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. Consequently, the non-crossover classes will 

 be increased and the crossover classes decreased. 

 In fact, the sum of the two crossover percentages 

 33 and 22 (55) is much greater than the apparent 

 amount (44) of crossing over when only white and 

 bar 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 vermihon to sable is 

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

 seen in the frontispiece). If crossing over occurs 

 between vermihon and sable the region between 



