of Thermo-electric Phenomena. 543 



-which is of the form 



X6-Y6 2 ; 

 and the neutral temperature of Camming is 



g ^ S_ A(« - tt ' )-B(/3 -/3' ) 

 e ° - Y - A(«-a')-B(/3-/3') • • • W 

 We mav write for (33) 



n=2=Y0(« o -0), (35) 



which will be precisely Tait's form (see Maxwell, p. 306) pro- 

 vided jY9 comes out to be the difference of the specific heats 

 of electricity in the two metals at the temperature 0. 

 To find @, one has from (26) 



or 



e a -iA(a-aO(^-^) ? ■ ■ • ( 36 ) 

 whence, from the definition of the specific heat (29), 



a a ±-jA(u-*y, ^ 

 similarly > . . . (37) 



<7 6 ^-jB(/3-/3')0;j 

 and therefore, (33), the condition in (35) 



jY6±(T a -a b . (38) 



is satisfied. 



The total electromotive force in a thermo-electric circuit is 

 obtained, either like (31) bv finding Hi — IJ 2 — ® a +© i; or by 



f 01 ll 

 forming the integral I ~~n~d@> anc ^ ^ s ^ am e is 



E^Y^-d^eo-ae^e,)}. . . (39) 



The law was originally given nearly in this shape by Avena- 

 rius*; but he omitted the two Thomson effects, and consequently 

 his formula was erroneous. The above form is that of Tait f, 

 who has verified it for moderate ranges of temperature. 



Tait also shows that if T ab stand for the temperature 6 at 

 which two metals A and B are neutral to one another, and 

 if <r a be equal to k a 6 (where h is a constant), then must 

 (k-lc^ + ik-k^ + ik-h)?,,^. 



Now from (34) and (37) 



(i„-A,)T oS =A(« - a '„)-B(A,-/S'o), • • (40) 

 and the cyclical sum of three, or of any number, of such terms 

 evidently vanishes. 



University College, London. 



* Pogg. Ann. vol. cxix. (1863). f Proc. R. S. Edin. 1870-71. 



