MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
93 
Table II.—Coat-colour Inheritance in Thoroughbred Horses. 
Pair of relatives. 
Division of 
bay range by 
the mean 
Ratio of 
variabilities. 
Coeffi¬ 
cients of 
correla¬ 
tion. 
Coefficients of 
regression. 
Num¬ 
ber of 
cases. 
X. 
y- 
Vx- 
Vy 
£ - 
£ = 
a ’yj (r x- 
1xy 
R.ri/- 
N. 
Sire. 
Colt. . 
•6111 
•5713 
•8712 
1T478 
•4913 
•4280 
•5639 
1300 
Sire. 
Filly . 
•6061 
•5719 
•8298 
1-2051 
•5422 
•4499 
•6534 
1050 
Dam 
• • • • • 
Colt. . 
•5359 
•6027 
•9500 
1 -0526 
•4862 
•4619 
•5118 
1000 
Dam 
. 
Filly . 
•5565 
•6051 
•9036 
U1067 
•5668 
•5122 
•6273 
1000 
Maternal grandsire 
Colt. . 
■6583 
•5867 
•7030 
1-4225 
•3590 
•2524 
•5107 
1000 
Maternal grandsire 
Filly . 
•6359 
•6042 
•7678 
1-3024 
•3116 
•2392 
•4058 
1000 
Colt 
’ (Half 
Colt. . 
siblings) 
•5908 
•5908 
1 
1 
•3551 
•3551 
■3551 
2000 
Colt 
(Whole 
Colt. . 
siblings) 
■5620 
•5620 
1 
1 
•6232 
•6232 
•6232 
2000 
Filly 
’ (Half 
Filly • 
siblings) 
•5665 
•5665 
1 
1 
■4265 
•4265 
•4265 
2000 
Filly 
(Whole 
FiHy . 
siblings) 
•5684 
•5684 
1 
1 
•6928 
•6928 
•6928 
2000 
Filly 
’ (Half 
Colt. . 
siblings) 
•5633 
•5865 
•9607 
1 -0409 
•2834 
•2723 
•2950 
1000 
Filly 
(Whole 
Colt. . 
siblings) 
•5410 
•5711 
•9555 
1-0466 
•5827 
•5568 
1-0466 
1000 
In this table Ih y = r X!l o- x j<r y , Ti, /X = Half-siblings* are those having the 
same dam, but different sires. Further, rj is measured from the brown end of the hay 
range up to the mean. 
(7.) On the Mean Coat-Colour of Horses .—If our theory he correct, this colour 
will not differ much from the median colour, and we notice at once a secular change 
going on. We have the following order : — 
Maternal grandsire of colt. 77 = '6583 
Maternal grandsire of filly.= ‘6359 
Sire of colt.= *6111 
Sire of filly.= - 6061 
Colt (mean value of seven series) . . . = ’5816 
Dam of colts. 77 = ‘5359 
Dam of fillies. =-5565 
Fillies (mean value of seven series) . . = ‘5753 
* I have introduced this expression in my paper on “The Law of Reversion,” ‘Roy. Soc. Proc.,’ vol. G6, 
as a convenient expression for a pair of offspring from same parents whatever he their sex. 
