456 Intra-Class and Inter-Class Correlations 
While the case is given as an illustration of method only, chosen primarily 
because of the small number of families, it is of rather unusual biological interest. 
These families were from inbred stock (sister by brother) derived originally 
from a single pair, thus representing as nearly as possible among unisexual 
organisms a "pure line." Yet we find a sensible sororal correlation*. I hope 
Dr Lutz will find time to collect really adequate data on this interesting 
problem. 
I illustrate on this data one of the most convenient features of the methods 
here described. If, for any reason, one wishes to compare the values of corre- 
lations determined with and without the inclusion of certain classes, the various 
determinations can be quickly made by the simple addition or subtraction of the 
summations of weighted products. For example, suppose one wishes to test the 
effect of omitting families 32, 575 and 587. S[n(n -1)] will be reduced by 
12 x 11 + 2 x 18 x 17 = 744; 
the first weighted population summation by 
11 x 830 + 17 x 1166 + 17 x 1246 = 50134; 
the second by 
11 x 57420 + 17 x 75658 + 17 x 86274 = 3384464, 
and the product summation by 
(830 2 - 57420) + (1166 2 - 75658) + (1246 2 - 86274) - 3381620. 
Deducting these from the comparable values given above for the population and 
calculating physical constants on the basis of the new weighted population N~, 
we find r = 1419. 
Illustration {III — Ab) 5. Direct Homotypic Correlation. 
The records of the number of ovules per pod in twelve individual trees of 
black locust, Robinia Pseud-acacia\, may illustrate the calculation of homo- 
typic correlations. The series is selected because of the wide variation in n. 
Naturally the smallness of the number of classes which renders the material 
convenient as an illustration of method, makes it of little value biologically. 
The seriations of numbers of ovules per pod and of numbers of seeds per pod 
appear in Tables VI and VII. The essentials for the calculation of r appear 
in Table VIII. 
* This may not of course be due to heredity. The environment of the unlaid eggs or differences in 
the experimental conditions during the larval period may be its source. But Dr Lutz considers sensible 
environmental heterogeneity out of the question. 
t The correlation between the number of ovules and number of seeds developing per pod has been 
discussed for the combined pods of this series in Biometrika, Vol. vi. pp. 441 — 442, 1909. 
