Journal of Agricultural Research voi. xix, No. i 



The first step in calculating product moment correlations was to reject 

 all cards which did not have values recorded for all the characters. This 

 left a population of 88. The cards were then sorted into the classes of the 

 first character (X of the formula) , and the classes were separated by stop 

 cards. While the cards were in this order the tabulator gave the summed 

 values for each of the characters for each class of the first charac- 

 ter (2xX and SxY"), the number of individuals in each class, and the 

 total value for each of the characters. Each of the entries in the table 

 thus formed (S^X and 2i"K) was then multiplied by the class value, and 

 the products were summed on a calculator, giving SX^ and SXY. 



These summations when multiplied by the number gave SX'- N for the 

 first character and "ZXY-N for the remaining characters in the formula 

 for all correlations with the first character. The totals for each character 

 multiplied by the total of the first character gave (SX)^ for the first 

 character and SX-S"K for the remaining characters. 



The cards were then sorted for the second character, and the same 

 procedure was followed. In each operation the totals should check, and 

 since each character entered as both X and Y, no additional checking is 

 necessary, each correlation being in efi'ect calculated twice with each 

 operation independently checked. The actual regression lines were 

 readily plotted by dividing the values SYX by the number of individ- 

 uals in the respective classes. 



The number of characters for which all correlations can be calculated 

 is limited, of course, by the number that can be recorded on a card. The 

 largest card at our disposal had 45 columns, which would accommodate 

 but 26 characters; and since we wished to consider 33 characters, a sec- 

 ond card was used on which the more important characters were repeated, 

 with the addition of the characters not recorded on the first card. 



The distributions in the alicole group were bimodal to an extent that 

 seemed to preclude the use of the product -moment method. Correlations 

 within this group were, therefore, calculated by Yule's method for the 

 coefficient of association. Biserial correlations were used to determine 

 the relation between alicole characters and characters outside this group. 



Probable errors are not given in the table, since all correlations were 

 calculated from the same population of 88 individuals. In the discussion, 

 correlations of less than 0.25, which is 3.5 times the error, are considered 

 insignificant. 



In discussions of genetic correlations it is necessari' to distinguish be- 

 tween the instances where two characters derived from the same parent 

 tend to be inherited together and those where one of the characters has 

 entered the hybrid from one parent and the correlated character has been 

 derived from the other parent. 



The terms "coherence" and "disherence" will here be used to designate 

 the direction of the correlations with respect to the parental com- 

 binations. 



