9 - 



B. HELLAND-HANSEN 



It is necessary for a proper solution of the problem in question to assume 

 that the catches from the different areas are representative. Unfortunately this is 

 very far from being the case with our material, which may actually give a false 

 impression for many of the areas even as regards quite a short period of time, 

 owing to the trawl-hours being far too few. When we come to a longer period, 

 such as one or more years, we are faced by another uncertainty, as the different 

 portions of that period are unequally represented. To get mathematical exactitude 

 we should require for such inequalities a new series of factors of proportion one 

 for each portion of the period. 



It will therefore be impossible by means of our material to solve a problem 

 like this one at all correctly; and it will be absolutely useless to undertake a 

 thorough mathematical study such as the above. I have therefore confined myself 

 to making some calculations of the total average [i.a) or the mean average 

 [m . a) without taking into account the factors mentioned. The values obtained 

 by this means merely give us an expression illustrating the composi- 

 tion of the material examined, and not an exact expression of the 

 general state. This part of our work must therefore be considered as merely a 

 first attempt to solve the important problems relating to the real numbers of the 

 different species at different times in the North Sea and its component parts. 



It is of course absurd to imagine that material sufficient to solve problems 

 like these could be obtained by a few small steamers. Compared with the great 

 extent of the waters to be examined their capabilities must at all times be small. 

 And the research steamers moreover have only been able to take part in this 

 work during part of the year. A point of great importance however has been 

 that they could fish in all localities irrespective of the number and size of fish. 

 Fishing steamers are forced in nearly every case to fish where the catch will best 

 repay them: or in other words they are bound to avoid the grounds where the 

 amount of fish is small. They are practically compelled therefore to search for those 

 places where they can catch the greatest possible quantity of the largest sizes. 

 Hence fishing steamers will never give us a true picture of the average occurrence 

 of fish within the different large areas. Their returns would show too high 

 figures for us to try to find from their catches the average aggregate per unit of 

 space in such a large area as the North Sea. It is not from them that we will 

 be able to get the requisite knowledge regarding the large areas, which they 

 have avoided in their search for more prolific fields. 



No doubt some similar sources of error will be present in our material too, 

 though they will not be anything like so serious. Even in a comparatively minor 

 area like the Great Fisher Bank there will be such a want of uniformity in the 



(a -\- b -\- c \ . , 



j_a, ) will only be right if the ratio between 



/ m n \ 



the sizes of the areas is equal to the ratio between the number of trawl-hours I — — 'a — y } ' 



- + - + - 



directly-found mean average ? ^ will be different: it will only be correct, when the areas 



3 

 are equally large (m ^ ti = o), and not otherwise. 



