454 Intra-Class and Inter-Class Correlations 
With Sheppard's correction this gives* in units of weighing 
20/) = 8778t, t O' 2 ) = 56350, 
2 (x')/N = 4 -389, o» = 8-828346. 
From Table III S [2 (*')?= 510496, 
(5104-96 -56350)/18000- (4-389)= 
and we have r= — --.- ',„ — - ='5759, 
agreeing exactly with the result from the conventional symmetrical table which 
will be published and discussed elsewhere. 
Illustration (III — Ab) 4. Fraternal Correlation when the Number of Com- 
binations is large. 
As material for an illustration of the calculation of fraternal (or rather 
sororal) correlation when the numbers are large, Dr Lutz kindly gave me the 
measurements of wing lengths in units of ^rd mm. for the females in fifteen 
families of the Pomace Fly, Drosophila ampelophila\. Table IV shows the 
distributions of wing length, the class centres only being indicated. Using 
the method of a former note§, I formed the symmetrical intra-family corre- 
lation surface shown in Table V. From this I deduced for the weighted 
population 
I = 66-200653, <r t = 7-107332, 
and for the first rough moments about 0 as origin of the individual arrays the 
numbers given in the last column of the table. Multiplying up by the grade 
of the array and summing simultaneously on the machine [|, I got 
2 (l l L) = 123391132, 
whence r = [2 (k'k')/N - b]/af = -15883. 
But, entirely without the labour of forming a heavy table, I find, from the 
first and second class (family) moments of Table IV, 
Sn (n-l)= 28148, 
8[(n- 1)2(0] = 1863416, 
8 [(n -1) % (Z' 2 )] = 123559412, 
£[2(0? = 126124937, 
8 2 Q' 2 )= 2733805. 
* Of course, where all the classes comprise the same number of individuals the weighting is 
uniform and the weighted population constants the same as are those calculated from the unweighted 
distributions. 
t Table III may be conveniently verified by the agreement of its summation with this number, 
t See Publications Carner/ie Institution of Washington, 143, pp. 38—40, for some details. 
§ American Naturalist, Vol. xlv. pp. 566—571, 1911. 
|| American Naturalist, Vol. xliv. pp, 693—699, 1910. 
