1891.] Mr Parker, On Contact- and Thermo-Electricity. 273 



to 0, there will be no thermal phenomenon in the system except at 

 J, and the heat absorbed there will be times the increase of 

 entropy, or q0(H B - H A ). This may be written qP BA , and we see 

 that Jr BA = Jr AB , Jr CA = Jr CB -f- Jr BA - 



Again, the work done on the plates B is — \qeV B , and the work 

 done on the plates A, \qsV A ; so that the total work done on the 

 system is -%qe (V B - V A ), or - \qB BA , if D BA stand for e(V B - V A ), 

 or the electromotive force of contact. Hence, since the increase of 

 energy is \qD BA + q(F B - ^a)> we nave 



%D BA + F B -F A = --hD BA + P BA , 

 or D BA + F B -F A = P BA =6(H B -H A ) (5). 



Combining equation (5) with the identity -^ = -^ , we get 



d^BA JT TT 



dd ~ ' A ' 



d (D BA \ F B -F 

 dO\e~) 2 



de\ e )~ dd dd 0d6 y 



dDi 



d0 



y (6), 



A _ dHg _ dH^ _ 1 t\ F _ „ , 

 )~ dd d0 ~0d0 K B Ah 



and P„,= 



dD 

 The result P=0 -=%■ has been given on four independent 

 dv 



occasions : — by Prof. J. J. Thomson in his Applications of Dynamics 



to Chemistry and Physics ; by Maxwell in his small Treatise on 



Electricity, where he has abandoned the older assumption that 



P = D; by Duhem ; and, lastly, by the present writer. 



Next, let the plates A and B be of the same metal in the same 

 molecular state but at slightly different temperatures 0,0 + d0. 

 Then if V and V be potentials of A and B, Q and Q' their charges, 

 we have 



TT=U o + e{hQ'V' + lQV} + Q'F(0 + d0) + QF(0), 



cj> = cf> o + Q'H(0+d0) + QH(0). 



If therefore we suppose the change of temperature at J to be 

 so gradual that the heat conducted across the junction while a 

 small charge q passes slowly from one plate to the other, can be 

 neglected, we easily find, if X be the ' specific heat of electricity,' 

 that is, the coefficient of the Thomson effect, or %d0 the quantity 



