi- 

 cient of conductivity. 



To divide metals into two classes w T e must not suppose 

 that the negative corpuscles do all the travelling : if they 

 did, moreover, the Hall effect, the magnetic influence on 

 the current, corresponding to the magnetic curvature of 

 cathode rays, would be much greater than it is. The facts 

 that the Hall effect is sinall, and that it has different signs in 



