MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 
Ill 
Grandsons (in four series) than granddaughters (in four same series). 
Nephews (in four series) than nieces (in four same series). 
Fathers (in two series) than mothers (in two series). 
Grandfathers (in four series) than grandmothers (in four like series). 
Uncles (in four series) than aunts (in four like series). 
The following female groups are more variable than the corresponding male 
groups:— 
Sisters of brothers than brothers of sisters. 
Wives than husbands. 
We have thus 21 series with male preponderance against only two with female 
preponderance of variability. 
Again, the mean range of tints 3, 4, 5, 6 in 22 male series equals 1’5424 cr x , and 
in 22 female series equals 1'6740 oy, or we have enough evidence to show that the 
ratio of male to female variability is about 1'08. # 
This greater variability of the male in eye-colour is of considerable interest. It 
does not appear to be a result of sexual selection, for so far as our comparatively small 
series weighs, husbands are less variable than wives. That mothers are, however, less 
variable than fathers seems to indicate that dark-eyed women are more fertile'!' than 
light-eyed, for we must bear in mind that mothers have on the average a darker eye- 
colour than wives. We have thus again reached the same conclusion as before, 
namely, that a dark-eyed element in the population with a prepotent fertility is 
replacing the blue-eyed element. 
The other female exception to the general rule of greater variability in the eye- 
colour of the male is that in mixed families the sisters appear to be more variable 
than their brothers, notwithstanding that brothers of brothers are more variable than 
sisters of sisters. In other words, so far as eye-colour is concerned an exceptional 
man is more likely to have brothers than sisters, but an exceptional woman also is 
more likely to have brothers than sisters. The inference is not very strong, as the 
excess method («) makes brothers of sisters and sisters of brothers of sensibly 
equal variability; it rests therefore on (B) and (y) only. Still it deserves fuller 
investigation. 
( b .) Let A and B be two grades of relationship, of which A refers to the older 
generation, and A and B refer to either sex. Then the variability of all the A’s 
* It is worth noting that the ratio of male to female variability in the coat-colour of horses is 1 '05 (see 
p. 96). In both cases the female is darker, i.e., has less of “ colour ” ; thus if we could take a coefficient of 
variation ratio instead of standard deviation ratio as the test, we should find the difference of variability 
less, possibly even zero. 
t For if mothers are to be less variable than wives, their distribution must be more compressed round 
the mean than that of wives ; this denotes that fertility is correlated with eye-colour, and the darker eye- 
colour goes with the greater fertility. [See Note II. at end of memoir, however.] 
