Then EC = ME - MCo ME is 422 million kilograms, MC iSj, in relative 

 units, 40a (see curve I in figure 1), Thus EC - 422 = 40ao PF = FN=ND-PD< 

 FN is 404 million kilograms, ND is 35a, PD = EC Thus PF = 404 - 35a - 

 422 = 40a = 5a - 18o Equation (l) then is s 



6 (422 - 40a) = 2„5 (5a - 18) = 30a 



Or 2, 487 - 257o5a 



a = 9o7 million kilograms 



Therefore, the value of the relative unit used in the construction of 

 figure 1 is knowno Each value of those curves can be converted into 

 kilograms o The optimum catch which is 40 o 4 relative units will be 

 9o7 X 40o4 = 392 million kilograms. 



It is now possible to reconstruct the progress of the fishing 

 in the North Sea between 1919 and 1940^ and if the values for a and 

 for the optimum catch are correct, then point A (lOOa) must have been 

 passed at about 1928 and point B (70a) at about 1935, while the fishing 

 standard shortly before the second World ?far must be somewhere between 

 60 percent and 70 percento 



In table 8, colxmin 13 and 14, the density is shown for each of 

 the years between 1919 and 1939. The densities were found in the 

 following manners 



The starting strength of the stock in 1919 was 190a | therefore, 

 the real strength must have been 190 x 9o7 = 1,845 million kilograms o 

 In 1919, 470 million kilograms were caughto However, the stock in= 

 creased also by a certain amount o The average strength of the fish 

 stock during that year will have been 1,845 - l/2 x 470 = 1,610 million 

 kilograms or 1^610 = 166a o 

 9o7 



From figure 1 we can see that 166a on curve II corresponds with 

 3la on curve lo This last sum shows the quantity by which a stock 

 with a weight of 1,610 million kilograms grows in one yearo It is 

 equal to 31 x 9o7 = 301 million kilograms. The starting strength in 

 1920 is thus 1,845 - 470 + 301 ~ 1,674 million kilograms. Again the 

 catch of 1920 was subtracted and the increase was calculated and added. 

 The same manipulation was repeated year after year. 



It is now apparent that the progress of the density of the fish 

 stock in the North Sea can be presented very well by an S-shaped 

 curve. According to the calculation, the value 100a and the level 

 1903-19 is reached in 1927, This is thus one year sooner than we 

 concluded from the progress of the catch-per-travel-day, A density 

 of 2 97a was reached in 1928, The variation between these conclusions, 

 arrived at in two different ways, certainly may be called slight. 



58 



