Ca =|[A(1 - u) + reB] (1 - r^) + reBd - feid - r^) + Tb 8(1 - re)' (12) 



represents the remaining contaminant in section A. 



The terms in (12) can be rearranged to give the equivalent expression 



C3 = A(l-rA)^ + rBB[(l-r^)' + (l-rAXl-rB) + (l-rB)']. (13) 



In (13) the sum involving the terms (1-r^) and (l-r_) is, except for 

 other constant ternris, similar to the expanded form of 



[(l-r.) + (l-rB)f-" 

 We can, therefore, write for the contaminant remaining in A at the 

 end of n tidal cycles 



Cn = A(l-rA)" + rBB[(l-r^f ~+(l-^)""(i-rB)+ ,,,. 



+ (l-r.Xl-rBf-^l(i-rB)^"-"]. ^ ' 



This last expression is too complicated to be of practical use. If, in 

 the second member on the right of (14), r^ and rg are replaced by 



we get 



f;fcrA ^Tr ;» ^- fA+re (15) 



2 



Cn = A(l-rA)" + nrB(l-r/" " . (16) 



On dividing and multiplying the second member on the right of (16) 

 by (1-r), we get 



Cn = A(l-rO" + (-Y37) B(l-r)". (17) 



n being the number of tidal cycles. 



Now, the numerical values of r^ and rg in practice are expected 



to lie between 1/10 and 1/50. When substituted into a relation such 



as T 



(1-r)^ * 



these values give ~^^~To' =0.3487, 



* L(l — r)T= _ - = 0.367, where e is the base of the natural logarithms. 



r-n " /i./lO ° 



