MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
87 
expressions as given above are somewhat complex. It is, however, necessary to keep 
the approximate values of these probable errors in view, and, as our results classify 
themselves easily into groups for which our data, as well as the intensity of heredity, 
are approximately the same, one series of these errors has been found for each group. 
(4.) If we have ground for our assumption that the variable at the basis of our 
tint classification can be so selected as to give a normal distribution, we may deter¬ 
mine the relative lengths on the scale of that variable occupied by each tint or shade. 
Thus if oq be the standard deviation of the variable for male eye-colour, <r 2 for 
female eye-colour, I measured the range on the scale in terms of cr i and ct , for 
Mr. Galton’s eight eye-colour tints for 3000 cases of male and 3000 cases of female 
eye-colour. I found the spaces occupied on the unknown scale to be as follows :—- 
No. 
Tint. 
Range in terms of o- 2 . 
Range in terms of o-j. 
1 
Light blue . • . . . 
OO 
oo 
2 
Blue, dark blue . . . 
1-39276 
1-34918 
3 
Grey, blue-green . . . 
•73468 
•77596 
4 
Dark grey, hazel . . . 
•40027 
■41992 
5 
Light brown .... 
•03893 
•00856 
6 
Brown. 
•43679 
•35895 
7 
Dark brown. 
•84161 
•64167 
8 
Very dark brown, black. 
00 
oo 
These results are not so regular as we might have hoped for, on the assumption 
that the ratio of oq/oq would be the same from whatever part of the scale it be 
determined. The general conclusion, however, would be that oq is slightly larger 
than oq, which is confirmed by other investigations. Actually a tint may be rather 
vaguely described, and where the data were obtained by untrained observers without 
the assistance of a plate of eye-colours, a good deal of rather rough classification is 
likely to have taken place. I do not think it would be safe to go further than stating 
that on the quantitative colour scale the tints as described must occupy spaces in 
about the following proportions :— 
Light 
Blue. 
Blue, 
Dark Blue. 
Grey, 
Blue-Green. 
Dark Grey, 
Hazel. 
Light 
Brown. 
Brown. 
Dark 
Brown. 
Very dark Brown, 
Black. 
OO 
1-37 
•75 
•41 
•02 
•40 
•74 
00 
Taking 2000 colts and 2000 fillies, the standard deviations being oq and oq respec¬ 
tively, I have worked out the coat-colour ranges in terms of oq and oq for each of 
the sixteen colours* occurring in the records. We have the following results ;— 
* See p. 92, below. 
