ELECTROMOTIVE FORCES IN THE VOLTAIC CELL. 



497 



Q units of electricity are transmitted against a force E, work E Q is done ; 

 also when they are transmitted np a difference of potential V — V, work 

 Q (V— V) is done; but, in an open circuit containing an electromotive 

 junction, V— V is produced by and is equal to E. Hence at an electro- 

 motive junction no work need be done by a current ; in other words, the 

 existence or non-existence of a Peltier effect has nothing to do with the 

 existence or non-existence of a local E.M.F. 



The fallacy of the argument, in either form, lies in over-precise 

 specification of locality ; gratuitously asserts as true for the junction, 

 what is only proved to be true for the whole circuit. It assumes that 

 there can be no work done at a junction if it be perfectly easy to drive 

 electricity either way across it — i.e., if there be no work done on the 

 whole. 



11. To exhibit the fallacy, consider a hydrostatic analogy. Two vessels 

 of water connected by a pipe in which is a motor of some kind, which 

 without leakage exerts a specified force on the water and maintains a 

 constant difference of potentials, but then remains stationary, doing no 

 further work. We typify it feebly in the diagram by an impracticable 

 close-fitting water-wheel driven by a weight without friction. 



Hydrostatic analogue of the true contact or Seebcck force, and of the real though 

 small difference of potential which it maintains between two metals in contact. 

 W is a weight driving a water-tight wheel until stopped by the difference of 

 potential set up. The hydraulic raising or lowering of the weight represents the 

 Peltier effect. 



V— V is the equivalent of the force exerted at the junction, and every- 

 thing is in equilibrium. It is perfectly easy for water to flow from one 

 vessel into the other under the influence of the slightest extra force, for 

 W helps the water up the hill V— V, when the flow is in that direc- 

 tion ; and, whenever the flow is reversed, it lets the water gently down 

 again, taking all its energy out of it. If water is made to flow from A 

 to B, say by pouring more into A, the weight W is lowered, or energy 

 disappears (heat absorbed) at the junction ; if it is made to flow from 

 B to A the weight is raised, or energy (say heat) is generated at the 

 junction. Thus there is a true Peltier effect at the junction despite the 

 existence of V— V and its equality to the junction force, and yet no re- 

 sistance is offered to the flow of water either way. Thus is the first form 

 of the argument controverted. 



To pump water from A to B by any other pipe would need work to 

 be done equal to Q (V-V), and to pump water against the force of W, 

 acting alone, would also need work E Q ; but when the water goes from 



1884. ^ ° KK 



