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FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



by calculating for values of y (catch magnitudes) the corresponding values of x 2 

 (relative number of catches) over a range of y from 10,000 to 5 and at intervals of 500 

 for the first 19 classes, of 25 for the next 19 classes, and of 5 for the next 4 classes. 

 For convenience the x 2 series was converted to values giving a cumulative total of 

 approximately 1,000 (actually 999.96). This table can be used for any range of catch 

 sizes in which the maximum is not more than 2,000 times as large as the minimum, 

 by first multiplying the empirical values by 10,000 times the reciprocal of the maxi- 

 mum catch. Linear interpolation is fairly accurate in the table ranges of 10,000 to 

 5,000 and of 500 to 250; but the work is facilitated and is more accurate for all parts 

 of the range when the tabular values are graphed. 



Table 8. — Relative number of catches of given magnitudes to be expected from a •population of organ- 

 isms distributed in the form of a normal frequency surface 



In table 9 there are given, as an example, the computations involved in determin- 

 ing the class limits for dividing the catch magnitudes into 5 categories, using the data 

 for stage A eggs from cruise I. Since the sampling of the plankton usually was of a 

 portion that permitted detection of eggs down to 20 per station, 20 was taken as 

 the minimum, giving a range of 5806 to 20 for catch magnitudes (first and last items 



in column 4 of the example). Multiplying these by ' gives 10,000 to 34 as the 



5,oUO 



corresponding tabular range (first and last items of column 3 of the example). Enter- 

 ing table 8 with catch magnitude 34, by interpolation, it is found equivalent to a 

 cumulative catch number of 755, and this figure is entered as the last item in column 



