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441 
a time when no fruits had attained a length of over 20 mm. It is quite probable that many of 
the fruits which were still developing when the material was examined would have fallen later. 
Thus while the investigation of the relationship between the number of flowers and the number 
of fruits developing per inflorescence during the time that the ovaries which fail to develop 
are being eliminated presents some points of particular interest, conclusions drawn from one 
series cannot be applied to any other of the same si)ecies. The series is here given merely as 
an illustration of a statistical method. 
Number of flowers furnishes our .v character and number of fruits developing our y character. 
For constants we get 
Mean x= 9-193 ±-243, Mean y= 3 396 ±-074, 
S. D. x= 5-924±-172, S. D. y= 1-801 ± '052, 
=64-444, Vy =53-038, 
p = -369, VJV^ = 1-215, 
r^^ = -457 ±-033. r^, =--649 ±-024. 
These figures seem to indicate that while there is a positive correlation of -457 between the 
number of flowers per inflorescence and the immber of fruits developing, the inflorescences 
are not all aflPected alike in the large elimination of ovaries which takes place. Only a portion 
of the flowers formed can develop into fruits, and the negative correlation of - -649 seems 
to show that the larger inflorescences lose not only actually but relatively more of their ovaries 
than do the smaller ones. But this conclusion can be applied only to this particular series of 
data. It may be found later that after the elimination is complete the correlation between the 
number of flowers and the deviation of the number of fruits per inflorescence from their 
probable number will rise to sensibly 0, or take a substantial positive value. 
Illustration II. Correlation between the number of ovules per pod and the number of seeds 
developing per pod in Rohinia Pseudacacia. 
The relationship between the number of ovules and the number of seeds in a sample of 
1427 pods of the black locust collected from 12 trees near Lawrence, Kansas, in the fall of 1905, 
is shown in Table II. The constants which interest us here are : 
X . = Ovules, y = Seeds, 
Mean x = 12-1794, Mean ^= 7-6874, 
S. D. x= 2-2763, S. D. y= 3-4938, 
=18-690, Vy =45-448, 
V^IVy = -4112, 
r,y = -693 ±-009. r^, = -365 ±-015. 
Here it appears from the substantial positive value of r^^ that the pods with the larger 
numbers of ovules are relatively more capable of maturing their seeds than those with fewer. 
But I may add that this is not true in the case of each individual tree, so that more data 
are necessary before we are justified in extending this conclusion to the species at large. 
Evidence from another leguminous plant will be of interest in this connection. 
Illustration III Correlation between the number of ovules per pod and the number of 
seeds developing per pod in Cercis Canadensis. 
Table III. is extracted from a forthcoming memoir on fertility in Cercis Canadensis. The 
correlations are : 
X = Ovules, y = Seeds, 
r^j, = -6855 ± 0040. r^, = -0070 ± -0087. 
Here r^^ is so close to 0 that there seems little doubt that there is essentially no relationship 
between the number of ovules per pod and the capacity of the pod for maturing its seeds. This 
point will be discussed in detail in the memoir. 
Biometrika vi 56 
