468 
Intra-Class and Inter-Class Correlations 
These formulae lend themselves readily to practical manipulation. The rough 
moments for the parental-offspring surface are generally available ; the others 
are obtained by rapid machine calculation. 
Illustration (V) 11. Avuncular Correlation in Garden Beans. 
As an illustration I take the calculation of the "avuncular" correlation in a 
series of forty families of garden beans — The Navy H series of former papers*. 
Table XIV gives the necessary data. The first part shows the weight of the seeds 
from the 40 parents, seriated individually with the sums and sums of squares of 
their values. Only a portion of the seeds (roughly 10) from each of these mothers 
were planted, and give the offspring arrays shown with their summations in the 
second part of the table. 
The direct parental correlation j- — that between the weight of the individual seed 
planted and the weight of the seeds which it produces — is given in Table XV. 
TABLE XV. 
Seed Weight in Garden Beans. 
Offspring Weight. 
3 | 4 
5 
6 
7 
8 
0 
10 
11 
12 
IS 
14 
15 
Totals 
5 
6 
7 
s 
0 
10 
11 
12 
13 
1 
1 
1 
2 
1 
3 
1 
2 
1 
10 
15 
7 
6 
6 
t 
21 
29 
30 
18 
1 
8 
21 
62 
74 
71 
31 
2 
4 
4 
18 
103 
137 
102 
51 
7 
4 
21 
100 
134 
77 
66 
14 
2 
4 
4 
55 
72 
54 
47 
10 
3 
1 
3 
19 
23 
25 
22 
3 
2 
4 
4 
3 
5 
12 
2 
3 
2 
3 
4 
2 
1 
8 
28 
79 
379 
489 
375 
258 
42 
10 
Totals 
3 
7 
41 
111 
270 
426 
416 
251 
98 
30 12 
1 
2 
1 
1668 
* American Naturalist, Vol. xlvi. pp. 313—343, 512—525, 656—674, 1912 ; Koux's Archiv f. Ent- 
toicklungsmcchanik der Organismen, Bd. xxxv. S. 500 — 522, 1912; Biometrika, Vol. ix. pp. 11 — 21. 
t The Editor has called my attention to the possibility of some misunderstandings which might be 
introduced by this illustration and I am glad to add a word of explanation concerning it. 
The chief question which is likely to be raised is : "What constitutes direct parental inheritance in 
a character like seed weight? " Some rather complicated biological questions are involved. The coats 
of the seed are a part of the plant individual which produces them — are in fact strict homotypes in 
Pearson's sense of the term. But the embryo — the cotyledons, hypocotyl and the plumule, the elements 
which constitute the major part of the weight of the seed — is strictly speaking a daughter plant. Hence 
an intra-individual correlation for seed weight is not a true homotypic correlation but a fraternal 
or sororal correlation. Thus from the embryological or genetic standpoint the correlation between the 
weight of the individual seed planted and the weights of the seed borne by the plant into which it 
develops is the true parental correlation. 
There are, however, two important modifying conditions. First, the correlation is between two 
individuals in an embryonic stage, not in the adult condition. It is somewhat analogous to the 
correlation between the larval characteristics of two successive generations of moths, and resembles 
still more closely the coefficient measuring the resemblance between a parent's weight at birth and 
