VON HELMHOLTZS THEORY. 449 



which traverses it. If q is the sum of the chemical energies for 

 unit electricity, we shall have 



We have seen that the electromotive force of an ordinary 

 Daniell's element varies very little with, the temperature, and we 

 shall therefore virtually have q E ; but this is not the case for all 



couples of the same kind. Thus, when silver is substituted for 



^E 



copper, we have for the ordinary temperature -7-= -0*0012 volt. 



a r 



It follows that E is less than q by about 0-36 volt, which is more- 

 over confirmed by experiment. For Latimer Clark's element we 



have about - = - o. 008 volt. 

 a I 



When the electromotive force increases with the temperature, 

 it exceeds the sum of the chemical energies. The couple tends 

 then to cool when the current passes. This is the case with 

 Von Helmholtz's calomel couple, in which the electromotive force 

 slightly increases with the temperature, or an analogous couple in 

 which chlorine is replaced by bromine. The electromotive force 

 measured is about 17 times that deduced from the chemical heat. 



1041. In order that a couple shall strictly satisfy Thomson's 

 law, we must have = 0, or l^ = 0. From this condition it follows 

 from equation (4) of 646 that 



The partial differential represents the variation of the thermal 

 capacity of the couple in consequence of the passage of unit elec- 

 tricity. The condition amounts to saying that the capacity of the 

 system is the same whether the chemical elements which enter into 

 the reactions are free or combined in other words, that for the 

 set of reactions produced by the current, the law of Wcestyn and 

 of Kopp is verified. Hence only those couples which satisfy this 

 law satisfy also the law of Thomson. 



VOL. II. G G 



