Karl Pearson 
379 
the grandchildren as they stand are not random samples of the grandchildren 
which would be due to the original individual. They are arbitrary and not properly 
representative groups. Thus the correlation of the foundation stock of 26 with 
their 1452 great-grandchildren is '059, greater than the value, -030, of the same 
individuals' correlation with their grandchildren. It may readily take any small 
value, because the grandchildren and great-grandchildren are not typical of the 
stock of the foundation individuals, there having been either one or two selections 
of two or three individuals of a quite arbitrary character in between. While 
therefore the correlations for these more distant generations are lower than in the 
case of parent and offspring, they are quite erratic, and I see no obvious method of 
allowing theoretically for these arbitrary intermediate selections of parents. It is 
safest to base the fundamental criticism on the result that the correlation of 
brethren is sensibly higher, and of "aunts and uncles" very sensibly lower than that 
of parents and offspring, a result absolutely opposed to the theory of the pure line. 
(6) But if those who lightly accept without criticism such results as those 
of Hanel have not the statistical training necessary to measure degree of resem- 
blance, they might at least have examined Hand's own tables carefully, and com- 
pared the average number of tentacles in the offspring of the parents possessing 
the highest and lowest numbers of tentacles which occur in each pure line. They 
would have found the following results : 
" Stammthier " 
Line 
Lowest Number 
of Parental 
Tentacles 
Number of 
Offspring 
Mean 
Highest Number 
of Parental 
Tentacles 
Number 
of 
Offspring 
Mean 
6 
1 
6 
83 
6-82 
65 
7-04 
6 
2a 
6 
66 
6-84 
8 
13 
7-46 
5 
2b 
5 
30 
6-70 
8 
29 
7-34 
8 
3 
6 
143 
7-42 
8 
199 
7-43 
7 
4 
7 
93 
7-60 
9 
64 
7-62 
6 
5 
6 
202 
6-69 
8 
7-15 
9 
6 
6 
183 
7-06 
12 
35 
7-69 
7 
6 
32 
7 03 
10 
31 
7-66 
7 
8 
7 
100 
6-67 
8 
23 
6-78 
8 
9 
6 
22 
7-32 
8 
101 
7-41 
8 
10 
6 
39 
7-39 
8 
116 
7-22 
6 
11 
5 
39 
6-90 
85 
7-11 
6 
12 
6 
154 
6-97 
8 
83 
7-05 
7 
13 
6 
89 
6-35 
8 
50 
6-36 
7 
14 
6 
24 
6-50 
8 
18 
6-61 
8 
15 
7 
21 
6-93 
9 
56 
7-73 
12 
!? 
8 
84 
7-08 
12 
25 
7-64 
10 
8 
31 
8-23 
10 
116 
8-45 
7 
18 
6 
119 
7-34 
9 
49 
7-35 
5 
19 
5 
49 
7-06 
9 
26 
7-30 
I 
20 
6 
95 
7-47 
9 
18 
7-44 
21 
6 
103 
7-49 
8 
39 
8-11 
7 
22 
7 
109 
7-67 
10 
23 
7-12 
5 
23 
5 
44 
7-22 
9 
85 
7-40 
7 
2.5 
7 
98 
8-05 
10 
60 
7-63 
9 
26 
7 
94 
7-17 
9 
78 
7-25 
