J. A. Harris 
319 
In both of the cases in which ^jE^ was calculated it is found to have a value 
not greatly exceeding 2-5 in the first case and falling somewhat short in the second. 
Judging merely from the statistics in hand, the deviations of the means of arrays 
from a straight line may be due to nothing more than the probable errors of 
random sampling. In the case of length and seeds for 1906 and length and ovules 
for 1907, ^lE^ was not calculated, since tj is slightly less than r. This theoretically 
impossible result is explained as follows. In calculating t] I followed the con- 
ventional practice of using the standard deviation for the population calculated 
without Sheppard's modification. In calculating r, however, Sheppard's correction 
was applied to both standard deviations. Had standard deviations without 
Sheppard's correction been used, r would have been lowered somewhat by the 
increase in the value of the product a-^a-.,, and would then be less than 77. It 
seems rather pedantic under the circumstances to recalculate the values of r, 
for biologically the results could have little increased value. For one year it is 
the correlation for length and ovules and for the other year it is the correlation 
for length and seeds which give such nearly identical values of r and 77. There is, 
therefore, no reason to think that the regression may be non-linear for ovules 
and not for seeds, or vice versa. 
For both ovules and seeds the constants for 1907 are about O'llO + "025 higher 
than in 190G. 
Possibly the more mature condition of the fruits gathered in 1907 may have 
as one of its results the raising of the coefficient of correlation for length of fruit 
and number of ovules or seeds. 
These constants are purely descriptive. They express the degree of inter- 
dependence betvveen length of fruit and number of ovules or seeds but do not 
explain anything concerning the cause of this interdependence. The correlation 
coefficients in themselves cannot even be considered adequate to establish the 
existence of a causal nexus inherent in the fruit primordium and finding expression 
in the relationship observed between length of fruit and number of ovules or 
seeds. There are two ways in which a correlation between fruit length and 
fertility might arise independently of any cause for such a relationship innate 
in the fruit. 
(a) Heterogeneity in the individuals from which the fruits were taken. 
(6) Correlation between both the length and the fertility of the fruit and 
some other organ of the plant, say length of peduncle. 
The first of these possible soui"ces of correlation is not open to investigation 
on the basis of our material. The second may more easily be taken into 
account. 
Both length of fruit and number of ovules and seeds are correlated with length 
of peduncle. What influence will this have upon the correlation between the 
length of the fruit and its fertility ? The best way of getting at this problem seems 
to be to determine the correlation between the length of the pod and its fertility 
41—2 
