p \a+a(l 4)5 ^^ CC^-O- The probable area which it blocks 



out is then all - CC^-Ol Thus, N = 3, y = a+a(l-0 + a{l-2C+C), or 

 for N = 3, y = all + (1-0 + (l-O'l Higher values of A' yield the 

 following areas: 



y = F{N,a) 



a 



a+a{l-0 



a+a{l-0 + ail-Cr 



N-l 



I 



N 



Pia) 



1 



1 



2 



(1-0 



3 



(1-^)^ 



4 



(l-CY 



d-o"-' «l/i-^^ 



/=o 



Thus, for any number of randomly distributed organ- 

 isms N within the beam, the total amount of the beam's 

 cross -sectional area which they will block out is 



N-l 



I 



y{a,N) = a^ (1-C) 

 /=0 



Given a hydrophotometer reading of received light 

 fraction K (or 100 K percent transmitted), we have 



K = 



N-l 



1 



1=0 



^(i_K) = a^ a-o' 



N-l 

 ^/=0 



23 



