obtain this, we must know one given value for the curve besides the 

 incline of the rate of increase at point 100 and the way in which the 

 rate of increase changes » To get this value, Graham used the change 

 which was found in the fish stock during the heavy decline of the 

 landings during the first World War,, From comparison of the nimbers 

 showing the catch-per-unit-of-time before and after the first World 

 War (which a re, therefore, a measure of the density of the fish stock 

 in both periods), it follows that the stock in the North Sea increased 

 le9 times during the years 1914-18e Graham estimates the respite for 

 the fish stock during those 4 years is equal to 2.7 years of complete 

 resto The curve, therefore, should conform to the condition that 

 after 2,7 years without fishing, the density should have been increased 

 from 100 to 190. 



These three conditions are enough to draw the curve and to cal- 

 culate the maximum strength, the limit. The S-curve for the Worth 

 Sea is dravm as curve II of figure lo The limit appears to be 22 3o 

 The calculated percentages of increase at different values for the 

 strength of the stock are explained in curve I of the same grapho 



The fishing intensity during the period 1933-35 was 50 percent 

 (Graham, 1935) j this increased later to 60 percent or 70 percent 

 (Russell, 1942), The strength of the fish stock at these values can 

 be read from curve II o It shows that the point of maximum production 

 and, therefore, of optimism catch was passed already in 1903o»l3, The 

 optimum catch can be obtained with a fishing standard of 37 percent, 

 that is a fishing intensity equal to about three-quarters of that 

 during the period 1933-35o The amoimt of fish which will be caught 

 by a lesser intensity is shown by curve I (by a state of equilibrium) 

 to be 12 percent larger than the amount the fish stock could bring 

 during the period 1933-35, with a strength of 70, 



To estimate the exact size of the optimum catch we must try to 

 replace the relative values of the curves by absolute values « The 

 only absolute values which are given are the total c atches from year 

 to year,' During the period 1903-13 as well as during the period 

 1919-40, there was a state of overfishingi thus, more was taken away 

 annually from the stock than was being replaced., The given amounts 

 include the allowable catch, increased with an amount with which the 

 fish stock had declined. The progress of diminishing is expressed 

 in the progress of the density of the stock. The trawler catch-per- 

 unit-of-time shows this. Figure 3 shows the progress of the catch^ 

 per-day at sea of English steam and sail trawlers during the period 

 1919-35. English statistics are used because they have a high 

 degree of accuracy and are thought to be representative of the North 

 Sea, Amounts are given for steam as well as for sail trawlers 

 because it may be assumed that the first have increased in power and 

 the sailing ships have diminished in capacity. 



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