50 LINKAGE 
factors as were present in P, unless an interchange 
has taken place between the two chromosomes. The 
best way to find out whether such an interchange 
has taken place is to mate the F, males and females 
to the double recessive type, black vestigial, because 
black and vestigial being recessive factors will not 
obscure the factors that are carried by the gametes 
of the F, to be tested. When the F; male is back- 
crossed to a black vestigial female, Fig. 21 (second 
line), only two classes of offspring are produced. 
Half of the flies are black vestigial and half are gray 
long. This must mean that there has been no cross- 
ing over in the hybrid F, male; for he produces only 
two kinds of gametes and these are of the kind that 
combined to produce him. In other words, the 
chromosomes received from his parents have re- 
mained intact. 
If we test the F, female, by back-crossing to a 
black vestigial male, the result is different. If such a 
female is bred to the double recessive male, black 
vestigial, four kinds of offspring result, as follows: 
Non-crossovers Crossovers 
Black, vestigial Gray, long Black, long Gray, vestigial 
41.5 per cent. 41.5 per cent. 8.5 per cent. 8.5 per cent. 
83 per cent. 17 per cent. 
Of these four classes the first two correspond to the 
combinations which the F, received from its parents, 
namely, black vestigial and gray long; the other two 
are classes that would be expected if crossing over had 
