88 PHYSICAL BASIS OF HEREDITY 



of a given age and under given environmental conditions. 

 In this case the percentages are 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 



If a pair of chromosomes in the Fj fly is represented as 

 carrying the genes of the characters here involved, one 

 memher of such a pair carries both a gene for black and 

 a gene for vestigial (Fig. 36) ; the homologous member 

 of the pair of chromosomes carries both of the normal 

 allelomorphs, vis., a gene for gray and a gene for long 

 wings. When crossing over takes place so that a gene 

 for black goes over into the other chromosome, the con- 

 verse phenomenon takes place, a gene for gray goes over 

 into the chromosome that gave up its black gene. It is the 

 constancy of this interchange that makes the phenomenon 

 reducible to exact mechanical treatment. 



The interchange is independent of the way in which the 

 genes enter the cross. For example, if a black long- 

 winged fly is crossed to a gray vestigial fly (Fig. 37), the 

 Fi offspring will be, as before, gray long. If an Fj 

 female (gray long) is back-crossed to a black vestigial 

 male, there will be four kinds of offspring, namely, the two 

 original combinations black long, and gray vestigial; 

 and the two crossover combinations, black vestigial, and 

 gray long, in the following proportions : 



Non-crossovers Crossovers 



Black long Gray vestigial Black vestigial Gray long 



41.5 per cent 41.6 per cent. 8.5 per cent 8.5 per cent 



83 per cent 17 per cent 



The interchange in the last cases is ia the reverse order 

 of that in the first case, but it is numerically identical. 

 In other words, it makes no difference whether the gene 

 for black and for vestigial enter the cross together, i.e., 



