46 Mr. C. V. Burton on 



Hence, if in order to establish the difference of potentials 

 P between A and B, the quantity M of electricity must cross 

 the junction, the work done by the E.M.F. E during the 

 operation is E.M., half this work being spent in producing 

 the Joule effect, and half in raising the electrostatic potential 

 energy of the system. 



But the E.M.F. E is due to molecular action in the 

 immediate neighbourhood of the junction, and, therefore, 

 when the E.M.F. E does work by causing a displacement of 

 electricity, a corresponding amount of molecular energy is 

 absorbed at the junction. 



Now, E being finite, suppose that the surface of contact at 

 the junction (fig. 2) is very small, and that the electro- 

 static capacities of the conductors are very great. Then M 

 will be very great, and so will EM. In fact, keeping the 

 junction as small as we please, we may increase EM in- 

 definitely by increasing the electrostatic capacity of the 

 system. 



But, by hypothesis, the E.M.F. E will always be maintained 

 so long as we keep to the same substances, and maintain 

 them at the same constant temperature. 



Hence, when the E.M.F. E does work, the molecular 

 energy absorbed is of such a nature that it can be supplied 

 in indefinite amount by a small finite junction maintained at 

 a constant temperature. 



There are only two kinds of energy which fulfil this con- 

 dition : — (1) Heat ; (2) Chemical action at the junction. 



First, suppose that the conductors A and B (fig. 2) are in- 

 capable of acting chemically upon one another. Then for 

 every quantity dM of electricity which crosses the junction in 

 the direction of the E.M.F. E, this E.M.F. does work EdM, 

 and an equivalent amount of heat is absorbed at the junction. 

 And, conversely, if electricity dM cross the junction in the 

 opposite direction, work will be done against those molecular 

 agencies at the junction which maintain the E.M.F. E, i. e. 

 the work done on the E.M.F. E will appear in the form of 

 heat. 



Hence, the true contact E.M.F. between two chemically 

 inactive conductors is equal to their coefficient of the Peltier 

 effect expressed in absolute measure. 



An argument sometimes advanced against this proposition 

 is substantially as follows (I quote from Professor Lodge's 

 paper in the Phil. Mag. for April 1885, p. 260) :-" When Q 

 units of electricity are transmitted against a force E, work EQ 

 is done ; also when they are transmitted up a difference of 

 potential V 1 — V, work Q (V 1 — V) is done ; but in an open 



