OCEANOGRAPHY AND FISHERIES 79 



F is the factor of concentration of h and I„ in marine organisms compared with sea water. 



Cr and Cn are the rates of uptake of Ir and L by the critical body organ. 



Cr=aIrfM (la) 



C„ = aI„fM (lb) 



where a is the fraction of the ingested isotope taken up by the body organ, and M is the weight 

 of marine organisms eaten per unit time. Moreover, 



dir 



dt 



dinb 



^=Cr-(K+B) In 

 Cn — B Inb 



dt 

 When the rates of uptake Cr and Cn are constant, the solutions are 



I,,=-^( 1 _e-'K-B„) +1^^^ e-.K.B,t (2a) 



1\. + D 



Inb=^(l-e-«')+I„b„e-=' (2b) 



where Irbo and Lbo are the initial body concentrations of Ir and In when t=0. 



The amounts of Ir and L in the body increase with increasing time toward an equilibrium 

 value, when t is long compared to Tpi and Tbi, given by 



I-KTB- ^^^> 



Inb=^ (3b) 



Dividing (3a) by (3b) we see that at equilibrium the specific activity in the critical body 

 organ of the radioactive isotope with respect to the non-radioactive species is 



]U_C / B \ 

 Inb Cn \K + By 



Substituting for Cr and Cn from (la) and (lb) 



U _ Ik / B \ 



Inb Inf VK + B/ 



It can be shown in a similar fashion that when marine food organisms accumulate an 

 element directly from sea water 



and therefore 



Solving for Ir 



Inf Ine \K-t-r>t/ 



Irb _ Ire / BBf \ 



U ~ U VK' + KBf + KB + BBfy 

 _Irb / K- + KB. + KB \ 



^'^~Inb^°^^^ BB, ) ^^^ 



