LINKAGE 63 



of gametes are actually produced, the results of the 

 experiment fulfil the theoretical expectation. 



There is a corollary of importance to this conclu- 

 sion. When a cross is made that involves only white 

 and bar, the double crossing over, that can be de- 

 tected only when an intermediate point is followed, 

 must still be supposed to take place. Whenever it 

 does take place white bar flies and red round flies 

 result. These will be added to the non-crossover 

 classes since they have the same external character- 

 istics. Hence the apparent non-crossover classes 

 will be increased and the crossovers decreased, so 

 that the sum of the value for W and M (33) and that 

 for M and B (22) is much greater than the value for 

 W and B (44) observed when only these two factors 

 are involved. Here then we have an explanation 

 of why long distances taken as a whole give too little 

 crossing over, as compared with the same distances 

 taken section by section. The lowered percentage 

 is an actual mathematical necessity owing to the 

 occurrence of double crossing over. 



In the case of double crossing over the two points 

 of crossing over can not be near together unless the 

 chromosomes are tightly twisted. Consequently, 

 when crossing over occurs at any point the region on 

 each side should be protected from further crossing 

 over. That this actually happens may now be dem- 

 onstrated. For example, from vermilion to sable is 

 10 units, and from sable to bar is 14 units more (as 

 seen in frontispiece). When crossing over occurs 

 between vermiUon and sable the region between 



