MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
113 
-occasion to refer to. Mean and standard deviation of eye-colour appear to have 
changed sensibly during the few generations covered by Mr. Galton’s eye data. 
It is difficult to understand how any obscurity about the recording of eye-colours 
could lead to anything but chaos in the numerical results. It does not seem to 
me possible that such results as we have reached under (a), (6), and (c), namely, 
greater variability in the male, greater variability in the stock of the female, and 
secular change in variability, can be due to any process of recording. I am forced to 
the conclusion that they are peculiar to the character under investigation, and are 
not due to the manner of taking the record or of dealing with it arithmetically. I 
have purposely avoided drawing attention to small differences and forming any con¬ 
clusions which did not depend on whole series of groups and substantial averages. 
(13.) On the Inheritance of Eye-colour, (a.) Assortative Mating. —Before we 
enter on the problem of inheritance, it is as well to look at the substantial 
correlation obtained between the eye-colour in husband and wife. When in 1895 
I reached the value ’0931 d= '0473 for stature, I wrote, “we are justified in con¬ 
sidering that there is a definite amount of assortative mating with regard to height 
going: on in the middle classes.’’* Since then we have worked out the coefficients of 
correlation in stature, forearm, and span for 1000 husbands and wives (instead of 
200) from my family data! cards. The results, which are very substantial, will be 
dealt with in another paper, and amply confirm my view that assortative mating is 
very real in the case of mankind. The value ('0931) cited above is in close agree¬ 
ment with the result now reached (T002 '0378) for eye-colour in the same 
material. The correlation between husband and wife for two very divergent 
characters is thus shown to be about '1, or is 25 per cent, greater than is required 
between first cousins\ by the law of ancestrcd heredity. 
This remarkable degree of likeness between husband and wife—the scientific 
demonstration that like seeks like—cannot he overlooked. It shows that sexual 
selection, at least as far as assortative mating is concerned, is a real factor 
of evolution, and that we must follow Darwin rather than Wallace in this 
matter. § 
( b.) Collateral Heredity. First Degree. —I deal first with this form of heredity, 
as it offers least points for discussion. The values of the correlation '5169 for 
brothers, and '4463 for sisters and sisters are considerably less than what we have 
found for coat-colour in horses, but, like the value '4615 for brothers and sisters, are 
substantially greater than '4 to be expected from the unmodified Galtonian law. 
They could be reached by making y greater than unity in my statement of the law 
of ancestral heredity.|| They could also be given by the law of exclusive inheritance 
* ‘ Phil. Trans.,’ A, vol. 187, p. 273. 
t See also ‘ Grammar of Science,’ second edition, pp. 429-437. 
t ‘ Roy. Soc. Proc.,’ vol. 62, p. 410. § 1 Roy. Soc. Proc.,’ vol. 66, p. 140 et seq. 
|| I have considered possible explanations of this apparently large assortative mating (i.) in both stature 
VOL. CXCV. —A. Q 
