BIOLOGY OF THE ATLANTIC MACKEREL 



197 



Table 9. — Example of the compulation of limits for 5 classes within each of which an equal number of 

 catches would be expected if the distribution of stage A eggs during cruise I conformed to a normal 

 frequency surface; and the actual and theoretical number of catches for these class limits 



2 of the example. It indicates that 755/1000 of the frequency surface is to be taken 

 into account. Then 755 is multiplied by the items in column 1 of the example, giving 

 the series of items in column 2. Successive differences in this series would represent 

 equal fifths of the frequency surface out to 755, but it is, of course, not necessary to 

 compute these differences. The corresponding catch magnitudes are secured by 

 entering table 8 in the column of "Number of catches, cumulative," and reading, by 

 graphical interpolation, from the column of "Magnitude of catch." This gives the 

 series of column 3 in the example. These represent the class limits within each of 

 which one-fifth of the catches would fall if the maximum and minimum had been 

 10,000 and 34, respectively, and the distribution of catch magnitudes conformed 

 perfectly to the distribution expected from a normal frequency surface. Since they 

 were, instead, 5,806 and 20, respectively, the factor 5,806/10,000 is used to convert 

 them from the tabular to the actual basis, giving the values in column 4 in the ex- 

 ample. Between each pair of successive figures there should be found, theoretically, 

 an equal number of catches of stage A eggs from cruise I. In the first column of 

 table 19, cruise I, the adjusted totals of individuals of stage A are given, and a count 

 of those lying between each pair of specified class limits gives the numbers in column 

 5 of the example. Since the total number of catches was 9, neglecting those below 

 20, the theoretical number for each class is 9/5, or 1.8, as given in column 6 of the 

 example. 



When the same computations are performed for the stage A eggs of cruises II, 

 III, and IV, and the actual number of catches are added together, by classes, 

 there results the series of values given under the appropriate heading in the first line 

 of table 10. There are now enough items in each class to apply the x 2 test; and the 

 probability P, that random variation would exceed the actual variation, is found to 

 be 0.85. This value would appear to be rather high; but when the work is done for 

 the remaining stages up to 22 mm. with due regard to the necessity of having fewer 

 classes for the later stages in order to keep the numbers per class high enough to use 

 the x 2 test, it is found that the values of P are distributed almost exactly as would 

 be expected, for there are 7 of them below and 8 above 0.5, and the mean is 0.53. 

 Hence it must be concluded that the catch magnitudes of stages up to 22 mm. larvae 

 are related to each other quite as would be expected had these stages been distributed 

 in the sea in conformity with the normal frequency surface. 



