C. Bar us — Expression in Thermo-electrics. 367 



under pressure,* and in connection with the examination of 

 rock magmasf made by Prof. J. P. Iddings and myself, can be 

 reproduced by an elementary equation, dr/dd = a—br, where 

 ;• denotes the resistance, 6 the temperature, a and b are con- 

 stants, and where a is probably introduced by observational 

 errors. 



4. Following out the suggestions of §§2, 3, I tested the ele- 

 mentary expression 



de/dd=-Ae (]) 



where e may be called the thermoelectric condition of an 

 element of length of either wire of the couple, at the temper- 

 ature d. A is a specific constant for the metal, and may be 

 either positive or negative. 



Let d, d be the temperatures of the hot and the cold junc- 

 tion, and d n the neutral temperature of the two given wires. 

 Let e n be the thermoelectric condition of one of the wires at 

 the neutral temperature n , Then (1) leads to the integral 



- e = S ( 2 ) 



where £ is the base of Napier's logarithms. Hence if the two 

 wires of the couple be distinguished by accents, the parts 

 which the hot junction contributes to the total electromotive 

 force E, will be 



e A(0 -0) e! A\0-0) 



— = e , and —r=£ : 



and the cold function contributes, 



e o A(d n -e ) e > A\e -e ) 



— = « , and —^ = s 

 e n e' n 



Hence since the observed or total electromotive force is E = 

 ed=e / — (e ± e' ) in the most general case ; and since e n — e' n 

 by definition, therefore 



(3) A = e n 1 £ ± £ ~\ e ±€ ) \ ' 



which is the equation required. With reference to (3) it is to 

 be noted that A, A', d n , may be either positive or negative ; 

 hence the exponents may represent either a sum or a difference. 

 Again if m be the temperature at which E is a maximum or 

 minimum, then 



A{0 -0 ) , A'lO - \ 



Ae Kn m) ±A'e y " m >=0, .... (4) 



whence m = 6 n + * A± J • 



* This Journal, xlii, p. 134, 1891. f This Journal, xliv, pp. 242, 255, 1892. 



