of Thermo-electric Phenomena. 539 



the assumptions founded on the model give for the electromo- 

 tive force developed at junctions, and to see if these values 

 satisfy the conditions which Thomson has laid down for them 

 from thermodynamic principles. Consider, therefore, a junc- 

 tion of two metals A and B, at the temperature 6, whose re- 

 sistances are r a and r d , such that r' a and r" a are the positive 

 and negative resistances respectively of the metal A (referring 

 to § 30 for an explanation of these terms), and r'b, v" b of B ; 

 also let v a and v f a be the out and in velocities (§ 29) of the 

 molecules of the metal A, and Vb and v' ' b those of the metal 

 B : then the force exerted on the positive cord is 



v--=(v*-<y-(v-<y>- ■ ■ ■ (2i) 



Now in § 29 we agreed to consider the difference of the out 

 and in velocities to be proportional to the absolute temperature 

 in any particular metal * : hence we shall have 



similarlv for the force acting on the negative cord we shall 

 have 



Hence the balance of force useful for urging the cords is 



U = F-F' = e{A(r' a -r" a )-B( l -> i -r" i )}. . (22) 



-j 



Now (§ 24) r is of the form h — ^— ; and from what was 



said in § 30 it is plain that h must not only vary for different 

 substances, but must have in general different values for the 

 positive and negative cord in any one substance. Call these 

 values h! and A x/ , so that h = h' + ti / . A also changes from one 

 substance to another, and so does a ; but I shall assume that 

 the latter is constant as regards the positive and negative cords ; 

 if, however, the sign of the specific heat of electricity in a sub- 

 stance were found to depend upon the temperature, then a 

 must also be split into two parts a! and a" . At present I shall 



* The account given in § 29 of the cause of the difference between the 

 out and in velocities at a junction cannot be held to apply satisfactorily 

 to the case of a junction of two different metals 5 for it makes the thermo- 

 electric power of a metal to depend on the substance with which it is 

 associated, instead of being a simple property of each individual metal and 

 its temperature — as it is known to be, because the metals can be arranged 

 in a thermo-electric series at any temperature. Hence, whatever influence 

 difference of atomic weight may have in producing the unsymmetrical 

 action very reasonably to be expected at a junction, it cannot act quite in 

 the manner suggested in § 29 ; for the difference between the out and in 

 velocities of any particular substance must really depend only on its own 

 physical properties, and not on those of the substance with which it is 

 put into contact. 



