OP ARTS AND SCIENCES. 



429 



If the direction of tlie change of potential were reversed, the above 

 expression would represent the excess of heat evolved at the hot 

 surface over that absorbed at the cold surface. 



In the case under consideration a difference of potential is created, 

 and an electrical displacement takes place throughout the tube. Let 

 e equal the total electromotive force, and dm the displacement. 



Let R equal the electrical resistance. 



Let 



edm = Rdnv'' -\- {Q^ -\- Qs) J. 



We have seen that 



dm = — Xd Ss, 

 for a constant difference of potential ; 



edm=.Rdm^ — dd.^^dm; 



de 



dm = 



^ + 



X 



R 



This equation shows that the electromotive force e is supported by an 



electromotive force -r^' 



This electromotive force is due to the differ- 



ence of temperature between A and B, and is maintained by the 

 absorption of heat at the warmer surface. 



Let this electromotive force be represented by dE ; 



XdE=de. 



From the definition of dd. 



dT 





dk 



"We have seen that -~ is of the form. 



=zX 



dE 

 dT 



/(^) IT_ 



dE a 



dT—f(x)X 



kf(x) 



-i]i. 



