of the Fishery Board for Scotland. 



277 



If this notion of the normal condition, or average as we should call it 

 now, had been rigorously worked out, there can be little doubt that it 

 would not only have altered the conclusions reached by Matthews, but 

 have forestalled to a certain extent the method now used by Heincke. 

 The turning-point of the whole investigation, in fact, depends upon the 

 rigorous determination of this normal or average condition. 



In effect, Matthews inclined in the opposite direction— dividing the 

 ground of variability into more numerous divisions, with the notion, 

 apparently, of showing that if two races could be taken from this field of 

 variation, so might three, or even a dozen. The result was that the 

 number of individuals under each heading diminished, rendering it more 

 and more difficult to see any differences, for the mind cannot grasp such 

 a great number of particulars. If the number of divisions be increased 

 they should be increased ad infinitum, i.e. the characters should be 

 represented as they are in nature. There must be some guiding principle 

 in order that the mind should be able to grasp the meaning of the 

 variations, and the simpler the principle the more likely is it to represent 

 the reality. One can understand, then, the position of Matthews — there 

 was difference, and yet no difference. At first sight one saw the 

 differences ; on scrutinising closer, endeavouring to grasp the meaning of 

 the variations, and endeavouring to take into account the infinite number 

 of possibilities that lay outside the bounds of the observed number, the 

 mind became more and more confused, and the only conscientious decision 

 was to examine an enormously larger number of specimens at every 

 season of the year, and for many years consecutively, before a definite 

 answer could be given. And such, in fine, were the conclusions of 

 Matthews. 



What, then, is the method of Heincke % Simply, to concentrate the 

 attention on the normal condition or average, to carefully eliminate all 

 errors likely to arise by imperfect observation or arising from different 

 ages, sex, seasons, or regions ; to get the average clear and distinct so as 

 to allow it to speak for the specimens examined ; and then further, by 

 the mathematical calculation of the possibility of error contained within 

 it, allow it to speak for the whole tribe, or race, or even species. 



As an approximation to this method the number of divisions in the 

 above Table, given by Matthews, may be reduced to two. 





Winter. 



Summer. 



Ratio of Fin Position. 



•751 to 795 



•796 to -839 



•751 to -795 



•796 to -839 





M.M. 











r Body. 



150 to 169 

 170 to 189 



50-0 

 70-0 



50-0 

 30-0 



50-0 

 29-6 



50-0 

 70-3 



Length ol 



190 to 209 

 210 to 229 

 230 to 249 



61-4 

 56*7 

 44-8 



38-6 

 433 

 55-2 



23-1 

 10-8 

 20-0 



76-9 

 89-2 

 80-0 



Percentage of all 

 Lengths. 



56-6 



43-4 



26-8 



73-2 



This Table * shows more clearly the difference between the two — 



* " Naturgeschichte des Herings," p. 24 et seq., on which this criticism is for the most 

 part based. 



