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 1 
increases faster than the deviations. But the relative proportions of 
these deviations shown under the headings of oa 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. 
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 le 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 
Dd Da? 
“and =a would have been almost the same. 
n 
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 conciusion 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 
