542 Harris: OVULES AND SEEDS IN CERCIS 
the direction of this line, the sign. The firm lines and solid dots 
below the zero bar stand for negative coefficients, while the 
broken lines and circles above the zero bar indicate the magnitude 
of positive coefficients. The ten large trees are omitted. 
Taking these results as they stand it would appear that the 
relationship between the number of ovules per pod and the 
capacity of the pod for maturing its seeds may vary, being some- 
times positive and sometimes negative. The light and dark line 
areas in the diagram are nearly equal, and their means lie about 
equally distant from the zero bar. 
But one cannot accept any statistical constant—average 
standard deviation or coefficient of correlation—as absolutely 
correct as a description of the material from which the sample 
investigated was drawn; all are too large or too small by an 
amount known to mathematicians as the probable error of random 
sampling. Is it not possible that the considerable range of vari- 
ation in the constants tabled here is due to purely statistical 
causes and has no biological significance whatever? I think we 
may proceed as follows. 
Assuming that there is no relationship between'the number of 
ovules per pod and the capacity of the pod for maturing its seeds— 
i. e., that r., = O—the deviation of the empirical means and the 
empirical standard deviation due to the probable errors of random 
sampling from the theoretical o may be determined. I illustrate 
with the 60 trees furnishing each 100 pods. 
The standard deviation of the coefficient of correlation is as 
pointed out above (1 — 7*)/ Vn. Clearly where » = 100 and fo: 
is actually 0 one would expect a standard deviation of 0.10 due 
merely to the errors of random sampling. But this standard 
deviation itself would have a probable error which for _the 60 
trees from which I have 100 pods would be .67449(0.1/V 120), OF 
0062. 
One must expect, therefore, if r,. be actually o, to find a 
standard deviation of 0.1000 + .0062 in the coefficients for the 
60 trees with 100 pods each due to no organic cause whatever but 
solely to the errors of random sampling. 
The probable error of the mean is .674490,/Vn. Substituting 
values with o = 0.1 as just indicated I find 
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