470 Intra-Class and Inter-Class Correlations 
I note that the parental relationship is the highest and the avuncular the 
lowest. These results cannot be discussed in detail until the final memoir from 
which they are abstracted is published, but it seems to me that they agree 
with Hanel's data for Hydra as analyzed by Pearson* in affording no support to 
Johannsen's conclusions concerning the ineffectiveness of selection within the pure 
line. 
If one desires a check, or if linearity of regression must be tested, one may pro- 
ceed by the method already described for the formation of condensed correlation 
tables f. 
Either ascendant or descendant seeds may be taken as the "first" or subject 
character. Since they are quickly formed, both have been drawn up for the con- 
venience of the reader and appear as Tables XVI — XVII. In them, the first two 
columns give the reduced tables for parents and offspring (or offspring and parents), 
the second two give the frequencies for the ascendants weighted with their 
descendants (or the descendants weighted with their ascendants) and the totals of 
the associated arrays. The final two columns are obtained by subtracting the first 
pair from the second, and give the avuncular relationship desired. Naturally, the 
final summations of these columns may be subtracted if linearity tests only are 
not desired. All the above constants may be checked directly from these tables. 
TABLE XVI. 
Parental 
Correlation 
Ascendant-Descendant 
Correlation 
Avuncular 
Correlation 
Weight of 
Ancestral 
Seed 
Frequency of 
Actual Parents 
Weighted with 
their Offspring 
Total 
Offspring 
Weight 
Weighted 
Frequency of 
Descendant 
Seeds 
Total Weight 
of AVeighted 
Descendant 
Seeds 
Weighted 
Frequency of 
Nepntic 
Seeds 
Total Weight 
of Weighted 
Nepotic 
Seeds 
3 
5 
6 
S 
9 
10 
11 
12 
18 
U 
8 
28 
79 
379 
489 
375 
258 
42 
10 
70 
210 
648 
3188 
4085 
3111 
2270 
396 
119 
35 
40 
294 
1147 
3389 
11510 
18095 
15184 
8247 
2406 
364 
45 
306 
340 
2526 
9313 
27780 
96824 
151467 
127618 
7 159 J 
22963 
3775 
487 
35 
40 
286 
1119 
3310 
1 1 131 
17606 
14809 
7989 
2364 
354 
45 
306 
340 
2456 
9103 
27132 
93636 
147382 
124507 
69321 
22567 
3656 
487 
Totals 
1668 
14097 
60756 
514990 
59088 
500893 
* Biometrika, Vol. vn. pp. 372—381, 1910. 
t American Naturalist, Vol. xlvi. pp. 477 — 486, 1912. 
