320 Morphology of the Fruit of Sanguinaria Canadensis 
characters for constant length of stem. In doing this we strip off, so to speak, 
the influence of the length of the stalk upon the coefficient of correlation 
between length and fertility of fruit and have our relationship uninfluenced by 
this character. 
The familiar formula for the partial correlation coefficient is 
In the present series x is length of fruit, y the number of ovules or seeds, as the 
case may be, and z, whose influence on the gross correlation is to be eliminated, is 
the length of the peduncle. 
The partial correlation coefficients for the total ovules and total seeds for the 
1906 series calculated by the above formula appear in Table 10. 
TABLE 10. 
Correlation bekveen Length of Fruit and Number of Ovules and Seeds 
per Fruit for Variable and Constant Lengths of Peduncle. 
Eelatiouship between Length of Fruit and 
Correlation 
Total Ovules per Pod 
For Variable Length of Peduncle 
•527 
For Constant Length of Peduncle 
•470 
Difference 
•057 
Total Seeds per Pod 
For Variable Length of Peduncle 
•576 
For Constant Length of Peduncle 
•517 
Difference 
•059 
The differences show that there is a small amount of the relationship between 
the length of the fruit and the number of ovules or seeds which it produces which 
is due to the correlation of both of the characters of the associated pair with 
peduncle length. But this influence is comparatively small. 
A question of very real interest is that concerning the relative magnitude of 
the correlation between the length of the fruit aud the number of ovules and the 
length of the fruit and the number of seeds. The results may be extracted from 
Table 7 for comparison in Table 11. 
While the correlation for length and seeds is the higher in both series, the 
excess above the relationship for length and ovules cannot be given much weight. 
I was at first somewhat surprised at this result, for I had rather expected that the 
length of a soft fruit of this kind was much more dependent upon the number of 
