MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
119 
Table IX.—Theoretical and Actual Results for Inheritance. 
Theory. 
Man. 
Horse. 
Hound. 
Daphnia. 
Relationship. 
Blended 
inherit¬ 
ance. 1 
Exclusive 
inherit¬ 
ance. 2 
Stature 3 . 
Head 
index. 4 
Eye- 
colour. 5 
Coat- 
colour. 6 
Coat- 
colour. 7 
Spine. 8 
Parental .... 
■3000 
•5000 
•3355 
•3348 
•4947 
•5216 
•3507 
[•3295] 
Mid-parental. 
•4242 
— 
•47 45 
•4735 
— 
_ 
— 
•4660 
Grandparental . . 
T500 
•2500 
— 
— 
•3166 
•3353 
T340 
[T360] 
G. Grandparental . 
•0750 
•1250 
— 
— 
— 
— 
•0404 
— 
Avuncular . . . 
T500 
•2500 
— 
— 
•2650 
— 
— 
— 
Whole sibling . 
•4000 
•4 to DO 
•4034 
•4025 
•4749 
•6329 
•5170 
•6934 
Half sibling . . . 
•2000 
•2 to - 5 
— 
— 
— 
•3550 
•1646 
— 
1 Mr. Galton’s unmodified hypothesis. See “ Law of Ancestral Heredity,” ‘ Roy. Soc. Proc.,’ vol. 62 
p. 397. 
2 Without any reversion. See “ Law of Reversion,” ‘ Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. The values 
for the fraternal correlation depend on the degree of prepotency of either parent within the union. 
3 See ‘ Phil. Trans.,’ A, vol. 187, p. 270. 
4 See ‘Roy. Soc. Proc.,’ vol. 62, p. 413. The paternal correlations, for reasons stated in the paper, are 
excluded from the result. 
5 See p. 113 et seq. of the present memoir. 
6 See p. 98 et seq. of the present memoir. The grandparental correlation is based on two cases only. 
7 See ‘Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. 
s See ‘Roy. Soc. Proc.,’ vol. 65, p. 154. I have deduced the value for parents and grandparents from 
Dr. Warren’s results for midparent and midgrandparent. The value for whole siblings I obtained from 
Dr. Warren’s measurements, which he with great kindness placed at my disposal. 
(14.) Conclusions .—The course of this investigation has not been without diffi¬ 
culties, and 1 am fully prepared to admit that more obscurity and greater probable 
errors are likely to arise when we deal with the inheritance of a character not directly 
measurable, than when we take that of a character to which we can at once apply a 
quantitative scale. But I contend that many of the characters, the inheritance of 
which it is most important to investigate, do not at present, and perhaps never will, 
admit of a quantitative measurement. We can arrange in order, we can classify, we 
can say more or less intense, but we cannot read off value on a scale. It is just such 
characters also, which the not highly trained observer can most easily appreciate and 
record. Hence we have been compelled to devise some method of dealing with them, 
and the present paper illustrates how the method invented can be applied to reach 
results of considerable interest and of substantial validity. 
