A. D. Darbishire 11 
rigidly selected and that secondly the coefficient of assortative mating between 
this parent and the other has been made equal to - 1. By this supposition we 
are enabled to apply a formula provided by Pearson {Phil. Trans. Vol. 200 A, 1902, 
pp. 39—40). 
A B 
Fig. 8. 
If we could make a diagram showing the frequency of any character, coat- 
colour or other, among mice in general, we may assume that the result would be 
something like Fig. 8 ; and the albino mice would be represented in relative 
frequency and position by one small strip (say A) oi such a diagram, the waltzing 
mice by another small strip (say B). 
Before the experiment began each set of mice, albinos and waltzers, formed 
a separate community, the individuals mating together, either at random or not, 
and having a standard deviation different from that of mice in general ; the 
assortative mating within these groups we may call and let us call the ratio 
between the standard deviation of albinos and that of mice in general /ij, the ratio 
between that of waltzers and that of mice in general jx.,. 
Now calling r^^, the coefficients of correlation between normal male and 
female mice and their young, and calling a-i the standard deviation of filial mice in 
general resulting from unselected unions, we have to find the relations between these 
quantities and S3, jK^, the standard deviation and parental correlation of the filial 
mice resulting from a cross, in which assortative mating has been carried so far 
that the coefficient of correlation between parents, which we will call p^.,, is equal 
to-1. 
In the memoir quoted, Pearson has shown* that these quantities are connected 
by the following relations : 
Writing for brevity 
and = 
^ '12 
* Pearson's investigation is not strictly applicable to the present case, because he does not consider 
the long-continued selection of parents in past generations involved in the statement that the races used 
are pure. 
2—2 
