MATHEMATICAL TREATMENT 



This study is based on the assumption that organisms 

 in the water will reduce the intensity of a beam of light. By 

 considering their sizes and population density in the volume 

 of water through which the light passes, we should be able 

 to treat the problem mathematically. By the method of least 

 squares, lines were computed for the scatter diagrams de- 

 picting the numbers of organisms or entities versus light 

 transmission for Gymnodinium flavum and total microconstituents. 

 Operations I and II (fig. 8). 







10 



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100 

 



10 



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50 



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I 



1 1 1 1 



III! 1 III! 



MM 1 III 



- 







LEAST-SQUARES LINE - 



- 







^ ^y^* 



- 





1 STANDARD DEVIATION 



^^^^^^x ' 



- 





— • 



^y 



^"" 





- 



• 





/ 







^^ • i 



n STANDARD DEVIATION. 



A 



1 



1 1 ^ 



1 1 1 1 1 III! 



1 1 1 1 1 III 



"T 1 1 1 — I I I I I 



n 1 1 — I — I I M I 



"T 1 1 — r 



LEAST-SQUARES LINE 



STANDARD DEVIATION 



1 STANDARD DEVIATION 



J Lj^U I I I I I I Li. I I I I I I M 



I I I 



10 20 



50 100 200 



500 1000 2000 



5000 



Figure 8. Least-squares lines illustrating the relationship between light attenuation and 

 number of microentities. A. Gymnodinimn flavum, Operation I, S. Gymnodiniian flavum, 

 Operation II. 



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