1899] METHOD OF TREATING VARIATIONS 417 



become smaller with the addition of every new character, and would 

 continue getting smaller if more were added, because the number n 

 increases faster than the deviations. But the relative proportions of 



2d 2 



these deviations shown under the headings of -— would remain almost 

 constant, as it does from the sixth character onwards. These propor- 

 tions show that the specimens from St. Andrews are several times 

 nearer to those from Aberdeen than to those from Grimsby. 



2d 



Further, from the columns of the simple deviations, — , we get an- 

 other important conclusion. The signs of the deviations are different, 

 and this shows that if two curves were drawn to represent the 

 deviations along the same axis of the characters of the groups from 

 Grimsby and Aberdeen, then the St. Andrews group would lie between. 

 It will have been noticed that instead of calculating the variations 

 for each character, the simple deviations are employed. The reason for 

 this is that when the average deviation is small, less than 1, as it is 

 for the most of these characters, and when therefore the average devia- 

 tions of both known groups are the same or nearly so, there is very 

 little error introduced by using the deviations directly. In this case 

 if the deviations had been expressed in terms of the probable error the 

 results would have shown larger numbers, as in the case of Prof. 



Heincke's example, but the proportions between the numbers under 



2d 2d 2 



— and — would have been almost the same. 



We may turn now from the mathematical to the biological aspect, 

 and however uninteresting the mathematical method may be to most 

 biologists the ideas which it springs from and the conceptions it leads 

 to will certainly be the reverse. Mathematical expressions for the 

 relations between the phenomena presented by living organisms, 

 figures or numbers for the facts of life and the changes in organs, are 

 utterly meaningless in themselves unless the biological standpoint is 

 carefully maintained in the foreground. And it is just in this that 

 one of the chief merits of Heincke's position lies. 



If the student of biology brings to his studies a wholesome scepticism 

 of what has hitherto been reported true or false, and yet in spite of his 

 scepticism still retains a strong desire to know and understand things, 

 he will soon come to the conclusion that the manner or method of 

 acquiring knowledge is of as much if not greater importance than the 

 actual knowledge. The phenomena of life, we say, form the raw 

 materials of knowledge, and yet the mind cannot grasp the complex 

 relations and interplay of structure with structure, of organism with 

 organism, and of those with the environment, by entering straightway 

 into the investigation of phenomena, here, there, and everywhere. Some 

 preconceived notions of the subject in hand, and even more, of the 

 right attitude of the observer to the things observed, must be formed ; 

 otherwise, however unwillingly, we shall fall into one of two grave 

 errors — either lay stress on the phenomena and pile up detail upon 



