448 HARRIS: NUMBER OF OVULES FORMED 
the physiology of seed production, but of considerable interest 
from the fact that in Staphylea there is a selective mortality with 
respect to number of ovules, ovaries with a smaller number of 
ovules being less capable of developing into mature fruits than 
those with a larger number.* 
The determination of the existence of such a relationship, 
especially the measurement of its intensity, presents considerable 
difficulty. It is desirable that degree of interdependence shall 
be expressed in terms of correlation, but there are dangers of 
spurious coefficients. Again, the work so far done has demon- 
strated very low correlations between somatic characters, or 
those of the fruit, and seed production. One would, therefore, 
anticipate very slight relationships between the number of ovules 
formed per fruit and its capacity for seed development. In such 
cases very large and numerous series of data are desirable. 
II. METHOD OF ANALYSIS 
I believe the following method of reasoning is valid. 
In a series (a population, to use the technical term) of poly- 
spermous fruits only a portion of the ovules develop into mature 
seeds. Let o be the number of ovules formed and s the number of 
seeds matured per fruit; both are variable; s is always some pro- 
portion of o. If there be no relationship between the absolute 
number of ovules formed and the capacity of the fruit for maturing 
its seeds, the most probable number of seeds for any pod is 9, 
where 
‘ p a s/o, i 
the bars indicating the mean value of the two variables. Now 
let s = s— po, or the deviation of any individual s from its 
probable value, on the assumption that the chances of an indi- 
vidual ovule developing into a seed are independent of the number 
of ovules in the ovary in which it is produced. The correlation 
coefficient between o and 2, r,z, should furnish the information we 
need. 
A convenient formula for Ps determination of this relation- 
* Harris, J. Arthur, Biometrika 7: 452-504. 1910; Science II. 32: 519-528. 
I9Q10; et pos Mo. 78: 521-538. I9I1 3 
