48 
Variation and Correlation in Umbelliferae 
The distribution of the numbers of umbel rays of 127 terminal umbels was as 
follows : 
TABLE VII. 
Variation of the yiumber of umbel rays of the terminal umhel of Sium latifolium. 
Number of 
umbel rays 
of the ter- 
minal umbel 
14 
15 
16 
17 
18 
19 
20 
21 
22 
2.3 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
Total 
Number of ter- 
minal umbels 
3 
4 
3 
6 
6 
1 
6 
8 
3 
5 
7 
10 
4 
4 
6 
9 
10 
9 
8 
5 
4 
4 
1 
1 
127 
Mean of umbel rays for 127 terminal umbels =25-638. 
S.D. of umbel rays for 127 terminal umbels = 5-948. 
Conclusions could not be drawn from this distribution, the number of variates 
being too small with respect to the great range of variation. 
Variation of the number of umbel rays of the lateral umbels. 
The lateral umbels again were sub-divided into groups belonging to plants with 
the same number of rays in the terminal umbels and into groups belonging to plants 
with the same number of lateral umbels. As the former groups were very small, 
they can give little or no information about preference for certain numbers. The 
latter groups have been united in Table VIII. 
Though the small number of umbels, of which the rays were counted, and the 
great range of variability make it necessary to be prudent in drawing conclusions, 
we think it probable that not only the numbers of the principal series are of 
importance in this case, but also other numbers as for instance 18 and 29. 
Correlations. 
The coefficient of correlation for the number of rays of terminal and lateral 
umbels was as follows: 
For Pastinaca sativa 0-7269 ± 0-0051. 
,, Anthriscus sylvestris ... 0-3033 i 0'0152. 
„ Sium latifolium 0-8693 ± 0-0070. 
It is remarkable that this coefficient of correlation is different for these three 
species of plants, and it would be worth examining if this coefficient has a constant 
value within certain limits for different local races of the same species of plants. 
In that case a number would have been found, characteristic of each particular 
species. 
