2 Mr. J. Swinburne on some 



and h for heat. If there is really local heating this will be 

 negative. There is no work done by the homogeneous 

 electrolyte, and the work done on it, in overcoming its re- 

 sistance, is assumed to be inappreciable. The work done on 

 the coulomb passing from the electrolyte to the_ plate forming 

 the pole p is similarly E +E ,. We have thus 



E = E +E + E ,+E h . 



pc ' no ' ph ' nh 



First assume that the chemical work done is not dependent on 

 the temperature of the cell. Let it discharge one coulomb 

 at temperature X and do work equal to E joules ; ~E e being 

 the electromotive force of the cell at that temperature. Of 

 this work E,^ -fE^ is supplied by chemical changes, and 

 E^+E^ by cooling of the cell. Let the cell now be 

 heated to the temperature 6, and let it be treated as a 

 secondary element, and charged with one coulomb. The 

 work done upon the cell is then E ; so 



E = E nC + E pC + E nA + E phe . 



The chemical work E nc9 and E pc6 is common to both pro- 

 cesses. If E0 were equal to E , the same work would be 

 done at the two temperatures, or E^ + E^ would be equal 

 to E nA + E P £9. 



But on letting the temperature of the cell fall to X again 



— — l (E„m + ^jphe) is available for external work ; so that we 



should have perpetual motion. E must therefore be greater 

 than Efl i? so that a margin is allowed for the available work. 

 We thus, by simple reasoning, arrive at Helmholtz's equation, 



The electromotive force needed to do the chemical work 

 may also vary with the temperature. For instance, if the 

 chemical changes involved in discharging are brought about 

 in a calorimeter at different temperatures, different heats may 

 be evolved. Suppose E nc and E ?c are less at a high tempera- 

 ture, and suppose at the lower temperature l there are 

 no Peltier effects at the plates, so that, for that temperature 

 at least, the cell obeys Sir William Thomson's law. If the 

 cell could be charged at with a low electromotive force of 

 E C 0, needed to bring the chemical changes about, and then 

 discharged at 0, with a higher electromotive force, perpetual 

 motion would be obtained. There must therefore be an 

 absorption of electric energy at 6 in addition to that needed 



