1912] HARRIS—STAPHYLEA 4II 
interdependence for length and seeds which would not be due to any 
direct physiological relationship at all, but solely to differentiation 
in the plants which produced them. 
The criticism that the correlations for pod characters may be 
due to heterogeneity of material has already been met for the 
present study, by analyzing the data from each individual inde- 
pendently. To make assurance doubly sure, we may determine 
the correlations (a) between the mean length of the fruit and the 
mean number of ovules per locule (7), and (b) between the mean 
length of the fruit and the mean number of seeds per locule (7), 
for the individual trees. Working by the brute force method we 
1906 1907 
To =0.0040.150 0.0100. 168 
1,=0.418+0.124 —0.371#0.145 
In both years 7, is only a fraction of its probable error, and no 
significance whatever can be given it. Statistically, 7, may be 
significant in both cases; for in 1906 7/E,=3.36, and in 1907 
r/E,=2.55. Biologically the two constants, of roughly the same 
numerical order but opposite in sign, mean nothing except that 
mean length and mean seeds do not seem to be closely related. 
Probably both are determined by largely independent causes. 
The substantial quantitative results are due solely to the probable 
errors of sampling.” 
nN 
* Reconsider in the light of these results the peculiar condition noted in table V, 
values of these constants for the samples from individual trees. The explanation 
seems to be quite simple. The magnitude of r depends upon the largeness of the 
denominator, ¢\¢, or o\¢;, as well as upon the numerator, S(lo) or S(Is), of the cor- 
relation formula. The mean ¢},0os¢; of the individuals are seen in table V to be much 
lower than the same constants for the population. For both series the correlation 
between A, and A, is insignificant, and consequently we see a low value for rio for 
the population because of the high value of o¢,. This is also the tendency for ris, 
but in this case, the inter-individual correlation for A; and As have material values 
which, although without biological significance because of their high probable errors, 
nevertheless have their influence upon the correlation constants for the population. 
n 1906, the inter-individual correlation is positive, and this tends to raise the popu- 
lation constant to about the same value as that for the mean of individuals, that 
is, 0.352 as compared with 0.387; but for 1907, the inter-individual correlation for 
means is negative and we find the discrepancy of 0. 202 against 0.364. These results 
emphasize the importance of a stringently analytical treatment of data. 
