PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 285 
ably,'"' but they are nearer together than to Mr. GAlton’s ’67, and being entirely inde¬ 
pendent series, may be taken to justify the statement made above that the coefficient 
for the middle classes can hardly exceed '5. Thus there is not, I think, sufficient 
ground at present for forming any definite conclusion as to the manner in which lineal 
is related to collateral heredity. It does not seem to me necessary that the coefficient 
for the former should be half that for the latter, as supposed by Mr. Galton. 
In some respects, indeed, the Special data verify the conclusions we may draw from 
the B-.F.F. data. Thus B.F.F., Special data, and the two components into which I 
have divided the latter, all four agree in making the younger brother taller than the 
elder brother. The variability of both brothers is practically equal in the Special 
data and slightly greater than that of the R.F.F. data—2'656 as compared with 2'626 
— a difference not significant, and which, if it were, might be put down to the 
mixture of classes in the Special data. 
Assuming that the regression coefficients in Table VIII. give the relative if not 
the absolute values for collateral inheritance, we draw from them a few suggestions 
for further inquiry when the statistics are forthcoming. In the first place, sisters are 
more like each other than brothers. At any rate, the younger sister is more like the 
elder sister than brother is like brother. If this appears to contradict the principle 
that sons are more like their parents than daughters, a solution of the paradox must be¬ 
sought in the relative variabilities of daughters, elder sisters, and younger sisters. 
To compare the strength of inheritance in brothers and sisters, we have to consider 
not ‘3100 and '4547, but these coefficients of regression multiplied and divided 
respectively by 13/12, or '3358 and *4197, whence we see that the brother takes 
more after the sister than the sister after the brother. 
It will be wise, however, to lay no great stress on these results, until a wider series 
of statistics has been collected. 
The following example must be taken only as the roughest approximation, but so 
far as it goes as confirming the above results. 
An exceptional grandmother in Badent had a length-breadth head index of 90, her 
20 grandchildren had a mean head index of 83'55, with a S.D. — 3*025. The mean 
head index of the general population^ was 83T5 with S.D. = 3’63. Thus, if r x be the 
regression of offspring on parent, and r % of offspring on each other, ?q- X 6’85 = '4, 
and \/{l — r 3 2 ) = 3'025/3'63. 
Hence, r x — '24 and r 2 = '55. Considering the large probable error of the S.D. of 
the fraternity ('32), these results indicate inheritance in head indices of the same order 
as in stature. 
* The difference is to be expected. Mr. Galton’s R.F.F. series allows for due weight being given to 
the variability in large families. My statistics take only four members at a maximum, and frequently 
only two out of each family. 
t O. Ammon, ‘ Die natiirliche Auslese beim Menschen,’ p. 13. Three children were unmeasured, and 
I have accordingly had to disregard this generation. 
J Calculated from results for 6748, Badenser, given by Ammon, p. 67. 
