312 Morphology of the Fruit of Sangninaria Canade^isis 
differences. I must point out, however, that the fact that our probable errors 
show that there are significant differences in the samples with which we are 
dealing does not justify us in concluding that there are differences in the popu- 
lations which they represent unless we are quite sure that our samples have 
been drawn in precisely the same way. Rocks, steep banks and gentle slopes, 
fallen logs and drifts of leaves are possibly all factors which make for heterogeneity 
in the environment of the individual organism in a plant formation which the 
ecologist would consider quite homogeneous. In collecting two samples a and h 
from such a habitat we might get constants differing sensibly with regard to their 
probable error merely by failing to have the several subhabitats contribute the 
same proportional number of individuals in each case. 
These points are emphasized because I do not wish to have these results 
interpreted as indicating that there is a real difference between the whole 
population of Sanguinaria at Meramec Highlands in the two years in question 
due to some peculiarity in the seasons themselves. There may be such a 
difference, but there is no strong evidence for such a conclusion in our data 
which were not collected in a way, nor for the purpose, to determine whether 
there is a real difference between the whole populations in different seasons. 
Turning aside from the contrasting of the constants for individual characters 
and taking a general view of the whole comparison table, I think the impression 
must be that the agreement between the two collections is very close. 
I think we may consider the two series of material upon which we propose to 
investigate certain morphological relationships as on the whole very similar in 
nature. Tests for the similarity of series of material used in morphological work 
have rarely been applied, but it would be desirable if some attention could be 
given to points like this. 
2. The Correlation between the Length of the Peduncle and the Length 
of the Fruit. 
It seems important to obtain some idea of the relationship between the degree 
of development of the fruit-stalk and the size attained by the fruit. The data 
appear in Table 1, 1906, and I have calculated both the coefficient of correlation,?", 
and the correlation ratio, tj. 
This latter constant, recently introduced by Pearson*, furnishes an adequate 
description of the interdependence of two variables when the rate of change of 
the dependent variable cannot be expressed by the slope of a straight line. 
The two constants have the values 
= -S^S ± -019 
7, = -379 ± -0181 
r,-r= on 
* Pearson, K., Drapers' Co. Research ilemoirs, Biometric Series, No. 2, Dulau & Co., 1905. 
t Here -E,, was calculated by Pearson's short formula, loc. cit. p. 20, 1905. 
