No. 548] CONDENSED CORRELATION TABLES 485 



From these gross values must be deducted, therefore, 

 the actual frequency for each grade of the subject and the 

 product of the frequency by the first and second power 

 of the grade in the case of direct intra-class correlation, 

 or the frequency of the grade and the sum of the first and 

 second powers of the values of the relative character in 

 the same fruit in the cross intra-class correlation. Data 

 for these are given in the table showing the correlation 

 for asymmetry and locular composition of the same fruit, 

 Table III. The second set of three columns in Tables 

 IV-VII gives the quantities so calculated from Table III 

 to be deducted. The final three columns are in each case 

 the working tables. 



The first and second moments for the (weighted) popu- 

 lation A and o- are given by the totals of the two final 

 columns. Or those for the subject character may be cal- 

 culated (and a check for the accuracy of the totals 

 secured) from the grade of the subject and the weighted 

 frequency column. 11 



From our working tables, indicating by S a summation 

 from our final tables, we determine by the methods of 

 Amee. Nat., Vol. 45, pp. 693-699, 1910, these values : 



For Asymmetry 



S(a') =121,938.5928, Ja = .363642, 

 S(a' 2 )= 71,692.2400, <r a = .285593. 



For Locular Composition 



SM= 469,001, J« = 1.398642, 

 S(c' 2 ) =1,231,335, <* = 1.309906. 



For Asymmetry and Locular Composition 



Table IV, S(a 1 'a t ')= 48,818.9505, r=.1637, 

 Table VI, ^(a 1 V) = 192,072.3309, 12 r=.1716, 

 Table V, £(£>/)= 192,072.3308, 12 r=.1716, 



"Of course in practise, the second population moment may be calculated 

 by fl[(n — 1)20^)], fl[(p - 1)2(2^], S[ (<Z - 1)2 ) L • • • , thuS 

 obviating the labor of forming the third columns, which are included here 

 for completeness of illustration merely 



"The difference of .0001 is due to the n 

 while they can be retained in the other. ( 



