If the ratio of light received by a hydrophotometer 

 photocell to that emitted by the light source is known, it is 

 possible, with the following assumptions, to calculate the 

 number of organisms present within the light beam. The 

 assumptions are: 



1. Only one type of organism or light-absorbing entity 

 is present in the beam and its average cross -sectional area 

 is known. 



2. The organisms are optically black, and no diffraction 

 occurs at their boundaries. 



3. The organisms are randomly distributed within the 

 beam. 



The following calculations were made: If a equals 

 the average absorption cross -sectional area of the individ- 

 ual organism, /3 the cross -sectional area of the light path, 

 and y the total cross -sectional area blocked by all the 

 organisms, then ^ represents the fraction of the beam 



blocked by all organisms present and2-2 represents the 



unblocked fraction of the emitted light which reaches the 



photocell. Since -—and /3 are known, it is necessary only 



to calculate y = F(N,a,fi) to determine N, the number of orga- 

 nisms within the beam. The approach to determining -y = F(N,a,^ 

 is statistical. 



If only one organism is present in the beam, then 

 the probability of its blocking out light equal to its own area 

 is 1, and the area it blocks is a . Thus, for N = 1, y = a. The 

 probability of a second organism's blocking exactly its own 

 area is no longer 1 because of the presence of the first, but 



is cZ2= 1-- which is nearly, but not quite, equal to 1. If 



- = C' then the probable area blocked by the second organism 



is a{l-0 and for N = 2, y = a+ad-O- 



The probability that the third organism will block 

 out exactly its own area is, by the same reasoning. 



22 



