A. D. Darbishire 
13 
fairly assume for r the value so often found by Pearson and his pupils, and we will 
therefore write r = ^ ; so that we have 
4^16 
which may clearly take a great number of values according to the value of yu., 
ranging from 0 when /ij = 0 to 1 when fii = cc . 
We have found the correlation between a variable group of selected parents, the 
mates being invariyble. To find the correlation between these invariable mates and 
their offspring we must write fii = 0 ; and we have, remembering that p^.^ = - 1, 
( I 
and %,' = a.^\l-7--^ + ''''^' 
4 
and writing r = ^, we have 
^/ 
3 Ua' 
4 "^16 
In the attempt to determine correlation between the invariable coat-colour of 
an albino mouse and the colour of its young, we meet with the difficulty that the 
correlation coefficient takes the indefinite form ^, and cannot therefore be directly 
evaluated. The only character of an albino connected with its colour which can 
be evaluated is ancestral purity or impurity, that is the absence or presence of 
pigmented individuals in its ancestry ; and if the albinos be classified into pure 
and impure it is found that tlie correlation between the presence of pigment in 
their ancestry and the amount of whiteness or the depth of colour in their hybrid 
children is invariably negative (cf. Tables VI. and VII.). On any theory of gametic 
purity the correlations should of course be zero ; they are in fact of quite 
significant magnitude, and considering the probable error of the method adopted 
they are not unlike. The values obtained are : 
Between purity of albino parent and 
(a) Amount of white coat in hybrid — 0'21 
(6) Colour of coat ... - 0-16 
the differences being well within the probable error of the method. 
