the case in fresh water, then (7i/<TyM>^- This means that 



/__iZw < , 3 



^ (Tf + 2a^ ' ^ o-f /(r„ + 2 ' ^ 



and the head-to-tail voltage in the fresh water is less than EqL. When the surrounding nnedium is 

 sea water (rf/(r\^,<l and the factor becomes greater than 1 so that the head-to-tail potential in sea 

 water is greater than EoL. 



The electric field Eg is the field that must be applied to produce a given head-to-tail potential, 

 V^. From eq. (10) this field is 



E,=^(^il^f^^). (II) 



Thus, for a fixed Vl, the field Eq varies inversely with the length of the fish and the conductivity of 

 the water. 



These results are qualitatively correct but due to the crudeness of the nnodel can give only a 

 rough estimate of the magnitudes involved. If we assume a ratio of conductivity of sea water to fresh 

 water of around 600, and the conductivity of fish intermediate between these two so that ((rf/o-^) sea = 

 1/25 and (crf/crw) fresh = 25, then the ratio of the electric fields required in sea and fresh water to 

 produce the Scime head-to-tail potential on a given fish is 



(Eq) sea 1/25 + 2 _ 2.04 



(Eq) fresh 25+2 27 " ' 



Under these assumed conditions the field in sea water would therefore need to be about 1/10 as large 

 as in fresh water. 



Current Density 



The current density in the fish is given by the product of the conductivity of the fish and the 



electric field in the fish, or Jf = ufEf. But Ef = - ^^f so that 



dz 



Ef = £„( TJ^-). 



" o-f + 2cr^ 

 Making use of equation (10) this is reduced to Ef = Vl/L. Thus 



Jf = ((rf/L)VL. (12) 



The current density in the fish is a constant (o-f/L) times the head-to-tail potential. These two 

 parameters are therefore equivalent and neither one can be said to be responsible for the physiological 

 response of the fish apart from the other. 



23 



