318 CARL HALLQVIST 

ted (col. 6, table 1) and compared with a series of ass. coefficients 
of several ideal phenotypical ratios belonging to various gametic ratios. 
The results are put together in table 1 (pag. 317). 
The accuracy of the values obtained in this or similar ways, as 
Emerson (1916) has pointed out, depends greatly on the question 
whether or not the proportions between certain groups of the zygotic 
distribution series meet the demands. which have to be raised (apart 
from the characteristic distribution at the gametic frequency in ques- 
tion). The characteristic feature of di-hybrid segregation values with 
9:3:3:1 as ground-type, whether free combination or linkage of the 
coupling or repulsion type are exhibited, is the equality of the 
Bv + bV 
9 
~ 
middle groups (Bv = bY, or )- The first group, BV, must be 
three times the last one when the sum of the middle groups (Bv +bV) 
is subtracted from the first group. That is, BV — (Bo + bV) —3 bo, 
BV — (Bv +.bV) 
or 3 — bv. These points are demonstrated in the 
scheme, pag. 320. If different linkage values are obtained for the 
same characters the accuracy of the different values should be con- 
trolled from this point of view. Such a control of the values in this 
cross shows that in two cases remarkable deviations from expectation 
have resulted, viz. in the case of number 1 of the F., table 1, and in 
ref. number 6 in F, in coupling. In the first case the difference 
between the middle groups is rather great. It is seen, however, that 
this deviation is of no importance as the value of the association 
coefficient, calculated with the middle groups reduced to half of the sum 
of values actually obtained, changes in so small a-degree that it still 
shows the best correspondence with the gametic ratio 1: 3,1. Thus 
the deviation from other calculations showed by this ratio does not 
depend on the difference in the values of the middle groups. 
In the second example, viz. the coupling in F, (ref. number 6), the 
last group, bv, is found to be too small in relation to BV — (Bv + bY). 
The values obtained are 33 and 144 respectively. The ideal ratio 
would be 44,5 : 132,75, consequently a deficit of more than 11 recessi- 
ves. If the association coefficient is calculated on the ideal ratio just 
mentioned the gametic frequency becomes 3.3: 1 instead of 3:1, and 
the linkage value becomes 23,3 instead of 25. It is therefore to be con- 
cluded from the mere disproportion between the first and the last 
groups that the result with regard to the coupling in F, (ref. number 
6) is doubtful. 
