432 PROCEEDINGS OP THE AMERICAN ACADEMY 



The electrical separation at a hot surface is, in general, greater than 

 that at a cold surface. Consequently, when the temperature of a 

 surface is raised, a certain amount of potential energy of electrical 

 separation appears. At the same time a quantity of potential energy 

 of superficial tension disappears. Moreover, as the surface contracts 

 to nothing, potential energy of electrical separation disappears and the 

 energy of heat appears. If the surface is kept constant, and no energy 

 is allowed to enter or leave it, the electrical energy developed by a 

 change of temperature must be equal to the decrease in k, and to the 

 increase in q of equation (/). 



The energy of electrical separation for an increment of temperature 

 dT \^ consequently 



die . rp 



for unit surface. 



If the two sides of the surface are electrically connected, the electri- 

 cal separation disappears. Nevertheless the value of P must remain 

 constant ; and the energy which leaves the surface must be replaced 

 by an equal amount of energy which can only be derived from the heat 

 at the surface. 



Consider that the two ends of a horseshoe-shaped platinum bar, 

 A B, are surrounded by a glass tube, A C B, containing dilute sul- 

 phuric acid. The ai-eas of the surfaces of contact of platinum and 

 acid are constantly equal to unity. 



In the beginning let the whole apparatus be at temperature T. The 

 total surface energies of A and B are equal, and consist of two parts 

 which are respectively equal. The potential energy of superficial 

 tension is the same at each surface ; and the electrical energy is the 

 same, since there is electrical equilibrium. 



Ijet the temperature of A be increased by d T. 



The total surface energy at A is still unchanged — aside from the 

 mere increase of heat — but the components of the total energy are 

 different. There is less energy of superficial tension, and greater 

 energy of electrical separation. Since the circuit is composed of con- 

 ductors there will be an establishment of electrical equilibrium ; and 

 the electricity separated at A from platinum to acid, will ilow toward 

 the right. To maintain the value of P at the surface A constant, heat 

 must be absorbed, and a steady current will thus be produced. 



