322 CARL HALLQVIST 

families belonging to different segregating types (F, and F,) of cross 9 
is given in table 3. Column 1 tabulates the families, which in the 
case of repulsion on the part of the parent families occupy the centre 
of the quadrate, and those which in cases of coupling occupy 
the corners. Thus all the families forming the denominator are tabu- 
lated in this column. Column 2 tabulates the families segregating in 
the ratio 3:1, that is the numerator. For sake of completeness the 
rest of the families is put together in col. 3, which is not used, 
however, when the linkage values are calculated. The total of the 
first col. is 123 families, the second is 76, and the result is the fol- 
lowing equation: 
123 
— iia 
n 
2001 40 

The standard error of the proportions 123 : 76 is + 4,5. This figure, 
simple or taken three times, added or subtracted, gives rise to displace- 
ments in the proportions of the families and corresponding changes 
in the gametic ratios as seen in the following: 
IM | 127,85 : 71,15 corresponding to n—3,; 
| 118,15 : 80,5: » » n—2,59 
137.538 ot EP » » n=45 
: NE) ’ ’ ’ 
à | 108,45 : 90,55 » » n=2, 
It should be stated that with regard to the constant pure 
red families showing coupling a fictitious value of their number 
has been used for the following reason. As the number of the 
pure red plants had been determined already in F,, and as it further 
appeared certain that all should show constancy in F,, no need of 
raising F,-families from them was present. In order to be able to 
use the formula, however, a value representing one third of the num- 
ber of the corner-families left has been used, in this case 5, which 
stands in about the same relation to the sum of the rest of the 
families as the pure reds to the sum of the rest of the phenotypes in 
I’, of the parent family no. 92—19. This procedure should be fol- 
lowed generally, partly because of the avoidance of an unconscious 
selection in the taking out of the parent plants, which this procedure 
makes possible, partly because of the nullification of an eventual poor 
vitality of the double recessives. 
The degree of the repulsion of this cross has been found to be 
1: 3,3 by means of the F,-method, and the F,-method gives the result 
