MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
103 
glance the distribution in eye-colour of a whole family in its numerous male and 
female lines. Such complete details of the various direct and collateral relationships 
I have not hitherto come across, and from them I was able to form, in the course of 
some months of work, the twenty-four tables of correlation which are given in 
Appendix II. These tables, for the first time, give the whole eight series of grand - 
parental and the whole eight series of avuncular relationships, besides such as we have 
deduced for other characters previously, i.e., the four parental, the three fraternal rela¬ 
tionships, and the table for assortative mating. The very great importance of this 
material will at once be obvious, and I cannot sufficiently express my gratitude to 
Mr. Galton for allowing me to make free use of his valuable data. 
At the same time we must pay due regard to the limitations of this material, which 
it is needful to enumerate, so that too great stress may not be laid on the irregularities 
and divergences which arise when we attempt to reduce the results to laws. These 
limitations are as follows :— 
(a.) While the data of about 780 marriages are given in the record, they belong 
to less than 150 separate families. All our relationships, therefore, contain pairs 
weighted with the fertility of the individual families. Thus it was necessary to enter 
every child of a mother, every nephew of an uncle, and so forth. In the horse data 
we could take 1000 distinct mares and give to each one foal only. That is not possible 
in the present case. 
( b .) The colour of eyes alters considerably with age. It is not clear that some of 
the eye-colours are not given for infants under twelve months, and certainly the eye- 
colours in the case of grandparents and others must have been taken in old, perhaps 
extreme old, age. In a large number of other cases of great grandfather, great great¬ 
grandfather, &c., great uncles, and so forth, the eye-colours must have been given 
from memory or taken from portraits—in neither alternative very trustworthy sources. 
Thus while the horse colour is always given for the yearling foal by the breeder, the 
eye-colour is given at very different ages, and comes through a variety of channels. 
(c.) The personal equation in the statement of eye-colour, when the scale contains 
only a list of tint-names is, I think, very considerable. The issue for the collection of 
data of a plate of eye-colours like that of Bertrand would be helpful, but we can 
hardly hope for a collection of family eye-colours so comprehensive as Mr. Galton’s 
to be again made for a long time to come. 
These causes seem to me to account for a good deal of the irregularity which appears 
in the numerical reduction of the results, but they are not, I hold, sufficient to largely 
impair the very great value of Mr. Galton’s material. 
In tabulating the data, I have followed the scale of tints adopted by Mr. Galton, 
and I have used the entire material available in the cases of the grandparental, 
avuncular, and marital relations. I nearly exhausted the data for the parental 
relationships, but in these tables, which were first prepared, I stopped short at 1000 
for the sake of whole numbers. I found, however, that it did not make the arithmetic 
