Theory of Thermoelectric and Thermionic Effects. 739 



By applying the second law of thermodynamics to a circuit 

 of two metals and substituting the values of P and a given 

 by (6) and (2), one finds, after integrating by parts, 



*i-*i-«(Vi-v 1 -^(v 1 -yo). • • • (9) 



From the energy equation the thermoelectromotive force 

 may be written in the forms: — 



T=ljJ '"' + ; (Yi -- V2 U . . . (io) 



e 



= i f fr-0i-fr»-*i)+«(Vi-r») ig(1 n 



= |v l -V,j''' + M' 9 ' ,c '- M 7^ + ^^(]2) 



*.' w 



The values in terms of J x J 2 , &c, may be derived by obvious 

 substitutions. The thermoelectric power ^-77 is given by 

 differentiating (10)— (13) respectively by the upper limit. 



-yr p 



These equations satisfy the conditions r—r = — and 



o 1 — a 2 = ^-q( -q J postulated by Lord Kelvin's theory. 



They are more general than those given by kinetic theory 

 methods which, it seems to the writer, can only be worked 

 out in rather simple cases which are not likely to exist in 

 nature. They agree with those given by Dr. Bohr when 

 the volume of the regions, within which the forces acting on 

 the electrons are appreciable, is small compared with the 

 A^olume in which these forces are negligible. This appears 

 to be the most general case which can be treated satisfactorily 

 by the kinetic theory method. The agreement in this case 

 seems strongly to support the validity of the thermodynamic 

 method, and to be subversive of the view that the assumption 

 of reversibility is an arbitrary one. 



