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 across 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 (88) 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 vermilion and sable the region between 
