PROF. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 281 
An examination of the above numbers brings out a fact which i am not sure has 
been noted before : namely, the alteration from dolicocephaly to brachycephaly appears 
to chiefly depend upon an alteration in the breadth and not in the length of the skull. 
We see too that, if variation be judged, not by standard-deviations, but by the 
coefficients of variation advocated in this paper, the breadth of skull is in all cases a 
sensibly more variable quantity than the length, and, further—a point to which I 
shall return on another occasion—that the more civilised races are the more variable. 
Both of these results have, I believe, very important bearing on the mathematico- 
statistical theory of evolution. On the present occasion the above example is only 
given to illustrate the relation of variation to correlation. 
(6.) Collateral Heredity. 
(a.) Stature in Man .—The whole theory of correlation as applied to uniparental 
inheritance may be at once applied to correlation between brothers, sisters and 
brothers and sisters. To illustrate the theory I give the following tables, again 
based on Mr. G Alton’s statistics. 
In the pairs sister-sister and brother-brother the elder sister or the elder brother 
has been taken first in order to ascertain the effect of earlier birth on correlation. 
In the pairs sister-brother, I had no data as to relative age. 
Table VI.—Variation. 
Class. 
Number. 
Mean Height 
in inches. 
Probable 
error of 
M.H. 
S.D. 
in inches. 
Probable 
error of S.D. 
Elder sisters of sisters .... 
595 
63-869 
•0617 
2-2303 
•0436 
Younger sisters of sisters . . 
595 
64-199 
0695 
2-5119 
•0491 
Elder brothers of brothers 
605 
-69 0174 
•0715 
2-6080 
•0506 ' 
Younger brothers of brothers 
605 
69-0814 
•0725 
2-6434 
•0513 
Sisters of brothers. 
1181 
63-9274 
•0440 
2-2430 
0311 
Brothers of sisters. 
1181 
69-0963 
-0533 
2-7164 
•0377 
Table VII. — Correlation. 
Class. 
Coefficient r. 
Probable error of r. 
Sister-sister. 
■4436 
■0203 
Brother-brother ...... 
•3913 
0216 
Sister-brother ....... 
•3754 
•0158 
2 o 
mdcccxcvi.—A. 
