No. 593] THE MECHANISM OF CROSSING-OVER 287 



If the per cent, of double cross-overs — per cent. AB 

 X per cent. BC (formnla 1), then the assumption that 

 separation frequencies AB and BC are independent is 

 correct. As offspring from a back-cross all show what 

 factors they received from the hybrid parent, a back- 

 cross involving the three factors A, B, and C at the same 

 time will answer the question at once, for all the cases 

 of coincident separation (double cross-overs) that occur 

 can be counted. But where the hybrids, instead of being 

 back-crossed, are inbred— a practice followed by adhor 

 ents of the reduplication hypothesis— then it is impos- 

 sible to tell which F 2 individuals come from gametes of 

 the classes which we may term double cross-overs, unless 

 one of these classes is the triple recessive, and then the 

 only double crossovers which can be known as such are 

 those very rare individuals that happen to result from 

 the union of two double crossover gametes. The British 

 workers have, therefore, not been able to find the pro- 

 portion of double cross-overs directly, to compare this 

 with formula 1, but have tried to determine the frequency 

 of coincidence indirectly, by using the method followed 

 in formula 2. That is, they determined the relations 

 existing between frequencies AC, AB, and BC, as calcu- 

 lated from their F, counts, for, as above shown, the 

 greater the frequency of double crossing-over, the more 

 will AC be cut down in proportion to AB and BC. And it 

 seemed evident that, if the relation of AC to AB and BC 

 was just that given bv Trow's formula (2), then coinci- 

 dence of separations must have the frequency demanded 

 on the assumption that separations (or "reduplications ) 

 AB and BC occur independently of one another. As a 

 matter of fact, however, this method offers no * nswe * 

 the question, unless almost impossibly largo < 2 cou ^ s 

 are obtained, for otherwise the independent rant >>m . ur-^ 

 tuations of these three value* in this kind of conn <n < 

 great that any deviation in AC due to excess or deficiency 

 of double crossing-over would be W^} 03 " ** 1 »; . 



The question was, however, immediately ^ and denm 

 tively answered in Drosophila, before Trow s paper ap- 



