430 PROCEEDINGS OF THE AMERICAN ACADEMY 



This equation shows that the variation of the secondary electro- 

 motive force — the electromotive force peculiar to the arrangement — 

 with the temperature, is inversely proportional to the temperature. 



The analogy between this thernio-electromotive force, which is 

 caused by a change in the superficial energy, and the electromotive 

 force of an ordinary thermo-electric circuit, is thus very close. It will 

 be remembered that for a thermo-electric circuit 



dT~ T ' 



If "we accept the conclusion of Lippmann,* that the temperature alters 

 the superficial tension only by altering the difference of potential, we 

 can consider the superficial tension only as a function of the difference 

 of potential, and the difference of potential as a function of the tem- 

 perature. 



dk dk de 



dT ~Te ' JT' 



This expression is also of the same form as the one already obtained ; 

 and shows that the variation of the diflTerence of potential with the 

 temperature is inversely proportional to the temperature. 



In the case of mercury and sulphuric acid, y- is -|- up to a certain 



. de . 



point, after which it is — . Consequently, for this case, -pp is -)- up 



to a certain point, and is afterwards — . This is the same as the 

 variation of the electromotive force of a thermo-electric circuit, on each 

 side of a neutral point. 



The cases already considered point to a close relation between 

 superficial energy and the energy of a thermo-electric current. In the 

 first case, however, a continuous current could be maintained only by 

 rapid changes, or vibrations, in the surface of separation of the mercury 

 and acid. 



By considering the area of the surface to remain unchanged, and 

 by investigating only the changes in tlie potential energy of the sur- 



* Annalcs de Cliimie et de Physique, 1877, p. 275. 



