104 
PROFESSOR K. PEARSON AND DR, A. LEE ON 
sensibly shorter, and I afterwards dropped this limitation. In the case of brethren 
I took 1500 of each case—I daresay I could have got 2000 out of the records. As 
the light-eyed brethren are entered first in Mr. G Alton’s MS., the First Brother 
in my unsymmetrical tables is always lighter-eyed than the Second Brother, hence 
the tables had to be rendered symmetrical by interchanging and adding rows and 
columns before we could reduce them. Thus the symmetrical tables have an apparent 
entry of 3000 pairs. Of course 1500 is the number used in finding the probable 
error of the correlation coefficient. The like difficulty does not occur in the brother- 
sister table, where indeed the difference of mean eye-colour for the two sexes would 
not allow of our making the table symmetrical. A comparison of the symmetrical 
with unsymmetrical tables for colts-colts and fillies-fillies, will show how little need 
there is for rendering the tables symmetrical when pairs are taken out of any similar 
class and tabulated without regard to the relative magnitude of the character in the 
two individuals of the pair, i.e,, Weatherby’s record places the individuals simply in 
order of birth and not of darkness or lightness of coat-colour. 
Table VII. gives the value of the chief numerical constants deduced from the twenty- 
four eye-colour tables in Appendix II. # 
(11.) On the Mean Eye-colour having regard to Sex and Generation. —In order to 
test the degree of weight to be given to our conclusions, I have drawn up a table o* 
probable errors for four typical cases—cases by no means selected to give the 
lowest possible values. Further, in Table VIII. I have given the probable error in 
the position of the median as determined in terms of the grey, blue-green range by 
the modification of Mr. Sheppard’s formula (see p. 95). The grey, blue-green range 
of eye-colour is about one-fifth of the total observed range, so that the probable error 
in the position of the median varies from about - 4 to 1 per cent, of that range. This 
is not a large error, but, relative to the small variations of value with generation and 
sex, it is sensible, and we must not draw too fine conclusions on the basis of single 
inequalities. 
Table VI.—Table of Probable Errors in Eye-colour Data. 
Relations. 
Vx 
% 
£ 
u 
u 
I'xy 
Mother and Son 
•0253 
•0188 
•0431 
•0267 
•0256 
•0283 
Maternal Grandmother 
and Granddaughter . 
•0348 
•0350 
•0767 
•0276 
■0314 
•0361 
Sister and Sister 
Maternal Aunt and 
•0244 
•0244 
— 
•0216 
•0216 
•0234 
Nephew. 
•0230 
•0186 
•0414 
•0255 
•0250 
•0302 
* The theoretical formula; by aid of which these constants were determined, have been indicated in the 
earlier part of this memoir, and in Part VII. of the present series on Evolution. The actual work of 
reduction has been most laborious, but I trust that our results are free from serious error. 
