FLOWER AND SEED COLOUR IN LUPINUS 323 

1:3,2 This must be considered a good correspondence in view of 
the standard error calculations. The value of n lies probably between 
3 and 4 corresponding to the crossover percentage 25—20. On account 
of the numerical relations of the F3-generation and the relatively 
good correspondence between the results of the coupling segre- 
gation as well as of the repulsion segregation it must be concluded 
that the value of n in all probability lies close to 3,5, which value 
corresponds to the crossover percentage 22,2. 

The use of back crosses in the determination of the gametic ratio 
in Lupinus angustifolius is for many reasons technically difficult, 
as said before. The number of seeds in each pod is very limited, so 
a very great number of crosses had to be made to obtain sufficient 
quantities of seed. Numerous pollinations, in addition, do not succeed. 
At best, seeds from 4—5 flowers only are obtained, from each plant. 
It may be of some interest to make a comparison between the pre- 
cision and the practical advantages of the F,- and F,-methods, as similar 
conditions prevail in other genera, which have furnished important 
data with regard to linkage, as Lathyrus, Triticum, Hordeum. The 
F;-method follows a more direct course, and the results would seem 
to be more reliable for this reason. This is particularly true in 
cases of repulsion, where the group of double recessives always is 
relatively small and consequently oftentimes doubtful. The associa- 
tion coefficient becomes uncertain in a corresponding degree. A 
fluctuation involving one or a few individuals may influence the ass. 
coeff. and displace the results considerably. The F,-method offers 
great advantage in this respect as no attention need to be paid to the 
frequency of the numerically small groups. The advantage of this 
method is most clearly seen in cases where the number of the indi- 
viduals in the recessive groups is decreased through poor vitality. 
MuLLER made use of the F,-method in Drosophila (1916, p. 354) in 
order to escape these difficulties. The advantage of the F,-method 
is less obvious in the cross 9, just discussed, as the linkage here is 
relatively loose. It is better seen in cross 8 where close linkage is pre- 
sent, as already stated (pag. 316). 
Although the F,-method certainly is to be preferred, especially in 
case of a segregation of repulsion type, great practical difficulties may 
be encountered in the raising of a sufficient number of families neces- 
sitating much work and expense. It may therefore be of some inte- 
rest to mention a short cut in the use of- the F,-method, which I intend 
