320 CARL HALLQVIST 

The gametic ratio may be determined in still another way. Tech- 
nical difficulties in raising a sufficient number of individuals in the 
back crosses render this method impossible in the case of Lupinus 
angustifolius. The gametic ratio may be calculated directly from the 
proportions between the families of certain segregating types in F;, 
and the result of the F,-analysis may be checked with the help of these 
proportion values. The linkage values have been determined in certain 
cases in this way by Murrer (1916) in Drosophila. 
AB Ab aB ab AB Ab aB ab 
1 n n 



AB 1 nl" on 


Ab | n 
aB | n 
ab 1 


By the usual checker scheme it is easy to demonstrate that in 
cases of repulsion (fig. 2 a) the relation between the number of families 
in the centre and in the middle parts of the periphery is a simple and 
constant function of the gametic ratio. The repulsion segregates and 
the constant simplex recessives belong to the centre — their number 
is 4n*> — the families of different types segregating in 3:1, 8n in 
number, belong to the middle parts of the periphery. Thus the re- 
4n? n 
— ——, The corner-families of 
sn 2 
the periphery do not need to be considered, partly because of the 
easy task to recognize them in the F,-analysis and to exclude them 
from the calculations, partly because of the small number of these 
families which makes possible their neglecting especially in cases of 
close linkage, that is when n attains large values. 
The same results are arrived at in cases of coupling with regard to 
lation between these two groups is 
families occupying other places in the quadrate (fig. 2b). Here it is the 
families in the centre which may be omitted. The corner-families 
give the numerator 4n°, while the denominator, 8n, is still the charac- 
teristic value of the middle parts of the periphery. Thus in cases of 
