326 Mathematical Contributions to the Theory of Evolution. 



of the parental characters as in the case of a blue eye streaked with 

 brown, eyes of two different colours, a piebald horse, &c. The occa- 

 sional appearance of particulate, where we are accustomed to blended 

 heritage, appears to be sometimes attributed to reversion. 



Neither coat-colour in the horse nor eye-colour in man appear to 

 obey the law of ancestral heredity. 



(3) In coat-colour we find the horses lighter than the mares, but a 

 secular change appears to be going on, and thoroughbred colts and fillies 

 of to-day are more alike in colour than those of two generations back. 

 The horse is somewhat more variable than the mare. The laws of 

 inheritance are in excellent accord with what we should expect from 

 the theory of exclusive inheritance without reversion ; they are incom- 

 patible with the law of ancestral heredity. The only important 

 divergence occurs in grandparental correlation. 



(4) In eye-colour we find man lighter than woman, but a secular 

 change is going on, and men and women to-day are more alike in eye- 

 colour than they were two generations back. This change in eye- 

 colour is possibly due to a correlation between eye-colour and fertility 

 in woman. Man is somewhat more variable than woman. The laws of 

 inheritance are not in accord with what we might expect from the law 

 of ancestral heredity. They are definitely divergent from it, but agree 

 well with exclusive heritage without reversion to ancestral types. 

 Here again the grandparental correlation appears to be anomalously 

 large. Great diversity exists, however, between the intensity of in- 

 heritance as exhibited by difi'erent lines of descent. For the first time 

 in this memoir, I believe, the strength of heredity for the eight 'gTand- 

 parental and the eight avuncular relationships is investigated. The 

 results obtained enable us, at least for eye-colour in man. to make the 

 following statements : — 



(i) Let A and B be the grades of relationship, of which A refers to 

 the older generation, and A and B may be of either sex. Then the 

 variability of all the A's which have female B's is invariably greater 

 than the variability of all the A's which have male B's. In other words, 

 women while less variable than men, come of more v^ariable stock. 



(ii) The younger generation takes as a whole more strongly after 

 its male than its female ascendants and higher collaterals. 



(iii) The younger generation is more highly correlated with an 

 ascendant or higher collateral reached by a line passing through one 

 sex only than by a line which changes sex. 



(iv) Men are slightly more highly correlated with their ascendants 

 and higher collaterals than women are. 



(5) The memoir concludes by insisting on the need for a wide deter- 

 mination of the intensity and form of inheritance for a great variety of 

 characters in many types of life. Until this has been achieved, 

 "plasmic mechanics" are merely hypothetical explanations of pheno- 



