ELECTRIC AND MAGNETIC SENSES 519 



Within the fish, these currents lead— according to Ohm's law— to a 

 dorsoventral ohmic potential difference 



/ 



J v 



D 



-pJ * ds, 



with p the resistivity of the tissues, J the current density, and the minus sign 

 indicating that it opposes the induced emf. Thus, the total dorsoventral 

 potential difference (the induced emf plus the ohmic voltage drop) equals 



/ 



D 



(vX B h -pJ) • ds. 

 V 



However, because of the relatively large volume and low resistivity of the 

 seawater, the fish is electrically almost completely short-circuited. That is, 

 the ohmic potential difference effectively counteracts the induced emf, or 



f D 



I - pJ * ds 



approaches 



(v X B h ) • ds, 



r 



and the total potential difference between the dorsal and ventral receptor 

 pores 



/ (vX B ;i -pJ) • ds 

 J v 



becomes negligibly small. On the other hand, the ampullae of Lorenzini 

 move through the earth's magnetic field with the same velocity as the fish, 

 inducing along their jelly-filled canals internal emfs of 



•amp 1 



(v XB h ) • ds 1 



''pore 1 



and 



r 



,-pore 2 



(vXB h )-ds 2 

 -4m p 2 



