of the Electromotive Forces in a Voltaic Cell. 57 



is no longer subjected to great pressure. But 2*3 p enters 

 into the expression and is familiarly spoken of as a form of 

 energy when the stream is steady — when there is a con- 

 tinuously acting pump somewhere in the circuit. In fact, 

 then, we see that when a pound of water rises in level from 

 A to B it receives h foot-pounds of energy if h is the dif- 

 ference in level, and it receives no energy from an outside 

 source at A B ; energy disappears in the pump, and work is 

 done between A and B. Now just as difference of potential 

 in electrical things is measured as the work which must be 

 done, on unit of electricity, in taking it from one point A to 

 another B through the dielectric, so the difference of level 

 between A and B represents the work done on a pound of 

 water in taking it from A to B through the air. And just as 

 the water in being raised from D to D' gains energy without 

 any work being done on it from an outside source, so we 

 may consider that electricity in passing from copper to zinc 

 may gain potential-energy without there being any external 

 source of energy at the junction. 



The preceding is even more than an analogy. There is a 

 tendency for electricity to leave copper and enter zinc at the 

 junction, which we are now prevented from calling the E.M.F. 

 of contact, but which we may call contact-force. It is 

 measured as the difference of potential established between 

 two metals which are in contact. There is no contact-force 

 in a piece of copper or in a piece of zinc. The contact-force 

 is analogous with pressure in water. There is a sudden rise 

 in level in the pipe from A to B which corresponds with a 

 sudden rise of potential from copper to zinc. There is a con- 

 sequent diminution of pressure from A to B which corresponds 

 with the contact-force at the junction. There is no contact- 

 force in a copper wire ; and hence it is necessary to give to 

 the pipe such an inclination that the potential-energy lost by 

 the water in flowing along the pipe shall be equal to the 

 energy given out in friction. In the voltaic circuit, similarly, 

 the tall of potential-energy is known to be equal to the heat 

 produced in overcoming resistance. 



The analogy may be carried still further, for we may obtain 

 the representation of thermoelectric effects. Suppose the 

 water to be slightly compressible, then maintaining any ver- 

 tical parts of the pipe at different constant temperatures will 

 help or oppose the action of the pump in the circuit. Thus, 

 not using a pump, let there be an endless pipe, rising sud- 

 denly from A to B, horizontal from B to C, falling suddenly 

 from C to D, and horizontal from D to A. Imagine this 

 filled with a slightly compressible fluid, and that the limb 



