J. A. Harris 
451 
Illustration {III — .4 a) 1. Symmetry in the Ovary of Hibiscus. 
The morphologist interested in the degree of perfection of morphogenetic 
processes may desire to measure the degree of precision with which the different 
" Anlagen" which go to make up a composite organ, say for example a quinque- 
locular fruit, are differentiated off from the common primordium and carried 
through embryogenesis. One convenient measure is furnished by the intra- 
ovarial coefficient of correlation. 
Take as an illustration a series of 1000 five-celled fruits of Hibiscus Syriacus 
from the Missouri Botanical Garden in the fall of 1905. Table I gives the sym- 
metrical intra-ovarial correlation surface for number of ovules per locule. 
Since all fruits have the same number of locules, the constants are not 
changed by weighting, hence, from Biometrika (Vol. Vlir., pp. 61 — 62; M.B.G., 
1905) we take 6= 6-4648, <r 0 = -892166. From Table I,. 
S (o.'o/yN = 841990/20000 = 42 0995, 
r = [S (o.'o^/N - o 2 }/<r 0 '= {42-0995 - (6-4648) 2 }/(-892166) 2 = -3843. 
TABLE I. Symmetry in the Ovary of Hibiscus. 
Ovules of Second Locule. 
3 
o 
o 
fa 
tin 
o 
cn 
<x> 
> 
O 
2 
3 
k 
5 
6 
7 
8 
Totals 
2 
1 
2 
6 
2 
1 
12 
3 
1 
7 
4 
8 
20 
4 
1 
12 
28 
132 
56 
23 
252 
5 
2 
1 
28 
220 
899 
255 
55 
1460 
6 
6 
7 
132 
899 
6384 
1871 
605 
9904 
7 
2 
4 
56 
255 
1871 
2014 
1134 
5336 
8 
1 
8 
23 
55 
605 
1134 
1190 
3016 
Totals 
12 
20 
252 
1460 
9904 
5336 
3016 
20000 
But in Biometrika (loc. cit. Table VI) we have seriations of total ovules per 
fruit, = 2 (o') for locules. From this and the distribution for individual locules 
we have for the product moments, by (vii), 
£ [2 (o')] 2 = 1054938, S{o'--)= 212948, m [n (n - 1)] = 20000, 
whence 
r = {S\ X (gOT - S (o'*Mmn (u -l)]-o^ { ^ Qm _ (6 . 4648) , /( . 8921G6) , = . 3843> 
avoiding all the labour of forming a correlation surface of 20000 entries, but giving 
no information at all as to the nature of the regression curve. 
Illustration (III — A a) 2. Intra-ovarial Correlation for Seed Production. 
Next consider a physiological problem from the same data. Table II gives 
the intra-ovarial (or inter-locular) correlation surface for seeds per locule. 
5 = 3-9056, a s = 1-756442, 8 (s 1 V)= 339360, 
whence r = [S (s 1 V)/20000 - (3-9056) 2 }/(l-756442)-= "5557. 
