Data for the Problem of Evolution in Man. 



321 



{d) The coefficient of assortative mating pi2 for parents weighted 

 with their fertility differs sensibly from that of unweighted parents Ti^. 

 Generally the effect of a relation between homogamy and fertility is to 

 increase the apparent coefficient of assortative mating. 



(e) The coefficients of parental heredity are also modified when we 

 take all and not a single representative of the offspring. 



5. Special Conclusions. — These depend on how we define homogamy. 

 When would the male and female be " alike " 1 Mr. Francis Galton, in 

 the case of stature in man, reduces the female to the male equivalent 

 by altering her stature in the ratio of mean male to mean female 

 stature. In my paper on the Law of Ancestral Heredity* I give 

 reasons for using as a factor of reduction the ratio of the male standard 

 deviation to the female standard deviation. Mr. Galton's method and 

 mine agree fairly closely in the case of man, for the coefficients of varia- 

 tion! of man and woman {i.e.^ lOOo-i/wi and lOOa-g/wo in our present 

 notation) are nearly equal for a considerable variety of organs. In either 

 case we should understand by a homogamous union one in which the 

 female organ reduced to the male equivalent was exactly equal to the 

 male organ. Accordingly the ratio of to ^2 would be that of m.-2 to 

 mi, or of 0-2 to 0-1 according to the hypothesis adopted. In the case of 

 man, if either hypothesis be used, the other would be nearly satisfied. 

 Hence, with a reasonable hypothesis as to what we mean by homogamy, 

 it follows that — 



(fl) No progressive change in the mean would arise in a species owing 

 to a relation between homogamy and fertility {h^ = 0, since either 

 lhlP2 = W^i or 0-2/0-1). 



(b) With equipotency of hereditary influence in the parents, the 

 race would not on my hypothesis alter its variability, and on Mr. 

 Galton's hypothesis only by an extremely small quantity of the fourth 

 order (if riz = r23, then by (vi) ^3 differs from 0-3 by a term of the 

 order ru^{pio-i -p^a-^f)- 



(c) The coefficient of assortative mating will be increased. For if 

 piCTi/s = p2^2/s = T, then 



^ _ ri2 + T2(l-rig2) 

 P''- l+r^l-n2') ' 



which is greater than ri2. If ri2 = 0, then pi2 = t2/(1 +t2), or a rela- 

 tion between homogamy and fertility would produce an apparent cor- 

 relation between husband and wife, if we weighted them with their 

 fertility, although they exercised no selective mating. This increase of 

 P12 is in complete agreement with the result obtained for the coefficient 



* ' Koy. See. Proc.,' vol. 62, p. 390. 

 t ' Phil. Trans.,' A, vol. 187, p. 276. 



