12 Result of Crossing Japanese Waltzing ivith Albino Mice 
we have 
S,'^ = {I - ^,Hl - i^c) - /S,3ni - f^i) - 2 (r,, - /3i, ix, /S3}, 
S3 i^is = 0-3 {ri3 - (1 - Ail) /3,3 - (?-i2 - P12 /ia) /Sas}- 
Now we are proceeding on the assumption that in the experiments under 
discussion the two coefficients of parental correlation i\3 and r.^ are equal ; we 
may therefore suppress their suffixes and write each = r ; further, we may express 
the purity of the original races used by writing for each of them r^^, the coefficient 
of assortative mating, = 1. 
We have then 
and our formulae become 
1-4(1- /^i') - 4 (1 - /^a') - ^ (1 ~ P^'i /^lA^a) 
and 
2, R.. 
r(l-/Ai) r(l-p,,//,y 
2^2 
Now suppose the suffix 1 to denote the parent whose correlations we are in- 
vestigating and let us first examine the waltzing parent, so that the suffix 2 denotes 
an albino ; we may fairly say that the ratio of the standard deviation of coat-colour 
among albinos to that of mice in general = 0, and we have for Ry^ the correlation 
between waltzing mice and their hybrid offspring, 
Ri'i — I — — ' ) 
rjh. 
and we see that the value to be expected depends (i) on the correlations between 
parent and offspring in those simpler cases of random mating first dealt with by 
Galton and Pearson in the Law of Ancestral Heredity, and (ii) on /^i, the ratio 
between the standard deviation of the selected race of waltzing mice and that of 
the general population from which they are descended. We have no means of 
evaluating jx^ in the case of coat-colour, but we know that it is small. We may 
