462 
Intra-Class and Inter-Class Correlations 
and by the mean product moment 
• ( xi ) 
taken about 0 as origin. Most simply they can be determined by the formation 
of an ordinary organic correlation table for the whole population which will then 
be described by N, 8(d), 8(d), S(y'), S(y'*) and 8(x'y'), where 8 denotes a 
summation for the individuals of the population. This correlation will generally 
be wanted for its own sake. 
Again two cases are possible (a) all the m classes are equally large, n is 
variable. The first two moments are given by the same formulae as in the direct 
intra-class correlation above, (viii) — (ix). The mean product moment around 0 is 
{8 [2 (d) 5 (y')3 - S[% W)]}/8 [n (n - 1)], (xii) 
or with a denominator of m [n(n — 1)] where the m classes are equally large. 
Illustration (III — Ba) 8. Gross inter -locidar (intra-ovarial) Correlation in 
Hibiscus. 
For a purpose quite foreign to my present one, the correlation between total 
ovules per fruit (=S(o') for locules) and total seeds per fruit (=S(s') for locules) 
has been tabled for the 1905 series of H. Syriacus. The Table has 17 x 36 entries, 
hence we reduce to the condensed form in Table XII. The organic correlation 
between the ovules and seeds of the same locule is shown in Table XIII. Taking 
the product moments of these two tables about 0, and subtracting that for locules 
from that for fruits to remove the products of the ovules and seeds of the same 
locule, and to reduce N from 8 (n") = 25000 to S[n (n-l)] = 20000, I find 
S [2 (</) 2 («')] = 637491, S(o's') = 128377, 
and, substituting physical constants from illustrations 1 and 2, I find 
= S { [S (o') S QQ] - 8 (o's )}/20000 - ds = 25-4557 - 6"4648 x 3-9056 _ 
r °> s *~~ a 0 a s -892166 x 1-756442 -'RO- 
TABLE XII. 
Correlation for Total Ovules and Total Seeds per Fruit 
in Hibiscus. 
Ovules 
f 
Total Seeds 
Ovules 
f 
Total" Seeds 
23 
32 
81 
1512 
2k 
3 
41 
S3 
80 
1575 
■ 25 
2 
26 
3k 
80 
1436 
26 
4 
51 
35 
85 
1746 
27 
18 
285 
36 
54 
1256 
28 
45 
708 
37 
54 
1129 
29 
107 
1847 
38 
34 
807 
30 
188 
3727 
39 
27 
691 
31 
125 
2322 
40 
13 
369 
