BATTERY PLACED IN A CONDUCTING MEDIUM. 255 



2. The' resistance of the battery may be neglected in comparison 

 with that of the interpolar conductor. The variation of potentials 

 in the interior of the battery is almost exactly the same as if it were 

 open. On the outside the fall of potential is continuous; and if 

 R is the resistance of the interpolar conductor, the current is 



it is then proportional to the number of couples. 



3. Finally, if the resistance of the interpolar is of the same order 

 as that of the battery, the potential rises by a constant quantity at 

 each contact, and sinks continuously, but to a less extent, from one 

 contact to the next ; the difference of potentials has a finite value, 

 less than in the case of an insulated battery, but which is greater 

 the greater the resistance of the interpolar, and by Ohm's law, 

 the current is 



268. BATTERY PLACED IN A CONDUCTING MEDIUM. We have 

 hitherto supposed that there is no loss of electricity by the lateral 

 surface of the battery. Imagine that a battery, of Volta's original 

 construction, made up with infinitely thin plates, is placed in a 

 conducting medium, and that electricity flows both from the sides 

 and from the ends ; this would be the case of a battery immersed in 

 water, if the effects of polarization are neglected. Let < be the 

 electromotive force of the battery for unit length, p the internal and 

 p the external resistance for unit length (220). 



The flow of electricity is still parallel to the generating surfaces 

 for the greater extent of each normal section of the battery, and part 

 escapes at each point, so that the equipotential surfaces are plane 

 and agree with the lateral surface, as in Fig. 55. 



Between the infinitely near points P and P', whose potentials are 

 V and V, the strength I of the current in the interior satisfies the 

 equation 



The current at each point is therefore given by the equation 



'-*-) 



